Valid HTML 4.0! Valid CSS!
%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nicholas John Higham",
%%%     version         = "1.95",
%%%     date            = "17 November 2023",
%%%     time            = "13:00:44 MST",
%%%     filename        = "higham-nicholas-john.bib",
%%%     address         = "School of Mathematics
%%%                        University of Manchester
%%%                        Manchester M13 9PL
%%%                        England",
%%%     telephone       = "+44 (0)161 275 5800",
%%%     FAX             = "+44 (0)161 275 5819",
%%%     checksum        = "30449 8621 37031 379764",
%%%     email           = "nick.higham at manchester.ac.uk (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "bibliography; BibTeX; Nicholas Higham",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of publications of
%%%                        Nicholas John Higham.  The companion LaTeX file
%%%                        higham-nicholas-john.ltx can be used to typeset
%%%                        this bibliography.
%%%
%%%                        At version 1.95, the year coverage looked
%%%                        like this:
%%%
%%%                             1983 (   2)    1997 (  13)    2011 (   4)
%%%                             1984 (   0)    1998 (  14)    2012 (   2)
%%%                             1985 (   2)    1999 (  11)    2013 (   5)
%%%                             1986 (   4)    2000 (   8)    2014 (   6)
%%%                             1987 (   5)    2001 (  12)    2015 (   5)
%%%                             1988 (   4)    2002 (   9)    2016 (  10)
%%%                             1989 (   6)    2003 (   7)    2017 (   7)
%%%                             1990 (  16)    2004 (   3)    2018 (  12)
%%%                             1991 (   4)    2005 (   9)    2019 (   9)
%%%                             1992 (  11)    2006 (   5)    2020 (   7)
%%%                             1993 (  15)    2007 (  10)    2021 (   9)
%%%                             1994 (  10)    2008 (  10)    2022 (   4)
%%%                             1995 (  10)    2009 (   8)
%%%                             1996 (  12)    2010 (   7)
%%%
%%%                             Article:        217
%%%                             Book:            14
%%%                             InCollection:     7
%%%                             InProceedings:   17
%%%                             MastersThesis:    1
%%%                             Misc:             3
%%%                             PhdThesis:        1
%%%                             Proceedings:      8
%%%                             TechReport:      39
%%%
%%%                             Total entries:  307
%%%
%%%                        This file is available as part of the BibNet
%%%                        Project.  The master copy is available for
%%%                        public access on ftp.math.utah.edu in the
%%%                        directory tree /pub/bibnet/authors.  It is
%%%                        mirrored to netlib.bell-labs.com in the directory
%%%                        tree /netlib/bibnet/authors, from which it is
%%%                        available via anonymous ftp and the Netlib
%%%                        service.
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================
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%%% # "\input bibnames.sty "
%%% # "\input path.sty "
%%% old: PREAMBLE{ "\newcommand{\noopsort}[1]{}" } - causes warnings with chapterbib.
@String{ack-nhfb = "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics, 110 LCB,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    FAX: +1 801 581 4148,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org| (Internet),
                    URL: \path|https://www.math.utah.edu/~beebe/|"}

@String{ack-njh =   "Nick Higham,
                    e-mail: \path|nick.higham@manchester.ac.uk|"}

%%% ====================================================================
%%% Departments/Institutions and their addresses:
@String{inst-CS-U-MARYLAND      = "Department of Computer Science, University
                                  of Maryland"}
@String{inst-CS-U-MARYLAND:adr  = "College Park, MD, USA"}

@String{inst-CS-U-TENN          = "Department of Computer Science, University
                                  of Tennessee"}
@String{inst-CS-U-TENN:adr      = "Knoxville, TN, USA"}

@String{inst-CS-U-UMEA          = "Institute of Information Processing,
                                  University of Ume{\aa}"}
@String{inst-CS-U-UMEA:adr      = "Sweden"}

@String{inst-HARWELL            = "{AERE} {Harwell} Laboratory"}
@String{inst-HARWELL:adr        = "Chilton, Oxon, England"}

@String{inst-MCCM               = "Manchester Centre for Computational
                                  Mathematics"}
@String{inst-MCCM:adr           = "Manchester, England"}

@String{inst-MCS-ARGONNE        = "Mathematics and Computer Science Division,
                                  Argonne National Laboratory"}
@String{inst-MCS-ARGONNE:adr    = "IL, USA"}

@String{inst-MIMS               = "Manchester Institute for Mathematical
                                  Sciences, The University of Manchester"}
@String{inst-MIMS:adr          = "Manchester, UK"}

@String{inst-ORNL               = "Oak Ridge National Laboratory"}
@String{inst-ORNL:adr           = "Oak Ridge, TN, USA"}

@String{inst-RAL                = "Atlas Centre, Rutherford Appleton
                                  Laboratory"}
@String{inst-RAL:adr            = "Didcot, Oxon, UK"}

@String{inst-U-DUNDEE           = "Department of Mathematics and Computer
                                  Science, University of Dundee"}
@String{inst-U-DUNDEE:adr       = "Dundee, Scotland"}

@String{inst-U-MANCHESTER       = "University of Manchester"}
@String{inst-U-MANCHESTER:adr   = "Manchester, England"}

@String{inst-UNIV-WATERLOO      = "University of Waterloo"}
@String{inst-UNIV-WATERLOO:adr  = "Waterloo, ON, Canada"}

@String{inst-UTK-CS             = "Department of Computer Science, University
                                  of Tennessee, Knoxville"}
@String{inst-UTK-CS:adr         = "Knoxville, TN 37996, USA"}

%%% ====================================================================
%%% Journal abbreviations:
@String{j-ACTA-NUMERICA         = "Acta Numerica"}

@String{j-BIT                   = "BIT"}

@String{j-BIT-NUM-MATH          = "BIT Numerical Mathematics"}

@String{j-BULL-AMS              = "Bulletin of the American Mathematical Society"}

@String{j-BULL-LOND-MATH-SOC    = "Bulletin of the London Mathematical Society"}

@String{j-CCPE                  = "Concurrency and Computation: Prac\-tice and
                                   Experience"}

@String{j-COMPUT-SCI-ENG        = "Computing in Science and Engineering"}

@String{j-COMPUT-STAT-DATA-ANAL = "Computational Statistics \& Data Analysis"}

@String{j-IEEE-COMPUT-SCI-ENG   = "IEEE Computational Science \& Engineering"}

@String{j-IJHPCA                = "The International Journal of High Performance
                                  Computing Applications"}

@String{j-IMA-BULL              = "IMA Bulletin"}

@String{j-IMA-J-NUMER-ANAL      = "IMA Journal of Numerical Analysis"}

@String{j-IMA-NUM-ANA-NEWSLETTER = "IMA Numerical Analysis Newsletter"}

@String{j-INT-J-NUMER-METHODS-ENG = "International Journal for Numerical Methods
                                  in Engineering"}

@String{j-J-COMPLEX-NETWORKS    = "Journal of Complex Networks"}

@String{j-J-FLUID-MECH          = "Journal of Fluid Mechanics"}

@String{j-LECT-NOTES-COMP-SCI   = "Lecture Notes in Computer Science"}

@String{j-LINEAR-ALGEBRA-APPL   = "Linear Algebra and Appl."}

@String{j-MATH-COMPUT           = "Math. Comp."}

@String{j-MATH-GAZ              = "Mathematical Gazette"}

@String{j-MATH-TODAY            = "Mathematics Today"}

@String{j-NA-DIGEST             = "NA Digest"}

@String{j-NUM-LIN-ALG-APPL      = "Numerical Linear Algebra with Applications"}

@String{j-NUM-MATH              = "Numer. Math."}

@String{j-NUMER-ALGORITHMS      = "Numerical Algorithms"}

@String{j-PARALLEL-COMPUTING    = "Parallel Computing"}

@String{j-PHILOS-TRANS-R-SOC-LOND-SER-A = "Philosophical transactions of the
                                  Royal Society of London Series A"}

@String{j-PROC-R-SOC-LOND-SER-A = "Proceedings of the Royal Society of London.
                                  Series A"}

@String{j-R-SOC-OPEN-SCI        = "Royal Society Open Science"}

@String{j-SIAM-J-MAT-ANA-APPL   = "SIAM J. Matrix Anal. Appl."}

@String{j-SIAM-J-NUMER-ANAL     = "SIAM Journal on Numerical Analysis"}

@String{j-SIAM-J-SCI-COMP       = "SIAM Journal on Scientific Computing"}

@String{j-SIAM-J-SCI-STAT-COMP  = "SIAM Journal on Scientific and Statistical
                                  Computing"}

@String{j-SIAM-NEWS             = "SIAM News"}

@String{j-SIAM-REVIEW           = "SIAM Review"}

@String{j-TOMS                  = "ACM Trans. Math. Software"}

%%% ====================================================================
%%% Publishers and their addresses:
@String{pub-ACM                 = "ACM Press"}
@String{pub-ACM:adr             = "New York, NY 10036, USA"}

@String{pub-AMS                 = "American Mathematical Society"}
@String{pub-AMS:adr             = "Providence, RI, USA"}

@String{pub-AP                  = "Academic Press"}

@String{pub-AW-LONGMAN          = "Ad{\-d}i{\-s}on-Wes{\-l}ey Longman"}
@String{pub-AW-LONGMAN:adr      = "Reading, MA, USA"}

@String{pub-CH                  = "Chapman and Hall"}
@String{pub-CH:adr-L            = "London"}

@String{pub-CHAPMAN-HALL-CRC    = "Chapman and Hall/CRC"}
@String{pub-CHAPMAN-HALL-CRC:adr = "Boca Raton, FL, USA"}

@String{pub-ELS                 = "Elsevier Science Publishers B.V."}
@String{pub-ELS:adr             = "Amsterdam, The Netherlands"}

@String{pub-IEEE                = "IEEE Computer Society Press"}
@String{pub-IEEE:adr            = "1109 Spring Street, Suite 300,
                                  Silver Spring, MD 20910, USA"}

@String{pub-LONGMAN-ST          = "Longman Scientific and Technical"}
@String{pub-LONGMAN-ST:adr      = "Essex, UK"}

@String{pub-KLUWER              = "Kluwer Academic Publishers"}
@String{pub-KLUWER:adr          = "Norwell, MA, USA, and Dordrecht, The
                                   Netherlands"}

@String{pub-OXFORD              = "Oxford University Press"}
@String{pub-OXFORD:adr          = "Walton Street, Oxford OX2 6DP, UK"}

@String{pub-PENGUIN             = "Penguin"}
@String{pub-PENGUIN:adr-H       = "Harmondsworth, UK"}
@String{pub-PENGUIN:adr-L       = "London"}
@String{pub-PENGUIN:adr-NY      = "New York"}

@String{pub-PRINCETON           = "Princeton University Press"}
@String{pub-PRINCETON:adr       = "Princeton, NJ, USA"}

@String{pub-SIAM                = "Society for Industrial and Applied
                                  Mathematics"}
@String{pub-SIAM:adr            = "Philadelphia, PA, USA"}

@String{pub-SPRINGER            = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SPRINGER:adr-B      = "Berlin"}
@String{pub-SPRINGER:adr-NY     = "New York"}

@String{pub-SV                  = "Springer-Verlag"}
@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg, Germany~/
                                    London, UK~/ etc."}

@String{pub-WORLD-SCI           = "World Scientific Publishing Co."}
@String{pub-WORLD-SCI:adr       = "Singapore; Philadelphia, PA, USA; River
                                   Edge, NJ, USA"}

%%% ====================================================================
@MastersThesis{Higham:1983:MCN,
  author =       "N. J. Higham",
  title =        "Matrix Condition Numbers",
  type =         "{M.Sc. Thesis}",
  school =       inst-U-MANCHESTER,
  address =      inst-U-MANCHESTER:adr,
  pages =        "iv + 86",
  month =        oct,
  year =         "1983",
  bibdate =      "Tue Mar 21 16:29:28 GMT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
}

@TechReport{Higham:1983:UBC,
  author =       "Nicholas J. Higham",
  title =        "Upper bounds for the condition number of a triangular
                 matrix",
  type =         "Numerical Analysis Report",
  number =       "86",
  institution =  inst-U-MANCHESTER,
  address =      inst-U-MANCHESTER:adr,
  month =        may,
  year =         "1983",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
}

@TechReport{Higham:1985:MCB,
  author =       "Nicholas J. Higham",
  title =        "Matrix Computations in {Basic} on a Microcomputer",
  type =         "Numerical Analysis Report",
  number =       "101",
  institution =  "Department of Mathematics, University of Manchester",
  address =      "Manchester, M13 9PL, UK",
  pages =        "62",
  month =        jun,
  year =         "1985",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  created =      "2013.10.02",
  updated =      "2013.10.02",
}

@PhdThesis{Higham:1985:NPN,
  author =       "Nicholas J. Higham",
  title =        "Nearness Problems in Numerical Linear Algebra",
  school =       inst-U-MANCHESTER,
  address =      inst-U-MANCHESTER:adr,
  pages =        "173",
  month =        jul,
  year =         "1985",
  bibdate =      "Tue Mar 21 16:29:32 GMT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
}

@Article{Higham:1986:CPD,
  author =       "Nicholas J. Higham",
  title =        "Computing the Polar Decomposition---with
                 Applications",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "7",
  number =       "4",
  pages =        "1160--1174",
  month =        oct,
  year =         "1986",
  CODEN =        "SIJCD4",
  ISSN =         "0196-5204",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM Journal on Scientific and Statistical Computing",
  journal-URL =  "http://epubs.siam.org/loi/sijcd4",
  mynote =       "N.A. Report 94, November 1984. (Proof in Appendix is
                 not in paper).",
}

@Article{Higham:1986:EAC,
  author =       "Nicholas J. Higham",
  title =        "Efficient Algorithms for Computing the Condition
                 Number of a Tridiagonal Matrix",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "7",
  number =       "1",
  pages =        "150--165",
  year =         "1986",
  CODEN =        "SIJCD4",
  ISSN =         "0196-5204",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM Journal on Scientific and Statistical Computing",
  journal-URL =  "http://epubs.siam.org/loi/sijcd4",
}

@Article{Higham:1986:MCB,
  author =       "Nicholas J. Higham",
  title =        "Matrix Computations in {Basic} on a Microcomputer",
  journal =      j-IMA-BULL,
  volume =       "22",
  pages =        "13--20",
  year =         "1986",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "IMA Bulletin",
}

@Article{Higham:1986:NMM,
  author =       "Nicholas J. Higham",
  title =        "{Newton}'s Method for the Matrix Square Root",
  journal =      j-MATH-COMPUT,
  volume =       "46",
  number =       "174",
  pages =        "537--549",
  month =        apr,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65F30 (65H10)",
  MRnumber =     "87d:65045",
  MRreviewer =   "Lars Eld{\'e}n",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 JSTOR database; Theory/Matrix.bib",
  acknowledgement = ack-njh,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Dept. of Math., Manchester Univ., UK",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "equation; iterative methods; mathematical convergence;
                 matrix algebra; matrix square root; Newton iteration;
                 Newton method; perturbation analysis; properties;
                 quadratic matrix",
  kwds =         "nla, matrix function, matrix square root, Newton's
                 method",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Higham:1987:CRS,
  author =       "Nicholas J. Higham",
  title =        "Computing Real Square Roots of a Real Matrix",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "88/89",
  pages =        "405--430",
  year =         "1987",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Higham:1987:EAB,
  author =       "Nicholas J. Higham",
  title =        "Error Analysis of the {Bj{\"o}rck--Pereyra}
                 Algorithms for Solving {Vandermonde} Systems",
  journal =      j-NUM-MATH,
  volume =       "50",
  number =       "5",
  pages =        "613--632",
  year =         "1987",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@InProceedings{Higham:1987:NLA,
  author =       "N. J. Higham and G. W. Stewart",
  title =        "Numerical Linear Algebra in Statistical Computing",
  crossref =     "Iserles:1987:SAN",
  pages =        "41--57",
  year =         "1987",
  bibdate =      "Thu May 29 17:14:49 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib",
  acknowledgement = ack-nhfb,
  xxpages =      "41--58",
}

@Article{Higham:1987:SCN,
  author =       "Nicholas J. Higham",
  title =        "A Survey of Condition Number Estimation for Triangular
                 Matrices",
  journal =      j-SIAM-REVIEW,
  volume =       "29",
  number =       "4",
  pages =        "575--596",
  month =        dec,
  year =         "1987",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1029112",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65F35",
  MRnumber =     "88j:65086",
  bibdate =      "Sat Mar 29 09:54:19 MDT 2014",
  bibsource =    "Compendex database;
                 http://epubs.siam.org/toc/siread/29/4;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  abstract =     "We survey and compare a wide variety of techniques for
                 estimating the condition number of a triangular matrix,
                 and make recommendations concerning the use of the
                 estimates in applications. Each of the methods is shown
                 to bound the condition number; the bounds can broadly
                 be categorised as upper bounds from matrix theory and
                 lower bounds from heuristic or probabilistic
                 algorithms. For each bound we examine by how much, at
                 worst, it can overestimate or underestimate the
                 condition number. Numerical experiments are presented
                 in order to illustrate and compare the practical
                 performance of the condition estimators.",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Univ of Manchester, Manchester, Engl",
  classification = "723; 921",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "computer programming --- Algorithms; condition number
                 estimation; mathematical techniques; Matrix Algebra;
                 matrix condition number; qr decomposition; rank
                 estimation; triangular matrices",
  onlinedate =   "December 1987",
}

@Article{Higham:1988:AFC,
  author =       "Nicholas J. Higham",
  title =        "Algorithm 674: {FORTRAN} Codes for Estimating the
                 One-Norm of a Real or Complex Matrix, with Applications
                 to Condition Estimation",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "381--396",
  month =        dec,
  year =         "1988",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65F35)",
  MRnumber =     "1 062 484",
  bibdate =      "Sat Aug 27 15:05:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "See also \cite{Higham:1989:CFC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p381-higham/;
                 http://www.acm.org/pubs/toc/Abstracts/0098-3500/214386.html",
  abstract =     "FORTRAN 77 codes SONEST and CONEST are presented for
                 estimating the 1-norm ( or the infinity-norm) of a real
                 or complex matrix, respectively. The codes are of wide
                 applicability in condition estimation since explicit
                 access to the matrix, $A$, is not required; instead,
                 matrix-vector products $ A x $ and $ A^T x $ are
                 computed by the calling program via a reverse
                 communication interface. The algorithms are based on a
                 convex optimization method for estimating the 1-norm of
                 a real matrix devised by Hager. We derive new results
                 concerning the behavior of Hager's method, extend it to
                 complex matrices, and make several algorithmic
                 modifications in order to improve the reliability and
                 efficiency.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
  keywords =     "algorithms; condition estimation; nla; software, nla,
                 condition estimation, software",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra.",
}

@Article{Higham:1988:CNS,
  author =       "Nicholas J. Higham",
  title =        "Computing a Nearest Symmetric Positive Semidefinite
                 Matrix",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "103",
  pages =        "103--118",
  year =         "1988",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Higham:1988:FSV,
  author =       "Nicholas J. Higham",
  title =        "Fast Solution of {Vandermonde}-like Systems Involving
                 Orthogonal Polynomials",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "8",
  number =       "4",
  pages =        "473--486",
  month =        oct,
  year =         "1988",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/8.4.473",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65H10 (65F30)",
  MRnumber =     "89k:65067",
  bibdate =      "Thu Aug 25 10:58:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 MathSciNet database",
  abstract =     "Consider the $ (n + 1) \times (n + 1) $
                 Vandermonde-like matrix $ P = [{pi - 1}(\alpha_{j -
                 1})] $, where the polynomials $ p_0 (x), \ldots {},
                 p_n(x) $ satisfy a three-term recurrence relation. We
                 develop algorithms for solving the primal and dual
                 systems, $ P x = b $ and $ P^T a = f $ respectively, in
                 $ O(n^2) $ arithmetic operations and $ O(n) $ elements
                 of storage. These algorithms generalize those of
                 Bj{\"o}rck \& Pereyra which apply to the monomial case
                 $ p_i(x) $. When the $ p_i(x) $ are the Chebyshev
                 polynomials, the algorithms are shown to be numerically
                 unstable. However, it is found empirically that the
                 addition of just one step of iterative refinement is,
                 in single precision, enough to make the algorithms
                 numerically stable.",
  acknowledgement = ack-nhfb # " and " # ack-njh,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@Article{Higham:1988:SPP,
  author =       "Nicholas J. Higham",
  title =        "The Symmetric {Procrustes} Problem",
  journal =      j-BIT,
  volume =       "28",
  number =       "1",
  pages =        "133--143",
  year =         "1988",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65F20 (41A29 73K05)",
  MRnumber =     "89g:65047",
  MRreviewer =   "N. Gass",
  bibdate =      "Thu Nov 12 18:12:56 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh # " and " # ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Higham:1989:AST,
  author =       "Nicholas J. Higham",
  title =        "The Accuracy of Solutions to Triangular Systems",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "26",
  number =       "5",
  pages =        "1252--1265",
  month =        oct,
  year =         "1989",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65F05 (65G05)",
  MRnumber =     "90i:65053",
  MRreviewer =   "James Weldon Demmel",
  bibdate =      "Mon Jan 20 15:27:00 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}

@Article{Higham:1989:CFC,
  author =       "Nicholas J. Higham",
  title =        "Corrigendum: ``{Algorithm} 674: {FORTRAN} Codes for
                 Estimating the One-Norm of a Real or Complex Matrix,
                 with Applications to Condition Estimation''",
  journal =      j-TOMS,
  volume =       "15",
  number =       "2",
  pages =        "168--168",
  month =        jun,
  year =         "1989",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:18:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "See \cite{Higham:1988:AFC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p168-higham/;
                 http://www.acm.org/pubs/toc/Abstracts/0098-3500/214391.html",
  abstract =     "We omitted giving this article an ACM algorithm number
                 when it was first published in its entirety in the
                 December 1988 issue of {\em TOMS}, Vol. 14, No. 4, pp.
                 381-396. To correct this, we do so here, and reprint
                 the title as a pointer to the original article.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
  keywords =     "algorithms",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra.",
}

@TechReport{Higham:1989:CTM,
  author =       "Nicholas J. Higham",
  title =        "A Collection of Test Matrices in {MATLAB}",
  type =         "Numerical Analysis Report",
  number =       "172",
  institution =  inst-U-MANCHESTER,
  address =      inst-U-MANCHESTER:adr,
  month =        jul,
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  mynote =       "Published version: \cite{Higham:1991:ACT}.",
}

@Article{Higham:1989:LGF,
  author =       "Nicholas J. Higham and Desmond J. Higham",
  title =        "Large Growth Factors in {Gaussian} Elimination with
                 Pivoting",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "10",
  number =       "2",
  pages =        "155--164",
  month =        apr,
  year =         "1989",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:1989:MCP,
  author =       "Nicholas J. Higham",
  title =        "Matrix Computations on a {PC}",
  journal =      j-SIAM-NEWS,
  volume =       "22",
  pages =        "16",
  month =        jan,
  year =         "1989",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@InProceedings{Higham:1989:MNP,
  author =       "Nicholas J. Higham",
  editor =       "M. J. C. Gover and S. Barnett",
  booktitle =    "Applications of Matrix Theory",
  title =        "Matrix Nearness Problems and Applications",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "1--27",
  year =         "1989",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
}

@TechReport{Demmel:1990:IEB,
  author =       "J. Demmel and N. Higham",
  title =        "Improved Error Bounds for Underdetermined System
                 Solvers",
  type =         "LAPACK Working Note",
  number =       "23",
  institution =  inst-UTK-CS,
  address =      inst-UTK-CS:adr,
  month =        aug,
  year =         "1990",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "UT-CS-90-113, August 1990.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn23.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn23.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Demmel:1990:SBA,
  author =       "J. Demmel and N. Higham",
  title =        "Stability of Block Algorithms with Fast Level 3
                 {BLAS}",
  type =         "LAPACK Working Note",
  number =       "22",
  institution =  inst-UTK-CS,
  address =      inst-UTK-CS:adr,
  month =        jul,
  year =         "1990",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "UT-CS-90-110, July 1990.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn22.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn22.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{DuCroz:1990:SMM,
  author =       "J. {Du Croz} and N. Higham",
  title =        "Stability of Methods for Matrix Inversion",
  type =         "LAPACK Working Note",
  number =       "27",
  institution =  inst-UTK-CS,
  address =      inst-UTK-CS:adr,
  month =        oct,
  year =         "1990",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "UT-CS-90-119, October, 1990.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn27.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn27.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Higham:1990:ACD,
  author =       "Nicholas J. Higham",
  editor =       "M. G. Cox and S. J. Hammarling",
  booktitle =    "Reliable Numerical Computation",
  title =        "Analysis of the {Cholesky} Decomposition of a
                 Semi-definite Matrix",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "161--185",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
}

@Article{Higham:1990:BEG,
  author =       "Nicholas J. Higham",
  title =        "Bounding the Error in {Gaussian} Elimination for
                 Tridiagonal Systems",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "11",
  number =       "4",
  pages =        "521--530",
  month =        oct,
  year =         "1990",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@InProceedings{Higham:1990:CEB,
  author =       "Nicholas J. Higham",
  editor =       "Philip J. Brown and Wayne A. Fuller",
  booktitle =    "Statistical Analysis of Measurement Error Models and
                 Applications, Contemporary Mathematics 112",
  title =        "Computing Error Bounds for Regression Problems",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "195--208",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
}

@Article{Higham:1990:EFM,
  author =       "Nicholas J. Higham",
  title =        "Exploiting Fast Matrix Multiplication Within the Level
                 3 {BLAS}",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "352--368",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65F99)",
  MRnumber =     "1 095 133",
  bibdate =      "Sun Sep 04 23:21:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "Describes algorithms based on Strassen's method which
                 are asymptotically faster than the standard $ {N}^3 $
                 algorithm, and in practice, faster for $ {N} \approx
                 100 $, and examines their numerical stability. See
                 \cite{Dongarra:1990:ASL,Demmel:1992:SBA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p352-higham/",
  abstract =     "The Level 3 BLAS (BLAS3) are a set of specifications
                 of FORTRAN 77 subprograms for carrying out matrix
                 multiplications and the solution of triangular systems
                 with multiple right-hand sides. They are intended to
                 provide efficient and portable building blocks for
                 linear algebra algorithms on high-performance
                 computers. We describe algorithms for the BLAS3
                 operations that are asymptotically faster than the
                 conventional ones. These algorithms are based on
                 Strassen's method for fast matrix multiplication, which
                 is now recognized to be a practically useful technique
                 once matrix dimensions exceed about 100. We pay
                 particular attention to the numerical stability of
                 these ``fast BLAS3.'' Error bounds are given and their
                 significance is explained and illustrated with the aid
                 of numerical experiments. Our conclusion is that the
                 fast BLAS3, although not as strongly stable as
                 conventional implementations, are stable enough to
                 merit careful consideration in many applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
  keywords =     "algorithms",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra. {\bf D.3.2}:
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77.",
}

@Article{Higham:1990:EMN,
  author =       "Nicholas J. Higham",
  title =        "Experience with a Matrix Norm Estimator",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "11",
  number =       "4",
  pages =        "804--809",
  month =        jul,
  year =         "1990",
  CODEN =        "SIJCD4",
  ISSN =         "0196-5204",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM Journal on Scientific and Statistical Computing",
  journal-URL =  "http://epubs.siam.org/loi/sijcd4",
  mynote =       "Timely Communication.",
}

@Article{Higham:1990:FMM,
  author =       "Nicholas J. Higham",
  title =        "Is Fast Matrix Multiplication of Practical Use?",
  journal =      j-SIAM-NEWS,
  volume =       "23",
  pages =        "12--??",
  month =        nov,
  year =         "1990",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@Article{Higham:1990:FPD,
  author =       "Nicholas J. Higham and Robert S. Schreiber",
  title =        "Fast Polar Decomposition of an Arbitrary Matrix",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "11",
  number =       "4",
  pages =        "648--655",
  month =        jul,
  year =         "1990",
  CODEN =        "SIJCD4",
  ISSN =         "0196-5204",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  annote =       "Prepublished as RIACS technical report 88.29 and NASA
                 Contractor Report 185412.",
  fjournal =     "SIAM Journal on Scientific and Statistical Computing",
  journal-URL =  "http://epubs.siam.org/loi/sijcd4",
}

@InProceedings{Higham:1990:HAG,
  author =       "Nicholas J. Higham",
  editor =       "D. F. Griffiths and G. A. Watson",
  booktitle =    "Numerical Analysis 1989, Proceedings of the 13th
                 Dundee Conference",
  title =        "How Accurate is {Gaussian} Elimination?",
  volume =       "228",
  publisher =    pub-LONGMAN-ST,
  address =      pub-LONGMAN-ST:adr,
  pages =        "137--154",
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  series =       "Pitman Research Notes in Mathematics",
  acknowledgement = ack-njh,
}

@TechReport{Higham:1990:IRE,
  author =       "Nicholas J. Higham",
  title =        "Iterative Refinement Enhances the Stability of {$ Q R
                 $} Factorization Methods for Solving Linear Equations",
  type =         "Numerical Analysis Report",
  number =       "182",
  institution =  inst-U-MANCHESTER,
  address =      inst-U-MANCHESTER:adr,
  month =        apr,
  year =         "1990",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  mynote =       "Contains proofs in the appendix that are not in
                 \cite{Higham:1991:IRE}.",
}

@Article{Higham:1990:RGH,
  author =       "Nicholas J. Higham",
  title =        "Review of {``G. H. Golub and C. F. Van Loan, Matrix
                 Computations, Second Edition, Johns Hopkins University
                 Press, Baltimore, Maryland, 1989''}",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "141",
  pages =        "289--292",
  year =         "1990",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Higham:1990:RMJ,
  author =       "Nicholas J. Higham",
  title =        "Review of {``M. J. C. Gover and S. Barnett, eds.,
                 Applications of Matrix Theory, Oxford University Press,
                 1989''}",
  journal =      j-MATH-GAZ,
  volume =       "74",
  number =       "468",
  pages =        "202",
  year =         "1990",
  CODEN =        "MAGAAS",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}

@Article{Higham:1990:SAA,
  author =       "Nicholas J. Higham",
  title =        "Stability Analysis of Algorithms for Solving Confluent
                 {Vandermonde}-like Systems",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "11",
  number =       "1",
  pages =        "23--41",
  month =        jan,
  year =         "1990",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:1991:ACT,
  author =       "Nicholas J. Higham",
  title =        "Algorithm 694: {A} Collection of Test Matrices in
                 {MATLAB}",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "289--305",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:52:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p289-higham/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
  keywords =     "algorithms; experimentation; performance; theory",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra.",
}

@Article{Higham:1991:IRE,
  author =       "Nicholas J. Higham",
  title =        "Iterative Refinement Enhances the Stability of {$ Q R
                 $} Factorization Methods for Solving Linear Equations",
  journal =      j-BIT,
  volume =       "31",
  number =       "3",
  pages =        "447--468",
  year =         "1991",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65F05 (65F10 65G05)",
  MRnumber =     "92h:65043",
  MRreviewer =   "James Weldon Demmel",
  bibdate =      "Fri Nov 13 07:00:34 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh # " and " # ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@InCollection{Higham:1991:SLE,
  author =       "Nicholas J. Higham",
  editor =       "Christine Bondi",
  booktitle =    "New Applications of Mathematics",
  title =        "Solving Linear Equations",
  publisher =    pub-PENGUIN,
  address =      pub-PENGUIN:adr-L,
  pages =        "33--56",
  year =         "1991",
  MRclass =      "65-01",
  MRnumber =     "1190077",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  mynote =       "Chapter 2.",
}

@Article{Higham:1991:TMP,
  author =       "Nicholas J. Higham",
  title =        "Three Measures of Precision in Floating Point
                 Arithmetic",
  journal =      j-NA-DIGEST,
  volume =       "91",
  number =       "16",
  year =         "1991",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "Electronic mail magazine:
                 \path|na.help@na-net.ornl.gov|.",
  acknowledgement = ack-njh,
  fjournal =     "NA Digest",
  mynote =       "Sunday, April 21, 1991.",
}

@TechReport{Demmel:1992:BLF,
  author =       "James Demmel and Nick Higham and Rob Schreiber",
  title =        "Block {LU} Factorization",
  type =         "LAPACK Working Note",
  number =       "40",
  institution =  inst-UTK-CS,
  address =      inst-UTK-CS:adr,
  month =        feb,
  year =         "1992",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "UT-CS-92-149, February 1992.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn40.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn40.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Demmel:1992:SBA,
  author =       "James W. Demmel and Nicholas J. Higham",
  title =        "Stability of Block Algorithms with Fast Level-3
                 {BLAS}",
  journal =      j-TOMS,
  volume =       "18",
  number =       "3",
  pages =        "274--291",
  month =        sep,
  year =         "1992",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:27:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "See
                 \cite{Dongarra:1990:ASL,Higham:1990:EFM,Dayde:1994:PBI}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p274-demmel/",
  abstract =     "Block algorithms are becoming increasingly popular in
                 matrix computations. Since their basic unit of data is
                 a submatrix rather than a scalar, they have a higher
                 level of granularity than point algorithms, and this
                 makes them well suited to high-performance computers.
                 The numerical stability of the block algorithms in the
                 new linear algebra program library LAPACK is
                 investigated here. It is shown that these algorithms
                 have backward error analyses in which the backward
                 error bounds are commensurate with the error bounds for
                 the underlying level-3 BLAS (BLAS3). One implication is
                 that the block algorithms are as stable as the
                 corresponding point algorithms when conventional BLAS3
                 are used. A second implication is that the use of BLAS3
                 based on fast matrix multiplication techniques affects
                 the stability only insofar as it increases the constant
                 terms in the normwise backward error bounds. For linear
                 equation solvers employing {\em LU} factorization, it
                 is shown that fixed precision iterative refinement
                 helps to mitigate the effect of the larger error
                 constants. Despite the positive results presented here,
                 not all plausible block algorithms are stable; we
                 illustrate this with the example of {\em LU}
                 factorization with block triangular factors and
                 describe how to check a block algorithm for stability
                 without doing a full error analysis.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra. {\bf F.2.1}: Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices.",
}

@Article{DuCroz:1992:SMM,
  author =       "Jeremy J. {Du Croz} and Nicholas J. Higham",
  title =        "Stability of Methods for Matrix Inversion",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "12",
  number =       "1",
  pages =        "1--19",
  year =         "1992",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/12.1.1",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65F05",
  MRnumber =     "92k:65047",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 MathSciNet database",
  abstract =     "Inversion of a triangular matrix can be accomplished
                 in several ways. The standard methods are characterized
                 by the loop ordering, whether matrix-vector
                 multiplication, solution of a triangular system, or a
                 rank-1 update is done inside the outer loop, and
                 whether the method is blocked or unblocked. The
                 numerical stability properties of these methods are
                 investigated. It is shown that unblocked methods
                 satisfy pleasing bounds on the left or right residual.
                 However, for one of the block methods it is necessary
                 to convert a matrix multiplication into the solution of
                 a multiple right-hand side triangular system in order
                 to have an acceptable residual bound. The inversion of
                 a full matrix given a factorization PA=LU is also
                 considered, including the special cases of symmetric
                 indefinite and symmetric positive definite matrices.
                 Three popular methods are shown to possess satisfactory
                 residual bounds, subject to a certain requirement on
                 the implementation, and an attractive new method is
                 described. This work was motivated by the question of
                 what inversion methods should be used in LAPACK.",
  acknowledgement = ack-nhfb # " and " # ack-njh,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@Article{Higham:1992:BEC,
  author =       "Desmond J. Higham and Nicholas J. Higham",
  title =        "Backward Error and Condition of Structured Linear
                 Systems",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "13",
  number =       "1",
  pages =        "162--175",
  month =        jan,
  year =         "1992",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:1992:CPT,
  author =       "Desmond J. Higham and Nicholas J. Higham",
  title =        "Componentwise Perturbation Theory for Linear Systems
                 with Multiple Right-Hand Sides",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "174",
  pages =        "111--129",
  year =         "1992",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Higham:1992:EMN,
  author =       "Nicholas J. Higham",
  title =        "Estimating the Matrix $p$-norm",
  journal =      j-NUM-MATH,
  volume =       "62",
  pages =        "539--555",
  year =         "1992",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Higham:1992:IWP,
  author =       "Nicholas J. Higham",
  title =        "{IMA} Workshop Participants {F}{\^e}te {Golub} on 60th
                 Birthday",
  journal =      j-SIAM-NEWS,
  volume =       "25",
  pages =        "3--??",
  month =        may,
  year =         "1992",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@Article{Higham:1992:JAF,
  author =       "Nicholas J. Higham",
  title =        "The Joy of Anonymous {FTP}",
  journal =      j-IMA-NUM-ANA-NEWSLETTER,
  volume =       "17",
  number =       "1",
  pages =        "61--64",
  month =        oct,
  year =         "1992",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "IMA Numerical Analysis Newsletter",
}

@Article{Higham:1992:LRM,
  author =       "Nicholas J. Higham",
  title =        "{LAPACK} Released in {March}",
  journal =      j-SIAM-NEWS,
  volume =       "25",
  pages =        "20",
  month =        may,
  year =         "1992",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@TechReport{Higham:1992:PTB,
  author =       "Nick Higham",
  title =        "Perturbation Theory and Backward Error for {$ A X - X
                 B = C $}",
  type =         "LAPACK Working Note",
  number =       "42",
  institution =  inst-UTK-CS,
  address =      inst-UTK-CS:adr,
  month =        apr,
  year =         "1992",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "UT-CS-92-153, April, 1992.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn42.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn42.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Higham:1992:SMM,
  author =       "Nicholas J. Higham",
  title =        "Stability of a Method for Multiplying Complex Matrices
                 with Three Real Matrix Multiplications",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "13",
  number =       "3",
  pages =        "681--687",
  month =        jul,
  year =         "1992",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@TechReport{Balle:1993:STM,
  author =       "Susanne M. Balle and Per Christian Hansen and Nicholas
                 J. Higham",
  title =        "A {Strassen}-Type Matrix Inversion Algorithm for the
                 {Connection Machine}",
  number =       "CNC/1993/028",
  institution =  "Centre for Novel Computing, " # inst-U-MANCHESTER,
  address =      inst-U-MANCHESTER:adr,
  type =         "Technical Report",
  pages =        "29",
  month =        oct,
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
}

@Article{Demmel:1993:IEB,
  author =       "James W. Demmel and Nicholas J. Higham",
  title =        "Improved Error Bounds for Underdetermined System
                 Solvers",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "14",
  number =       "1",
  pages =        "1--14",
  month =        jan,
  year =         "1993",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  mynote =       "Also LAPACK Working Note \#23.",
}

@Article{Hammarling:1993:CHW,
  author =       "Sven Hammarling and Nicholas J. Higham and Bo
                 K{\aa}gstr{\"o}m",
  title =        "{CERFACS} Hosts Workshop on Reliability of
                 Computations",
  journal =      j-SIAM-NEWS,
  volume =       "26",
  pages =        "4",
  month =        jul,
  year =         "1993",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@Article{Higham:1993:AFP,
  author =       "Nicholas J. Higham",
  title =        "The accuracy of floating point summation",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "14",
  number =       "4",
  pages =        "783--799",
  month =        jul,
  year =         "1993",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/0914050",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65G05 (65B10)",
  MRnumber =     "94a:65025",
  bibdate =      "Thu Aug 23 06:36:53 2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://citeseer.nj.nec.com/higham93accuracy.html;
                 http://citeseer.nj.nec.com/rd/4651150%2C296147%2C1%2C0.25%2CDownload/http%253A%252F%252Fciteseer.nj.nec.com/cache/papers2/cs/14280/http%253AzSzzSzwww.maths.man.ac.ukzSz%257EnareportszSznarep198.pdf/higham93accuracy.pdf;
                 http://citeseer.nj.nec.com/rd/4651150%2C296147%2C1%2C0.25%2CDownload/http%253A%252F%252Fwww.maths.man.ac.uk/%257Enareports/narep198.ps.gz",
  abstract =     "The usual recursive summation technique is just one of
                 several ways of computing the sum of $n$ floating point
                 numbers. Five summation methods and their variations
                 are analyzed. The accuracy of the methods is compared
                 using rounding error analysis and numerical
                 experiments. Four of the methods are shown to be
                 special cases of a general class of methods, and an
                 error analysis is given for this class. No one method
                 is uniformly more accurate than the others, but some
                 guidelines are given on the choice of method in
                 particular cases.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Manchester Univ., UK",
  classification = "C4110 (Error analysis in numerical methods); C5230
                 (Digital arithmetic methods)",
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "Floating point numbers; Floating point summation;
                 Numerical experiments; Recursive summation technique;
                 Rounding error analysis",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Error analysis",
}

@InCollection{Higham:1993:CCL,
  author =       "Nicholas J. Higham",
  editor =       "M. Chu and others",
  booktitle =    "The {Lanczos} Collected Papers with Commentaries",
  title =        "{Commentary on C. Lanczos, ``Introduction'' to
                 ``Tables of Chebyshev Polynomials $ S_n(x) $ and $
                 C_n(x) $'', Nat.\ Bur.\ Stand., Appl.\ Math.\ Series 9,
                 1952, v--xxvi}",
  publisher =    "????",
  address =      "????",
  year =         "1993",
  bibdate =      "Wed Nov 1 08:00:18 2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "To appear.",
  acknowledgement = ack-njh,
}

@InProceedings{Higham:1993:CEA,
  author =       "Nicholas J. Higham and Philip A. Knight",
  title =        "Componentwise Error Analysis for Stationary Iterative
                 Methods",
  crossref =     "Meyer:1993:LAM",
  pages =        "29--46",
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  series =       "IMA Volumes in Mathematics and its Applications",
  acknowledgement = ack-njh,
}

@Article{Higham:1993:FPB,
  author =       "Nicholas J. Higham and Philip A. Knight",
  title =        "Finite Precision Behavior of Stationary Iteration for
                 Solving Singular Systems",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "192",
  pages =        "165--186",
  year =         "1993",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  mynote =       "Special issue for Proceedings of Workshop on
                 Computational Linear Algebra in Algebraic and Related
                 Problems.",
}

@Book{Higham:1993:HWM,
  author =       "Nicholas J. Higham",
  title =        "Handbook of Writing for the Mathematical Sciences",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xii + 241",
  month =        jun,
  year =         "1993",
  ISBN =         "0-89871-314-5",
  ISBN-13 =      "978-0-89871-314-5",
  LCCN =         "QA42.H54 1993",
  bibdate =      "Tue Mar 1 12:03:19 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook3.bib",
  price =        "US\$21.50",
  acknowledgement = ack-njh,
  note-1 =       "[From the publisher]: Having trouble with your latest
                 math paper? Giving a presentation that you just can't
                 pull together? Struggling with your thesis or trying to
                 get your first article published in a technical
                 journal? Handbook of Writing for the Mathematical
                 Sciences is the book for you!

                 This handy volume provides information on virtually
                 every issue you will face when writing a technical
                 paper or talk, from choosing the right journal to
                 handling your references. You'll also get an overview
                 of the entire publication process--invaluable for
                 anyone hoping to publish in a technical journal.",
  note-2 =       "To write a truly impressive paper, you'll need to
                 understand the anatomy of a research paper and the
                 steps involved in revising a draft. This book offers
                 discussions of these fundamental topics, along with
                 illustrative and provocative examples. Also included
                 are chapters on standard English usage, using computers
                 for writing and research, and writing technical
                 material when English is a foreign language.

                 This handbook provides much-needed advice on handling
                 the basic ingredients of a research paper, like
                 definitions, theorems, examples, and equations. In
                 addition, appendices provide essential reference
                 material, including summaries of \LaTeX{} symbols and
                 Emacs commands, addresses of mathematical societies,
                 and a list of papers that have won expository writing
                 prizes.",
  note-3 =       "This book is ideal for graduate students and teachers.
                 Among its special features:

                 \begin{itemize} \item Detail and extensive use of
                 examples make it an excellent teaching tool

                 \item Discusses \TeX{} and other software tools for
                 preparing publications

                 \item Thorough treatment, with examples, of how to
                 write slides (transparencies) for a mathematical
                 talk.

                 \item Comprehensive index and extensive bibliography
                 make it an excellent reference

                 \item Readable for everyone in the field--from
                 undergraduates to seasoned professionals
                 \end{itemize}",
  note-4 =       "About the Author: Nicholas J. Higham is a Reader in
                 Mathematics at the University of Manchester, UK. He is
                 the author of more than 40 publications and is a member
                 of the editorial board of the SIAM Journal on Matrix
                 Analysis and Applications.",
  tableofcontents = "Preface \\
                 1: General Principles \\
                 2: Writer's Tools and Recommended Reading \\
                 3: Mathematical Writing \\
                 4: English Usage \\
                 5: When English is a Foreign Language \\
                 6: Writing a Paper \\
                 7: Revising a Draft \\
                 8: Publishing a Paper \\
                 9: Writing a Talk \\
                 10: Computer Aids for Writing and Research \\
                 Appendix A: The Greek Alphabet \\
                 Appendix B: Summary of \TeX{} and \LaTeX{} Symbols \\
                 Appendix C: GNU Emacs--The Sixty+ Most Useful Commands;
                 \\
                 Appendix D: Mathematical Organizations in the UK and
                 USA \\
                 Appendix E: Winners of Prizes for Expository Writing;
                 \\
                 Appendix F: Glossary \\
                 Bibliography \\
                 Index",
}

@Article{Higham:1993:ODS,
  author =       "Nicholas J. Higham",
  title =        "Optimization by Direct Search in Matrix Computations",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "14",
  number =       "2",
  pages =        "317--333",
  month =        apr,
  year =         "1993",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@TechReport{Higham:1993:PSV,
  author =       "Nicholas J. Higham and Pythagoras Papadimitriou",
  title =        "Parallel Singular Value Decomposition via the Polar
                 Decomposition",
  type =         "Numerical Analysis Report",
  number =       "239",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  month =        oct,
  year =         "1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  mynote =       "Longer version of \cite{Higham:1994:PAC}.",
}

@InProceedings{Higham:1993:PTBa,
  author =       "Nicholas J. Higham",
  title =        "Perturbation theory and backward error for {$ A X - X
                 B = C $}",
  crossref =     "Moonen:1993:LAL",
  pages =        "391--392",
  year =         "1993",
  bibdate =      "Thu May 29 18:39:54 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
}

@Article{Higham:1993:PTBb,
  author =       "Nicholas J. Higham",
  title =        "Perturbation theory and backward error analysis for {$
                 A X - X B = C $}",
  journal =      j-BIT,
  volume =       "33",
  number =       "1",
  pages =        "124--136",
  year =         "1993",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65F05 (65G05)",
  MRnumber =     "96a:65036",
  bibdate =      "Fri Nov 13 07:00:34 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit33.html",
  acknowledgement = ack-njh # " and " # ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@TechReport{Higham:1993:TMT,
  author =       "Nicholas J. Higham",
  title =        "The {Test Matrix Toolbox} for {Matlab}",
  type =         "Numerical Analysis Report",
  number =       "237",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "76",
  month =        dec,
  year =         "1993",
  bibdate =      "Tue Mar 30 17:06:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  abstract-1 =   "We describe version 2.0 of the Test Matrix Toolbox for
                 Matlab 4. The toolbox contains a collection of test
                 matrices, routines for visualizing matrices, and
                 miscellaneous routines that provide useful additions to
                 Matlab's existing set of functions. There are 58
                 parametrized test matrices, which are mostly square,
                 dense, nonrandom, and of arbitrary dimension. The test
                 matrices include ones with known inverses or known
                 eigenvalues; ill-conditioned or rank deficient
                 matrices; and symmetric, positive definite, orthogonal,
                 defective, involutary, and totally positive matrices.",
  abstract-2 =   "We describe version 2.0 of the Test Matrix Toolbox for
                 Matlab The visualization routines display surface plots
                 of a matrix and its (pseudo-) inverse, the field of
                 values, Gershgorin disks, and two- and
                 three-dimensional views of pseudospectra. We explain
                 the need for collections of test matrices and summarize
                 the features of the collection in the toolbox. We give
                 examples of the use of the toolbox and explain some of
                 the interesting properties of the Frank and Pascal
                 matrices, and of random, magic square and companion
                 matrices. The leading comment lines from all the
                 toolbox routines are listed.",
  acknowledgement = ack-njh,
  keywords =     "test matrix, Matlab, pseudospectrum, visualization,
                 Frank matrix, Pascal matrix, companion matrix, magic
                 square matrix, random matrix",
}

@Article{Higham:1994:BVT,
  author =       "Nicholas J. Higham",
  title =        "{\BibTeX}: {A} Versatile Tool for {\LaTeX} Users",
  journal =      j-SIAM-NEWS,
  volume =       "27",
  pages =        "10, 11, 19",
  month =        jan,
  year =         "1994",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@Book{Higham:1994:HWM,
  author =       "Nicholas J. Higham",
  title =        "Handbook of Writing for the Mathematical Sciences",
  publisher =    "Nippon Hyoron Sha",
  address =      "Tokyo",
  pages =        "x + 235",
  year =         "1994",
  ISBN =         "4-535-78211-3",
  ISBN-13 =      "978-4-535-78211-2",
  bibdate =      "Wed Sep 28 09:02:11 GMT 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "Japanese edition of \cite{Higham:1993:HWM}, translated
                 by Shoji Okumura and Takemitsu Hasegawa.",
  acknowledgement = ack-njh,
}

@Article{Higham:1994:MSD,
  author =       "Nicholas J. Higham",
  title =        "The Matrix Sign Decomposition and Its Relation to the
                 Polar Decomposition",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "212/213",
  pages =        "3--20",
  year =         "1994",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Jan 3 12:21:48 GMT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@InProceedings{Higham:1994:NPA,
  author =       "Nicholas J. Higham and Pythagoras Papadimitriou",
  editor =       "John G. Lewis",
  booktitle =    "Proceedings of the Fifth SIAM Conference on Applied
                 Linear Algebra",
  title =        "A New Parallel Algorithm for Computing the Singular
                 Value Decomposition",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "80--84",
  year =         "1994",
  ISBN =         "0-89871-336-6",
  ISBN-13 =      "978-0-89871-336-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
}

@Article{Higham:1994:PAC,
  author =       "Nicholas J. Higham and Pythagoras Papadimitriou",
  title =        "A Parallel Algorithm for Computing the Polar
                 Decomposition",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "20",
  number =       "8",
  pages =        "1161--1173",
  month =        aug,
  year =         "1994",
  CODEN =        "PACOEJ",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "Parallel Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191",
}

@TechReport{Higham:1994:SCPa,
  author =       "Nicholas J. Higham",
  title =        "A Survey of Componentwise Perturbation Theory in
                 Numerical Linear Algebra",
  type =         "Numerical Analysis Report",
  number =       "241",
  institution =  inst-U-MANCHESTER,
  address =      inst-U-MANCHESTER:adr,
  month =        feb,
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "To appear in Mathematics of Computation 1943--1993, W.
                 Gautschi, ed. Proceedings of Symposia in Applied
                 Mathematics, American Mathematical Society.",
  acknowledgement = ack-njh,
}

@InProceedings{Higham:1994:SCPb,
  author =       "Nicholas J. Higham",
  editor =       "Walter Gautschi",
  booktitle =    "{Mathematics of Computation} 1943--1993: {A} Half
                 Century of Computational Mathematics",
  title =        "A Survey of Componentwise Perturbation Theory in
                 Numerical Linear Algebra",
  volume =       "48",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "49--77",
  year =         "1994",
  bibdate =      "Fri Mar 24 08:51:18 GMT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  series =       "Proceedings of Symposia in Applied Mathematics",
  acknowledgement = ack-njh,
}

@Article{Higham:1994:SPI,
  author =       "Nicholas J. Higham and Alex Pothen",
  title =        "Stability of the Partitioned Inverse Method for
                 Parallel Solution of Sparse Triangular Systems",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "15",
  number =       "1",
  pages =        "139--148",
  month =        jan,
  year =         "1994",
  CODEN =        "SJOCE3",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@Article{Higham:1994:WDM,
  author =       "Nicholas J. Higham",
  title =        "Which Dictionary for the Mathematical Scientist?",
  journal =      j-IMA-BULL,
  volume =       "30",
  number =       "5/6",
  pages =        "81--88",
  year =         "1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "IMA Bulletin",
}

@TechReport{Braconnier:1995:CFV,
  author =       "Thierry Braconnier and Nicholas J. Higham",
  title =        "Computing the Field of Values and Pseudospectra Using
                 the {Lanczos} Method with Continuation",
  type =         "Numerical Analysis Report",
  number =       "279",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "20",
  month =        nov,
  year =         "1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
  note =         "Submitted to " # j-BIT,
  bibdate =      "Fri Jun 10 12:38:34 2011",
  acknowledgement = ack-nhfb,
}

@Article{Demmel:1995:SBF,
  author =       "James W. Demmel and Nicholas J. Higham and Robert S.
                 Schreiber",
  title =        "Stability of Block {$ L U $} Factorization",
  journal =      j-NUM-LIN-ALG-APPL,
  volume =       "2",
  number =       "2",
  pages =        "173--190",
  year =         "1995",
  CODEN =        "NLAAEM",
  ISSN =         "1070-5325 (print), 1099-1506 (electronic)",
  ISSN-L =       "1070-5325",
  bibdate =      "Wed Apr 5 12:48:23 GMT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "To appear.",
  acknowledgement = ack-njh,
  fjournal =     "Numerical Linear Algebra with Applications",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
}

@TechReport{Higham:1995:DPS,
  author =       "Nicholas J. Higham",
  title =        "Diagonal Pivoting Stability \dots",
  type =         "Numerical Analysis Report",
  number =       "2xx",
  institution =  inst-U-MANCHESTER,
  address =      inst-U-MANCHESTER:adr,
  month =        jun,
  year =         "1995",
  bibdate =      "Tue Mar 21 16:31:40 GMT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "In preparation.",
  acknowledgement = ack-njh,
}

@TechReport{Higham:1995:IRLa,
  author =       "Nicholas J. Higham",
  title =        "Iterative Refinement for Linear Systems and {LAPACK}",
  type =         "Numerical Analysis Report",
  number =       "277",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "17",
  month =        sep,
  year =         "1995",
  bibdate =      "Mon Apr 21 19:26:38 GMT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "To appear in " # j-IMA-J-NUMER-ANAL # " (14) 1997.",
  acknowledgement = ack-njh,
  mynote =       "Also LAPACK Working Note 104.",
}

@TechReport{Higham:1995:IRLb,
  author =       "N. J. Higham",
  title =        "Iterative Refinement and {LAPACK}",
  type =         "LAPACK Working Note",
  number =       "104",
  institution =  inst-UTK-CS,
  address =      inst-UTK-CS:adr,
  month =        oct,
  year =         "1995",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "UT-CS-95-308, October 1995.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn104.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn104.pdf",
  acknowledgement = ack-nhfb,
  mynote =       "Also Manchester Numerical Analysis Report 277.",
}

@Article{Higham:1995:MPF,
  author =       "Nicholas J. Higham and Philip A. Knight",
  title =        "Matrix Powers in Finite Precision Arithmetic",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "16",
  number =       "2",
  pages =        "343--358",
  month =        apr,
  year =         "1995",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Tue Aug 29 09:11:08 GMT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  mynote =       "Page numbers from SIAM.",
}

@Article{Higham:1995:RHA,
  author =       "Nicholas J. Higham",
  title =        "Review of {``Howard Anton and Chris Rorres, Elementary
                 Linear Algebra: Applications Version, Seventh edition,
                 Wiley, New York, 1994.''}",
  journal =      j-IMA-BULL,
  volume =       "31",
  number =       "7/8",
  pages =        "122--123",
  year =         "1995",
  bibdate =      "Mon Aug 14 03:43:49 GMT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "IMA Bulletin",
}

@TechReport{Higham:1995:SDP,
  author =       "N. J. Higham",
  title =        "Stability of the Diagonal Pivoting Method with Partial
                 Pivoting",
  type =         "LAPACK Working Note",
  number =       "105",
  institution =  inst-UTK-CS,
  address =      inst-UTK-CS:adr,
  month =        oct,
  year =         "1995",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "UT-CS-95-309, October 1995.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn105.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn105.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Higham:1995:SPT,
  author =       "Nicholas J. Higham",
  title =        "Stability of Parallel Triangular System Solvers",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "16",
  number =       "2",
  pages =        "400--413",
  month =        mar,
  year =         "1995",
  CODEN =        "SJOCE3",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Wed Jul 5 10:32:41 GMT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  mynote =       "Page numbers from SIAM.",
  xxnote =       "Check month: apr or mar??",
}

@TechReport{Higham:1995:TMT,
  author =       "Nicholas J. Higham",
  title =        "The {Test Matrix Toolbox} for {{\sc Matlab}}, Version
                 3.0",
  type =         "Numerical Analysis Report",
  number =       "276",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "70",
  month =        sep,
  year =         "1995",
  bibdate =      "Thu Sep 28 10:50:20 GMT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  note =         "Supersedes Numerical Analysis Report No. 237. In
                 preparation.",
  URL =          "http://p2chpd-cluster.univ-lyon1.fr/P2CHPD/matlab/pdf_doc/otherdocs/testmatrix.pdf",
  acknowledgement = ack-njh,
}

@Article{Braconnier:1996:CFV,
  author =       "Thierry Braconnier and Nicholas J. Higham",
  title =        "Computing the Field of Values and Pseudospectra Using
                 the {Lanczos} Method with Continuation",
  journal =      j-BIT-NUM-MATH,
  volume =       "36",
  number =       "3",
  pages =        "422--440",
  month =        sep,
  year =         "1996",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  MRclass =      "65F15",
  MRnumber =     "97d:65015",
  bibdate =      "Fri Nov 13 07:00:34 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "International Linear Algebra Year (Toulouse, 1995).",
  URL =          "http://www.mai.liu.se/BIT/contents/bit36.html",
  acknowledgement = ack-njh # " and " # ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Carlisle:1996:LSY,
  author =       "David P. Carlisle and Nicholas J. Higham",
  title =        "{\LaTeXe}: {Should} You Upgrade To It?",
  journal =      j-SIAM-NEWS,
  volume =       "29",
  number =       "1",
  pages =        "12",
  month =        jan # "\slash " # feb,
  year =         "1996",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Mon Feb 19 08:51:53 GMT 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@TechReport{Cheng:1996:MCA,
  author =       "Sheung Hun Cheng and Nicholas J. Higham",
  title =        "A Modified {Cholesky} Algorithm Based on a Symmetric
                 Indefinite Factorization",
  type =         "Numerical Analysis Report",
  number =       "289",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "18",
  month =        apr,
  year =         "1996",
  bibdate =      "Fri Feb 14 19:47:12 GMT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "To appear in " # j-SIAM-J-MAT-ANA-APPL # ".",
  acknowledgement = ack-njh,
}

@Article{Hammarling:1996:HPP,
  author =       "Sven Hammarling and Nicholas J. Higham",
  title =        "How to Prepare a Poster",
  journal =      j-SIAM-NEWS,
  volume =       "29",
  number =       "4",
  pages =        "20, 19",
  month =        may,
  year =         "1996",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Tue May 14 11:26:42 GMT 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@Book{Higham:1996:ASN,
  author =       "Nicholas J. Higham",
  title =        "Accuracy and Stability of Numerical Algorithms",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xxviii + 688",
  year =         "1996",
  ISBN =         "0-89871-355-2 (paperback)",
  ISBN-13 =      "978-0-89871-355-8 (paperback)",
  LCCN =         "QA297.H53 1996",
  MRclass =      "65Fxx, 15-04, 65-02, 65G50",
  bibdate =      "Tue Jan 30 11:01:35 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
  price =        "US\$39.00",
  URL =          "http://www.ma.man.ac.uk/~higham/asna.html",
  acknowledgement = ack-njh # " and " # ack-nhfb,
  remark =       "Typeset with \LaTeX2e.",
  tableofcontents = "Principles of Finite Precision Computation \\
                 Relative Error and Significant Digits \\
                 Sources of Errors \\
                 Precision Versus Accuracy \\
                 Backward and Forward Errors \\
                 Conditioning \\
                 Cancellation \\
                 Solving a Quadratic Equation \\
                 Computing the Sample Variance \\
                 Solving Linear Equations \\
                 Accumulation of Rounding Errors \\
                 Instability Without Cancellation \\
                 Increasing the Precision \\
                 Cancellation of Rounding Errors \\
                 Rounding Errors Can Be Beneficial \\
                 Stability of an Algorithm Depends on the Problem \\
                 Rounding Errors Are Not Random \\
                 Designing Stable Algorithms \\
                 Misconceptions \\
                 Rounding Errors in Numerical Analysis \\
                 Floating Point Arithmetic \\
                 Floating Point Number System \\
                 Model of Arithmetic \\
                 IEEE Arithmetic \\
                 Aberrant Arithmetics \\
                 Exact Subtraction \\
                 Fused Multiply-Add Operation \\
                 Choice of Base and Distribution of Numbers \\
                 Statistical Distribution of Rounding Errors \\
                 Alternative Number Systems \\
                 Elementary Functions \\
                 Accuracy Tests \\
                 Inner and Outer Products \\
                 The Purpose of Rounding Error Analysis \\
                 Running Error Analysis \\
                 Notation for Error Analysis \\
                 Matrix Multiplication \\
                 Complex Arithmetic \\
                 Miscellany \\
                 Error Analysis Demystified \\
                 Other Approaches \\
                 Summation \\
                 Summation Methods \\
                 Error Analysis \\
                 Compensated Summation \\
                 Other Summation Methods \\
                 Statistical Estimates of Accuracy \\
                 Choice of Method \\
                 Polynomials \\
                 Horner's Method \\
                 Evaluating Derivatives \\
                 The Newton Form and Polynomial Interpolation \\
                 Matrix Polynomials \\
                 Norms \\
                 Vector Norms",
}

@InCollection{Higham:1996:CCL,
  author =       "Nicholas J. Higham",
  editor =       "M. Chu and others",
  booktitle =    "The {Lanczos} Collected Papers with Commentaries",
  title =        "{Commentary on C. Lanczos, ``Introduction'' to
                 ``Tables of Chebyshev Polynomials $ S_n(x) $ and $
                 C_n(x) $'', Nat.\ Bur.\ Stand., Appl.\ Math.\ Series 9,
                 1952, v--xxvi}",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "1996",
  bibdate =      "Fri Jun 10 12:38:34 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
  note =         "To appear",
  acknowledgement = ack-nhfb,
}

@TechReport{Higham:1996:FCS,
  author =       "Nicholas J. Higham",
  title =        "Factorizing Complex Symmetric Matrices with Positive
                 Definite Real and Imaginary Parts",
  type =         "Numerical Analysis Report",
  number =       "298",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "12",
  month =        nov,
  year =         "1996",
  bibdate =      "Mon May 19 12:01:10 GMT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "Published in \cite{Higham:1998:FCS}.",
  acknowledgement = ack-njh,
}

@TechReport{Higham:1996:MIM,
  author =       "Nicholas J. Higham and Sheung Hun Cheng",
  title =        "Modifying the Inertia of Matrices Arising in
                 Optimization",
  type =         "Numerical Analysis Report",
  number =       "295",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "17",
  month =        sep,
  year =         "1996",
  bibdate =      "Mon Feb 24 12:42:49 GMT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "To appear in " # j-LINEAR-ALGEBRA-APPL # ".",
  acknowledgement = ack-njh,
}

@Article{Higham:1996:RAN,
  author =       "Nicholas J. Higham",
  title =        "Review of {``Acta Numerica 1994 and Acta Numerica
                 1995, Cambridge University Press''}",
  journal =      j-MATH-TODAY,
  volume =       "32",
  number =       "1/2",
  pages =        "28--??",
  year =         "1996",
  ISSN =         "1361-2042",
  ISSN-L =       "1361-2042",
  bibdate =      "Sat Sep 24 08:44:10 2011",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/Bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
  acknowledgement = ack-nhfb # " and " # ack-njh,
  fjournal =     "Mathematics Today",
  journal-URL =  "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
}

@Article{Higham:1996:RDB,
  author =       "Nicholas J. Higham",
  title =        "Review of {``Dario Bini and Victor Y. Pan. {\em
                 Polynomial and Matrix Computations. Volume 1:
                 Fundamental Algorithms}, Birkh{\"a}user, 1994''}",
  journal =      j-MATH-COMPUT,
  volume =       "65",
  number =       "214",
  pages =        "888--889",
  year =         "1996",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Wed Jul 17 08:54:13 GMT 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Higham:1996:RMB,
  author =       "Nicholas J. Higham",
  title =        "Review of {``Are Magnus Bruaset. A Survey of
                 Preconditioned Iterative Methods, volume 328 of Pitman
                 Research Notes in Mathematics. Longman Scientific and
                 Technical, Essex, UK, 1995.''}",
  journal =      j-IMA-BULL,
  volume =       "32",
  number =       "3/4",
  pages =        "60",
  year =         "1996",
  bibdate =      "Wed Apr 17 16:22:01 GMT 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "IMA Bulletin",
}

@TechReport{Higham:1996:SBE,
  author =       "Desmond J. Higham and Nicholas J. Higham",
  title =        "Structured Backward Error and Condition of Generalized
                 Eigenvalue Problems",
  type =         "Numerical Analysis Report",
  number =       "297",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "24",
  month =        nov,
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "Submitted to " # j-SIAM-J-MAT-ANA-APPL,
  bibdate =      "Fri Nov 15 12:27:07 GMT 1996",
  acknowledgement = ack-njh,
}

@TechReport{Cox:1997:ASN,
  author =       "Anthony J. Cox and Nicholas J. Higham",
  title =        "Accuracy and Stability of the Null Space Method for
                 Solving the Equality Constrained Least Squares
                 Problem",
  type =         "Numerical Analysis Report",
  number =       "306",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "20",
  month =        aug,
  year =         "1997",
  bibdate =      "Sat Oct 31 10:24:09 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "To appear in " # j-BIT # ", 39(1): 1999",
  acknowledgement = ack-njh,
}

@TechReport{Cox:1997:SHQ,
  author =       "Anthony J. Cox and Nicholas J. Higham",
  title =        "Stability of {Householder $ Q R $} Factorization for
                 Weighted Least Squares Problems",
  type =         "Numerical Analysis Report",
  number =       "301",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "17",
  month =        feb,
  year =         "1997",
  bibdate =      "Mon May 19 14:24:46 GMT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "To appear in Numerical Analysis 1997, Proceedings of
                 the 17th Dundee Conference.",
  acknowledgement = ack-njh,
}

@InCollection{Higham:1997:CCL,
  author =       "Nicholas J. Higham",
  editor =       "William R. Davis and others",
  booktitle =    "Cornelius Lanczos Collected Published Papers with
                 Commentaries",
  title =        "{Commentary on C. Lanczos, ``Introduction'' to
                 ``Tables of Chebyshev Polynomials $ S_n(x) $ and $
                 C_n(x) $'', Nat.\ Bur.\ Stand., Appl.\ Math.\ Series 9,
                 1952, v--xxvi}",
  volume =       "VI(3)",
  publisher =    "????",
  address =      "????",
  pages =        "557--559",
  year =         "1997",
  bibdate =      "Wed Aug 13 08:39:47 GMT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "To appear.",
  acknowledgement = ack-njh,
  mynote =       "Volume VI, Part 3, pp. 557--559.",
}

@Article{Higham:1997:IRL,
  author =       "Nicholas J. Higham",
  title =        "Iterative refinement for linear systems and {LAPACK}",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "17",
  number =       "4",
  pages =        "495--509",
  month =        oct,
  year =         "1997",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/17.4.495",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65F30",
  MRnumber =     "98e:65036",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 http://www3.oup.co.uk/imanum/hdb/Volume_17/Issue_04/;
                 MathSciNet database",
  note =         "Preprint published as Numerical Analysis Report 277,
                 Manchester Centre for Computational Mathematics,
                 Manchester, England, and as LAPACK Working Note 104.",
  URL =          "http://www3.oup.co.uk/imanum/hdb/Volume_17/Issue_04/170495.sgm.abs.html",
  abstract =     "The technique of iterative refinement for improving
                 the computed solution to a linear system was used on
                 desk calculators and computers in the 1940s and has
                 remained popular. In the 1990s iterative refinement is
                 well supported in software libraries, notably in
                 LAPACK. Although the behaviour of iterative refinement
                 in floating point arithmetic is reasonably well
                 understood, the existing theory is not sufficient to
                 justify the use of fixed precision iterative refinement
                 in all the LAPACK routines in which it is implemented.
                 We present analysis that provides the theoretical
                 support needed for LAPACK. The analysis covers both
                 mixed and fixed precision iterative refinement with an
                 arbitrary number of iterations, makes only a general
                 assumption on the underlying solver, and is relatively
                 short. We identify some remaining open problems.",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@Article{Higham:1997:MHI,
  author =       "Nicholas J. Higham",
  title =        "{Manchester} Hosts Inaugural Meeting of {UK} and
                 {Irish SIAM Section}",
  journal =      j-SIAM-NEWS,
  volume =       "30",
  number =       "3",
  pages =        "3",
  month =        apr,
  year =         "1997",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@InProceedings{Higham:1997:RDD,
  author =       "Nicholas J. Higham",
  title =        "Recent Developments in Dense Numerical Linear
                 Algebra",
  crossref =     "Duff:1997:SAN",
  pages =        "1--26",
  year =         "1997",
  bibdate =      "Fri Jul 11 16:11:28 GMT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
}

@Article{Higham:1997:RJR,
  author =       "Nicholas J. Higham",
  title =        "Review of {``James R. Schott, Matrix Analysis for
                 Statistics, Wiley, 1997''}",
  journal =      j-MATH-TODAY,
  volume =       "33",
  number =       "5",
  pages =        "161--162",
  year =         "1997",
  ISSN =         "1361-2042",
  ISSN-L =       "1361-2042",
  bibdate =      "Sun Oct 12 15:29:25 GMT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "Mathematics Today",
  journal-URL =  "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
  oldlabel =     "high97:scho97",
}

@TechReport{Higham:1997:SBF,
  author =       "Nicholas J. Higham",
  title =        "Stability of Block $ \mathrm {LDL^T} $ Factorization
                 of a Symmetric Tridiagonal Matrix",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  year =         "1997",
  bibdate =      "Wed Aug 20 15:29:39 GMT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "In preparation.",
  acknowledgement = ack-njh,
}

@Article{Higham:1997:SDP,
  author =       "Nicholas J. Higham",
  title =        "Stability of the Diagonal Pivoting Method with Partial
                 Pivoting",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "18",
  number =       "1",
  pages =        "52--65",
  month =        jan,
  year =         "1997",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Sun Mar 2 11:16:54 GMT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@TechReport{Higham:1997:SIMa,
  author =       "Nicholas J. Higham",
  title =        "Stable Iterations for the Matrix Square Root",
  type =         "Numerical Analysis Report",
  number =       "305",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "20",
  month =        apr,
  year =         "1997",
  bibdate =      "Mon Jun 16 12:13:21 GMT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "Published in \cite{Higham:1997:SIMb}.",
  acknowledgement = ack-njh,
}

@Article{Higham:1997:SIMb,
  author =       "Nicholas J. Higham",
  title =        "Stable iterations for the matrix square root",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "15",
  number =       "2",
  pages =        "227--242",
  month =        "????",
  year =         "1997",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65F30 (65F05)",
  MRnumber =     "98d:65055",
  bibdate =      "Mon Sep 29 08:36:51 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/7/6/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/7/6/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@InProceedings{Higham:1997:TLA,
  author =       "Nicholas J. Higham",
  editor =       "Ronald F. Boisvert",
  booktitle =    "Quality of Numerical Software: {Assessment} and
                 Enhancement",
  title =        "Testing Linear Algebra Software",
  publisher =    pub-CH,
  address =      pub-CH:adr-L,
  pages =        "109--122",
  year =         "1997",
  bibdate =      "Mon Feb 3 09:14:23 GMT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
}

@Article{Cheng:1998:MCA,
  author =       "Sheung Hun Cheng and Nicholas J. Higham",
  title =        "A Modified {Cholesky} Algorithm Based on a Symmetric
                 Indefinite Factorization",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "19",
  number =       "4",
  pages =        "1097--1110",
  month =        oct,
  year =         "1998",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Fri Dec 4 12:14:09 MST 1998",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/19/4;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/30289",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@TechReport{Cheng:1998:NDP,
  author =       "Sheung Hun Cheng and Nicholas J. Higham",
  title =        "The Nearest Definite Pair for the {Hermitian}
                 Generalized Eigenvalue Problem",
  type =         "Numerical Analysis Report",
  number =       "325",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "15",
  month =        may,
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "Submitted to " # j-LINEAR-ALGEBRA-APPL,
  bibdate =      "Mon May 11 14:55:05 GMT 1998",
  acknowledgement = ack-njh,
  oldlabel =     "chhi98",
}

@TechReport{Cox:1998:BEB,
  author =       "Anthony J. Cox and Nicholas J. Higham",
  title =        "Backward Error Bounds for Constrained Least Squares
                 Problems",
  type =         "Numerical Analysis Report",
  number =       "321",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "20",
  month =        apr,
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "Submitted to " # j-BIT,
  bibdate =      "Fri Apr 17 12:13:36 GMT 1998",
  acknowledgement = ack-njh,
  oldlabel =     "cohi98c",
}

@TechReport{Cox:1998:RWB,
  author =       "Anthony J. Cox and Nicholas J. Higham",
  title =        "Row-Wise Backward Stable Elimination Methods for the
                 Equality Constrained Least Squares Problem",
  type =         "Numerical Analysis Report",
  number =       "319",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "18",
  month =        mar,
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "To appear in " # j-SIAM-J-MAT-ANA-APPL,
  bibdate =      "Fri Aug 14 18:34:14 GMT 1998",
  acknowledgement = ack-njh,
  oldlabel =     "cohi98r",
}

@InProceedings{Cox:1998:SHQ,
  author =       "Anthony J. Cox and Nicholas J. Higham",
  title =        "Stability of {Householder QR} Factorization for
                 Weighted Least Squares Problems",
  crossref =     "Higham:1998:NAP",
  pages =        "57--73",
  year =         "1998",
  bibdate =      "Mon Aug 29 22:30:58 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  series =       "Pitman Research Notes in Mathematics",
  acknowledgement = ack-nhfb,
}

@Article{Higham:1998:BNR,
  author =       "Nicholas J. Higham",
  title =        "Book News \& Reviews: Review of {``Christoph W.
                 Ueberhuber, Numerical Computation: Methods, Software
                 and Analysis, Springer-Verlag, 1997''}",
  journal =      j-IEEE-COMPUT-SCI-ENG,
  volume =       "5",
  number =       "1",
  pages =        "79--79",
  month =        jan # "\slash " # mar,
  year =         "1998",
  CODEN =        "ISCEE4",
  ISSN =         "1070-9924 (print), 1558-190X (electronic)",
  ISSN-L =       "1070-9924",
  bibdate =      "Sat Jan 9 08:57:23 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://dlib.computer.org/cs/books/cs1998/pdf/c1079.pdf",
  acknowledgement = ack-njh # " and " # ack-nhfb,
  fjournal =     "IEEE Computational Science \& Engineering",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=99",
  mynote =       "Jan-Mar",
  oldlabel =     "high98:uebe97",
}

@TechReport{Higham:1998:FCP,
  author =       "Nicholas J. Higham",
  title =        "{$ Q R $} Factorization with Complete Pivoting and
                 Accurate Computation of the {SVD}",
  type =         "Numerical Analysis Report",
  number =       "324",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "26",
  month =        sep,
  year =         "1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "Submitted to " # j-LINEAR-ALGEBRA-APPL,
  bibdate =      "Mon Sep 14 14:06:12 GMT 1998",
  acknowledgement = ack-njh,
  oldlabel =     "high98q",
}

@Article{Higham:1998:FCS,
  author =       "Nicholas J. Higham",
  title =        "Factorizing complex symmetric matrices with positive
                 definite real and imaginary parts",
  journal =      j-MATH-COMPUT,
  volume =       "67",
  number =       "224",
  pages =        "1591--1599",
  year =         "1998",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65F15 (15A23 65F10 65G05)",
  MRnumber =     "1 474 652",
  bibdate =      "Thu Oct 15 16:27:48 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Higham:1998:HWM,
  author =       "Nicholas J. Higham",
  title =        "Handbook of Writing for the Mathematical Sciences",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  edition =      "Second",
  pages =        "xvi + 302",
  year =         "1998",
  ISBN =         "0-89871-420-6 (paperback), 0-89871-955-0 (e-book)",
  ISBN-13 =      "978-0-89871-420-3 (paperback), 978-0-89871-955-0
                 (e-book)",
  LCCN =         "QA42 .H54 1998",
  bibdate =      "Wed Oct 30 14:21:33 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook3.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface to the second edition \\
                 Preface to the first edition \\
                 1. General principles \\
                 2. Writer's tools and recommended reading \\
                 3. Mathematical writing \\
                 4. English usage \\
                 5. When English is a foreign language \\
                 6. Writing a paper \\
                 7. Revising a draft \\
                 8. Publishing a paper \\
                 9. Writing and defending a thesis \\
                 10. Writing a talk \\
                 11. Giving a talk \\
                 12. Preparing a poster \\
                 13. TeX and LaTeX \\
                 14. Aids and resources for writing and research \\
                 Appendix A. The Greek alphabet \\
                 Appendix B. Summary of TeX and LaTeX symbols \\
                 Appendix C. GNU Emacs commands \\
                 Appendix D. Mathematical and other organizations \\
                 Appendix E. Prizes for expository writing \\
                 Glossary \\
                 Bibliography \\
                 Name index \\
                 Subject index",
}

@Article{Higham:1998:MIM,
  author =       "Nicholas J. Higham and Sheung Hun Cheng",
  title =        "Modifying the Inertia of Matrices Arising in
                 Optimization",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "275-276",
  pages =        "261--279",
  year =         "1998",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Mon Jul 27 12:37:04 GMT 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  oldlabel =     "hich98",
}

@TechReport{Higham:1998:NAS,
  author =       "Nicholas J. Higham",
  title =        "Notes on Accuracy and Stability of Algorithms in
                 Numerical Linear Algebra",
  type =         "Numerical Analysis Report",
  number =       "333",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "42",
  month =        aug,
  year =         "1998",
  bibdate =      "Mon Sep 7 09:59:00 GMT 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "To appear in proceedings of EPSRC Numerical Analysis
                 Summer School, Leicester University, July 1998.",
  acknowledgement = ack-njh,
  oldlabel =     "high98a",
}

@Article{Higham:1998:NWE,
  author =       "Nicholas J. Higham and David J. Silvester",
  title =        "``{Nothing was Ever the Same Again}''",
  journal =      j-SIAM-NEWS,
  volume =       "31",
  number =       "7",
  pages =        "1, 8",
  month =        sep,
  year =         "1998",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Wed Sep 16 11:49:30 GMT 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "https://www.siam.org/news/news.php?id=868",
  abstract =     "In 1948, the world's first stored-program computer
                 performed its first (dramatic) computation at the
                 University of Manchester; this spring, researchers
                 gathered at Manchester to celebrate 50 years of
                 progress in computers and numerical analysis.",
  acknowledgement = ack-njh,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
  keywords =     "Manchester ``Baby'' computer",
}

@Article{Higham:1998:SBE,
  author =       "Desmond J. Higham and Nicholas J. Higham",
  title =        "Structured Backward Error and Condition of Generalized
                 Eigenvalue Problems",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "20",
  number =       "2",
  pages =        "493--512",
  year =         "1998",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/S0895479896313188",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Fri Dec 4 12:14:09 MST 1998",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/20/2;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/31318",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Cheng:1999:NDP,
  author =       "Sheung Hun Cheng and Nicholas J. Higham",
  title =        "The nearest definite pair for the {Hermitian}
                 generalized eigenvalue problem",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "302-303",
  number =       "1--3",
  pages =        "63--76",
  day =          "1",
  month =        dec,
  year =         "1999",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Mon Oct 9 10:54:40 MDT 2000",
  bibsource =    "http://www.elsevier.com/locate/laa;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/30/19/117/25/30/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/30/19/117/25/30/article.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Cox:1999:ASN,
  author =       "Anthony J. Cox and Nicholas J. Higham",
  title =        "Accuracy and Stability of the Null Space Method for
                 Solving the Equality Constrained Least Squares
                 Problem",
  journal =      j-BIT-NUM-MATH,
  volume =       "39",
  number =       "1",
  pages =        "34--49",
  month =        "????",
  year =         "1999",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  bibdate =      "Thu Oct 16 08:15:34 2003",
  bibsource =    "http://www.mai.liu.se/BIT/contents/bit39.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 OCLC Article1st database",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Cox:1999:BEB,
  author =       "A. J. Cox and N. J. Higham",
  title =        "Backward error bounds for constrained least squares
                 problems",
  journal =      j-BIT-NUM-MATH,
  volume =       "39",
  number =       "2",
  pages =        "210--227",
  month =        "????",
  year =         "1999",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  bibdate =      "Thu Oct 16 08:15:34 2003",
  bibsource =    "http://www.mai.liu.se/BIT/contents/bit39.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 OCLC Article1st database",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Higham:1999:BRL,
  author =       "Nicholas J. Higham",
  title =        "Book Review: {{\em Linear Algebra (Pure and Applied
                 Mathematics)}, by Peter D. Lax: 250 pp., \pounds 55.00,
                 ISBN 0-471-11111-2 (John Wiley \& Sons, 1996)}",
  journal =      j-BULL-LOND-MATH-SOC,
  volume =       "31",
  number =       "3",
  pages =        "374--375",
  month =        may,
  year =         "1999",
  CODEN =        "LMSBBT",
  DOI =          "https://doi.org/10.1112/S0024609397264167",
  ISSN =         "0024-6093 (print), 1469-2120 (electronic)",
  ISSN-L =       "0024-6093",
  bibdate =      "Thu Aug 25 10:49:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://blms.oxfordjournals.org/content/31/3/374.full.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin of the London Mathematical Society",
  journal-URL =  "http://blms.oxfordjournals.org/content/by/year",
}

@Article{Higham:1999:FBR,
  author =       "Nicholas J. Higham",
  title =        "Featured Book Review: {Selected} Books on Numerical
                 Linear Algebra",
  journal =      j-SIAM-REVIEW,
  volume =       "41",
  number =       "3",
  pages =        "607--610",
  month =        sep,
  year =         "1999",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/SIREAD000041000003000605000001",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-njh,
  created =      "1999.05.20",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  updated =      "2014.07.26",
}

@Article{Higham:1999:FTP,
  author =       "Nicholas J. Higham",
  title =        "A Fitting Tribute to a Pioneering Numerical Analyst
                 [{Cleve Moler}]",
  journal =      j-SIAM-NEWS,
  volume =       "32",
  number =       "10",
  pages =        "3",
  month =        dec,
  year =         "1999",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib",
  note =         "Celebrating Cleve Moler's 60th birthday!",
  URL =          "https://www.siam.org/news/news.php?id=796",
  acknowledgement = ack-njh,
  created =      "2000.01.05",
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
  updated =      "2000.01.05",
}

@InCollection{Higham:1999:NAS,
  author =       "Nicholas J. Higham",
  title =        "Notes on Accuracy and Stability of Algorithms in
                 Numerical Analysis",
  crossref =     "Ainsworth:1999:GSG",
  pages =        "48--82",
  year =         "1999",
  bibdate =      "Wed Jul 14 14:57:11 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
}

@Article{Higham:1999:RPD,
  author =       "Nicholas J. Higham",
  title =        "Review of {``Peter D. Lax, \booktitle{Linear Algebra},
                 Wiley, 1997''}",
  journal =      j-BULL-LOND-MATH-SOC,
  volume =       "31",
  pages =        "374--375",
  year =         "1999",
  CODEN =        "LMSBBT",
  ISSN =         "0024-6093 (print), 1469-2120 (electronic)",
  ISSN-L =       "0024-6093",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  created =      "1999.05.27",
  fjournal =     "Bulletin of the London Mathematical Society",
  journal-URL =  "http://blms.oxfordjournals.org/content/by/year",
  updated =      "1999.05.27",
}

@Article{Higham:1999:SBE,
  author =       "Desmond J. Higham and Nicholas J. Higham",
  title =        "Structured Backward Error and Condition of Generalized
                 Eigenvalue Problems",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "20",
  number =       "2",
  pages =        "493--512",
  month =        apr,
  year =         "1999",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Fri Dec 4 12:14:09 MST 1998",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/20/2;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/31318",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:1999:SBL,
  author =       "Nicholas J. Higham",
  title =        "Stability of block {LDL$^T$} factorization of a
                 symmetric tridiagonal matrix",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "287",
  number =       "1--3",
  pages =        "181--189",
  day =          "15",
  month =        jan,
  year =         "1999",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Fri May 28 08:42:54 MDT 1999",
  bibsource =    "http://www.elsevier.com/locate/laa;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://www.elsevier.com/cas/tree/store/laa/sub/1999/287/1-3/6193.pdf;
                 http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1999&volume=287&issue=1-3&aid=6193",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@InProceedings{Cheng:2000:ALM,
  author =       "Sheung Hun Cheng and Nicholas J. Higham",
  title =        "Approximating the logarithm of a matrix with variable accuracy",
  crossref =     "Watson:2000:NAD",
  pages =        "??--??",
  year =         "2000",
  acknowledgement = ack-nhfb,
  bibdate =      "Tue Nov 28 11:45:46 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
}

@Article{Cox:2000:RWB,
  author =       "Anthony J. Cox and Nicholas J. Higham",
  title =        "Row-Wise Backward Stable Elimination Methods for the
                 Equality Constrained Least Squares Problem",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "21",
  number =       "1",
  pages =        "313--326",
  month =        jan,
  year =         "2000",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Sat Jan 22 14:39:17 MST 2000",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/21/1;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/33595",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Davies:2000:NSG,
  author =       "Philip I. Davies and Nicholas J. Higham",
  title =        "Numerically Stable Generation of Correlation Matrices
                 and Their Factors",
  journal =      j-BIT-NUM-MATH,
  volume =       "40",
  number =       "4",
  pages =        "640--651",
  month =        dec,
  year =         "2000",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1023/A:1022384216930",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65F18",
  MRnumber =     "MR1799307 (2002g:65045)",
  MRreviewer =   "Ram Shanmugam",
  bibdate =      "Wed Jan 4 15:06:04 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=40&issue=4;
                 http://www.mai.liu.se/BIT/contents/bit40.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=40&issue=4&spage=640",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT. Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Higham:2000:BAM,
  author =       "Nicholas J. Higham and Fran{\c{c}}oise Tisseur",
  title =        "A Block Algorithm for Matrix $1$-Norm Estimation, with
                 an Application to $1$-Norm Pseudospectra",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "21",
  number =       "4",
  pages =        "1185--1201",
  month =        oct,
  year =         "2000",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/S0895479899356080",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F20 (65F15)",
  MRnumber =     "MR1780268 (2001d:65051)",
  bibdate =      "Fri Oct 27 07:23:32 MDT 2000",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/21/4;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/35608",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:2000:FCP,
  author =       "Nicholas J. Higham",
  title =        "{$ Q R $} factorization with complete pivoting and
                 accurate computation of the {SVD}",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "309",
  number =       "1--3",
  pages =        "153--174",
  year =         "2000",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/S0024-3795(99)00230-X",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "65F20 (15A23)",
  MRnumber =     "MR1758366 (2001c:65049)",
  MRreviewer =   "Jesse L. Barlow",
  bibdate =      "Sat Apr 16 17:54:53 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  remark =       "Proceedings of the International Workshop on Accurate
                 Solution of Eigenvalue Problems (University Park, PA,
                 1998)",
}

@Book{Higham:2000:MG,
  author =       "Desmond J. Higham and Nicholas J. Higham",
  title =        "{MATLAB} Guide",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xxii + 283",
  year =         "2000",
  ISBN =         "0-89871-469-9",
  ISBN-13 =      "978-0-89871-469-2",
  LCCN =         "QA297 .H5217 2000",
  MRclass =      "65-04 (00A20)",
  MRnumber =     "MR1787308 (2001e:65003)",
  bibdate =      "Tue Jan 23 09:04:18 2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  keywords =     "Matlab; numerical analysis -- data processing",
}

@Article{Higham:2000:NAQ,
  author =       "Nicholas J. Higham and Hyun-Min Kim",
  title =        "Numerical analysis of a quadratic matrix equation",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "20",
  number =       "4",
  pages =        "499--519",
  month =        oct,
  year =         "2000",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/20.4.499",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65F30 (15A24)",
  MRnumber =     "MR1795295 (2001i:65054)",
  bibdate =      "Mon Feb 12 16:52:03 2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 http://www3.oup.co.uk/imanum/hdb/Volume_20/Issue_04/",
  URL =          "http://www3.oup.co.uk/imanum/hdb/Volume_20/Issue_04/200499abs.pdf;
                 http://www3.oup.co.uk/imanum/hdb/Volume_20/Issue_04/pdf/200499.pdf",
  abstract =     "The quadratic matrix equation $ A X^2 + B X + C = 0 $
                 in $ n \times n $ matrices arises in applications and
                 is of intrinsic interest as one of the simplest
                 nonlinear matrix equations. We give a complete
                 characterization of solutions in terms of the
                 generalized Schur decomposition and describe and
                 compare various numerical solution techniques. In
                 particular, we give a thorough treatment of functional
                 iteration methods based on Bernoulli's method. Other
                 methods considered include Newton's method with exact
                 line searches, symbolic solution and continued
                 fractions. We show that functional iteration applied to
                 the quadratic matrix equation can provide an efficient
                 way to solve the associated quadratic eigenvalue
                 problem $ (\lambda^2 A + \lambda B + C) x = 0 $.",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@Article{Higham:2000:QFC,
  author =       "Nicholas J. Higham",
  title =        "{QR} factorization with complete pivoting and accurate
                 computation of the {SVD}",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "309",
  number =       "1--3",
  pages =        "153--174",
  day =          "15",
  month =        apr,
  year =         "2000",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Mon Oct 9 10:54:41 MDT 2000",
  bibsource =    "http://www.elsevier.com/locate/laa;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/30/19/126/25/34/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/30/19/126/25/34/article.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Higham:2000:RJJ,
  author =       "Nicholas J. Higham",
  title =        "Review of {``Jack J. Dongarra, Iain S. Duff, Danny C.
                 Sorensen, and Henk A. van der Vorst,
                 \booktitle{Numerical Linear Algebra for
                 High-Performance Computers}, Society for Industrial and
                 Applied Mathematics, Philadelphia, PA, USA, 1998''}",
  journal =      j-SIAM-REVIEW,
  volume =       "42",
  number =       "3",
  pages =        "529",
  month =        sep,
  year =         "2000",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/SIREAD000042000003000513000001",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Oct 6 15:10:21 GMT 2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-njh,
  created =      "2000.10.06",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  updated =      "2014.07.26",
}

@TechReport{Anjos:2001:SPA,
  author =       "M. F. Anjos and N. Higham and M. Takouda and H.
                 Wolkowicz",
  title =        "A semidefinite programming approach for the closest
                 correlation matrix problem",
  number =       "CORR 2001-in progress",
  institution =  inst-UNIV-WATERLOO,
  address =      inst-UNIV-WATERLOO:adr,
  year =         "2001",
  bibdate =      "Wed Sep 9 06:36:42 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib",
  acknowledgement = ack-nhfb,
}

@Article{Cheng:2001:ALM,
  author =       "Sheung Hun Cheng and Nicholas J. Higham and Charles S.
                 Kenney and Alan J. Laub",
  title =        "Approximating the logarithm of a matrix to specified
                 accuracy",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "22",
  number =       "4",
  pages =        "1112--1125",
  year =         "2001",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/S0895479899364015",
  ISSN =         "1095-7162",
  ISSN-L =       "0895-4798",
  MRclass =      "65F30",
  MRnumber =     "MR1825853 (2002a:65069)",
  MRreviewer =   "Jin Yun Yuan",
  bibdate =      "Sat Apr 16 17:54:57 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@TechReport{Cheng:2001:ILB,
  author =       "S. Cheng and N. Higham",
  title =        "Implementation for {LAPACK} of a Block Algorithm for
                 Matrix $1$-Norm Estimation",
  type =         "LAPACK Working Note",
  number =       "152",
  institution =  inst-UTK-CS,
  address =      inst-UTK-CS:adr,
  month =        aug,
  year =         "2001",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "UT-CS-01-470, August 2001.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn152.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn152.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Cheng:2001:PIB,
  author =       "Sheung Hun Cheng and Nicholas J. Higham",
  title =        "Parallel Implementation of a Block Algorithm for
                 Matrix $1$-Norm Estimation",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2150",
  pages =        "568--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:53 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2150.htm;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2150/21500568.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2150/21500568.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Davies:2001:ACM,
  author =       "Philip I. Davies and Nicholas J. Higham and
                 Fran{\c{c}}oise Tisseur",
  title =        "Analysis of the {Cholesky} Method with Iterative
                 Refinement for Solving the Symmetric Definite
                 Generalized Eigenproblem",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "23",
  number =       "2",
  pages =        "472--493",
  year =         "2001",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/S0895479800373498",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F15",
  MRnumber =     "MR1871323 (2002i:65039)",
  MRreviewer =   "David Scott Watkins",
  bibdate =      "Fri Feb 22 09:58:16 MST 2002",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/23/2;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/37349",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@TechReport{Higham:2001:BEM,
  author =       "Nicholas J. Higham and Fran{\c{c}}oise Tisseur",
  title =        "Bounds for Eigenvalues of Matrix Polynomials",
  type =         "Numerical Analysis Report",
  number =       "371",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "16",
  month =        jan,
  year =         "2001",
  bibdate =      "Wed Sep 9 06:38:11 2015",
  note =         "To appear in " # j-LINEAR-ALGEBRA-APPL,
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
  acknowledgement = ack-nhfb,
}

@Article{Higham:2001:EPA,
  author =       "Nicholas J. Higham",
  title =        "Evaluating {Pad{\'e}} approximants of the matrix
                 logarithm",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "22",
  number =       "4",
  pages =        "1126--1135",
  year =         "2001",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/S0895479800368688",
  ISSN =         "1095-7162",
  ISSN-L =       "0895-4798",
  MRclass =      "65F30 (65D15)",
  MRnumber =     "MR1824061 (2002d:65039)",
  MRreviewer =   "Assem Deif",
  bibdate =      "Sat Apr 16 17:55:00 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:2001:P,
  author =       "Nicholas Higham and Roger Horn and Thomas J. Laffey
                 and Ferran Puerta",
  title =        "Preface",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "332--334",
  number =       "1",
  pages =        "1--1",
  day =          "1",
  month =        aug,
  year =         "2001",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Wed Jul 25 17:54:46 MDT 2001",
  bibsource =    "http://www.elsevier.com/locate/laa;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/30/19/157/25/25/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/30/19/157/25/25/article.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Higham:2001:RMA,
  author =       "Nicholas J. Higham",
  title =        "Review of {``Michael Alley, \booktitle{The Craft of
                 Editing: A Guide for Managers, Scientists and
                 Engineers}. Springer-Verlag, 2000''}",
  journal =      j-SIAM-REVIEW,
  volume =       "43",
  number =       "1",
  pages =        "202",
  month =        mar,
  year =         "2001",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/SIREAD000043000001000179000001",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  created =      "2001.04.19",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  updated =      "2014.07.26",
}

@Article{Higham:2001:SQM,
  author =       "Nicholas J. Higham and Hyun-Min Kim",
  title =        "Solving a quadratric matrix equation by {Newton}'s
                 method with exact line searches",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "23",
  number =       "2",
  pages =        "303--316",
  year =         "2001",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/S0895479899350976",
  ISSN =         "1095-7162",
  ISSN-L =       "0895-4798",
  MRclass =      "65H10 (65F30)",
  MRnumber =     "MR1871314 (2002j:65055)",
  bibdate =      "Sat Apr 16 17:55:00 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Tisseur:2001:SPP,
  author =       "Fran{\c{c}}oise Tisseur and Nicholas J. Higham",
  title =        "Structured pseudospectra for polynomial eigenvalue
                 problems, with applications",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "23",
  number =       "1",
  pages =        "187--208",
  year =         "2001",
  CODEN =        "SJMAEL",
  ISSN =         "1095-7162",
  ISSN-L =       "0895-4798",
  MRclass =      "15A18 (15A22 65F15)",
  MRnumber =     "MR1856605 (2002k:15024)",
  MRreviewer =   "Jesse L. Barlow",
  bibdate =      "Sat Apr 16 17:55:00 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Book{Higham:2002:ASN,
  author =       "Nicholas J. Higham",
  title =        "Accuracy and Stability of Numerical Algorithms",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  edition =      "Second",
  pages =        "xxx + 680",
  year =         "2002",
  DOI =          "https://doi.org/10.1137/1.9780898718027",
  ISBN =         "0-89871-521-0 (hardcover), 0-89871-802-3 (e-book)",
  ISBN-13 =      "978-0-89871-521-7 (hardcover), 978-0-89871-802-7
                 (e-book)",
  LCCN =         "QA297 .H53 2002",
  MRclass =      "65G50 (65-02)",
  MRnumber =     "MR1927606 (2003g:65064)",
  bibdate =      "Wed Oct 30 14:20:02 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  abstract =     "\booktitle{Accuracy and Stability of Numerical
                 Algorithms} gives a thorough, up-to-date treatment of
                 the behavior of numerical algorithms in finite
                 precision arithmetic. It combines algorithmic
                 derivations, perturbation theory, and rounding error
                 analysis, all enlivened by historical perspective and
                 informative quotations. This second edition expands and
                 updates the coverage of the first edition (1996) and
                 includes numerous improvements to the original
                 material. Two new chapters treat symmetric indefinite
                 systems and skew-symmetric systems, and nonlinear
                 systems and Newton's method. Twelve new sections
                 include coverage of additional error bounds for
                 Gaussian elimination, rank revealing $ L U $
                 factorizations, weighted and constrained least squares
                 problems, and the fused multiply-add operation found on
                 some modern computer architectures.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
  tableofcontents = "List of Figures \\
                 List of Tables \\
                 Preface to Second Edition \\
                 Preface to First Edition \\
                 About the Dedication \\
                 1: Principles of Finite Precision Computation \\
                 2: Floating Point Arithmetic \\
                 3: Basics \\
                 4: Summation \\
                 5: Polynomials \\
                 6: Norms \\
                 7: Perturbation Theory for Linear Systems \\
                 8: Triangular Systems \\
                 9: $ L U $ Factorization and Linear Equations \\
                 10: Cholesky Factorization \\
                 11: Symmetric Indefinite and Skew-Symmetric Systems \\
                 12: Iterative Refinement \\
                 13: Block LU Factorization \\
                 14: Matrix Inversion \\
                 15: Condition Number Estimation \\
                 16: The Sylvester Equation \\
                 17: Stationary Iterative Methods \\
                 18: Matrix Powers \\
                 19: QR Factorization \\
                 20: The Least Squares Problem \\
                 21: Underdetermined Systems \\
                 22: Vandermonde Systems \\
                 23: Fast Matrix Multiplication \\
                 24: The Fast Fourier Transform and Applications \\
                 25: Nonlinear Systems and Newton's Method \\
                 26: Automatic Error Analysis \\
                 27: Software Issues in Floating Point Arithmetic \\
                 28: A Gallery of Test Matrices \\
                 Appendix A: Solutions to Problems \\
                 Appendix B: Acquiring Software \\
                 Appendix C: Program Libraries \\
                 Appendix D: The Matrix Computation Toolbox \\
                 Bibliography \\
                 Name Index \\
                 Subject Index",
}

@Article{Higham:2002:CNC,
  author =       "Nicholas J. Higham",
  title =        "Computing the nearest correlation matrix---a problem
                 from finance",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "22",
  number =       "3",
  pages =        "329--343",
  month =        jul,
  year =         "2002",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/22.3.329",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65F30 (91B02)",
  MRnumber =     "MR1918653 (2003d:65037)",
  bibdate =      "Fri Oct 18 09:49:23 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 http://www3.oup.co.uk/imanum/hdb/Volume_22/Issue_03/",
  URL =          "http://www3.oup.co.uk/imanum/hdb/Volume_22/Issue_03/220329.sgm.abs.html;
                 http://www3.oup.co.uk/imanum/hdb/Volume_22/Issue_03/pdf/220329.pdf",
  abstract =     "Given a symmetric matrix, what is the nearest
                 correlation matrix that is, the nearest symmetric
                 positive semidefinite matrix with unit diagonal? This
                 problem arises in the finance industry, where the
                 correlations are between stocks. For distance measured
                 in two weighted Frobenius norms we characterize the
                 solution using convex analysis. We show how the
                 modified alternating projections method can be used to
                 compute the solution for the more commonly used of the
                 weighted Frobenius norms. In the finance application
                 the original matrix has many zero or negative
                 eigenvalues; we show that for a certain class of
                 weights the nearest correlation matrix has
                 correspondingly many zero eigenvalues and that this
                 fact can be exploited in the computation.",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "convex analysis; correlation matrix; nearness problem;
                 positive semidefinite matrix; weighted",
}

@Article{Higham:2002:DDH,
  author =       "Nicholas J. Higham and Fran{\c{c}}oise Tisseur and
                 Paul M. {Van Dooren}",
  title =        "Detecting a definite {Hermitian} pair and a hyperbolic
                 or elliptic quadratic eigenvalue problem, and
                 associated nearness problems",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "351--352",
  pages =        "455--474",
  day =          "15",
  month =        aug,
  year =         "2002",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/S0024-3795(02)00281-1",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "93B60 (15A18 93B40 93C05)",
  MRnumber =     "MR1917487 (2003f:93047)",
  MRreviewer =   "A. Barraud",
  bibdate =      "Fri Aug 9 09:25:01 MDT 2002",
  bibsource =    "http://www.elsevier.com/locate/laa;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "Fourth special issue on linear systems and control",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@TechReport{Higham:2002:MCT,
  author =       "Nicholas J. Higham",
  title =        "The {Matrix Computation Toolbox} for {MATLAB} (Version
                 1.0)",
  type =         "Numerical Analysis Report",
  number =       "410",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "19",
  month =        aug,
  year =         "2002",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  acknowledgement = ack-njh,
  created =      "2002.08.23",
  updated =      "2002.08.23",
}

@Article{Higham:2002:MPP,
  author =       "Nicholas J. Higham and Fran{\c{c}}oise Tisseur",
  title =        "More on pseudospectra for polynomial eigenvalue
                 problems and applications in control theory",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "351--352",
  pages =        "435--453",
  day =          "15",
  month =        aug,
  year =         "2002",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/S0024-3795(01)00542-0",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "93B60 (15A18 65F15)",
  MRnumber =     "MR1917486 (2003e:93035)",
  MRreviewer =   "Pablo A. Iglesias",
  bibdate =      "Fri Aug 9 09:25:01 MDT 2002",
  bibsource =    "http://www.elsevier.com/locate/laa;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "Fourth special issue on linear systems and control",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Higham:2002:RAN,
  author =       "Nicholas J. Higham",
  title =        "Review of {``Arnold Neumaier. \booktitle{Introduction
                 to Numerical Analysis}. Cambridge University Press,
                 2001''}",
  journal =      j-SIAM-REVIEW,
  volume =       "44",
  number =       "3",
  pages =        "492--493",
  month =        sep,
  year =         "2002",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/SIREAD000044000003000477000001",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-njh,
  created =      "2002.09.25",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  updated =      "2014.07.26",
}

@Article{Higham:2002:RMO,
  author =       "Nicholas J. Higham",
  title =        "Review of {``Michael Overton, \booktitle{Numerical
                 Computing with IEEE Floating Point Arithmetic:
                 Including One Theorem, One Rule of Thumb, and One
                 Hundred and One Exercises}. Society for Industrial and
                 Applied Mathematics, Philadelphia, PA, USA, 2001''}",
  journal =      j-SIAM-REVIEW,
  volume =       "44",
  number =       "2",
  pages =        "287--288",
  month =        jun,
  year =         "2002",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/SIREAD000044000002000279000001",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-njh,
  created =      "2002.07.16",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  updated =      "2014.10.13",
}

@Article{Higham:2002:SQM,
  author =       "Nicholas J. Higham and Hyun-Min Kim",
  title =        "Solving a Quadratic Matrix Equation by {Newton}'s
                 Method with Exact Line Searches",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "23",
  number =       "2",
  pages =        "303--316",
  month =        apr,
  year =         "2002",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Fri Feb 22 09:58:16 MST 2002",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/23/2;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/35097",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Tisseur:2002:SPP,
  author =       "Fran{\c{c}}oise Tisseur and Nicholas J. Higham",
  title =        "Structured Pseudospectra for Polynomial Eigenvalue
                 Problems, with Applications",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "23",
  number =       "1",
  pages =        "187--208",
  month =        jan,
  year =         "2002",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Wed Oct 23 08:36:32 MDT 2002",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/23/1;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/37145",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Bojanczyk:2003:ECI,
  author =       "Adam Bojanczyk and Nicholas J. Higham and Harikrishna
                 Patel",
  title =        "The equality constrained indefinite least squares
                 problem: theory and algorithms",
  journal =      j-BIT,
  volume =       "43",
  number =       "3",
  pages =        "505--517",
  year =         "2003",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1023/B:BITN.0000007020.58972.07",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65F20",
  MRnumber =     "MR2026712 (2004m:65049)",
  bibdate =      "Sat Apr 16 17:55:00 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT. Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Bojanczyk:2003:SIL,
  author =       "Adam Bojanczyk and Nicholas J. Higham and Harikrishna
                 Patel",
  title =        "Solving the Indefinite Least Squares Problem by
                 Hyperbolic {QR} Factorization",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "24",
  number =       "4",
  pages =        "914--931",
  month =        oct,
  year =         "2003",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/S0895479802401497",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F30 (90C20)",
  MRnumber =     "MR2003312 (2004f:65054)",
  MRreviewer =   "David Scott Watkins",
  bibdate =      "Fri Aug 15 05:16:20 MDT 2003",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/24/4;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/40149",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Davies:2003:SPA,
  author =       "Philip I. Davies and Nicholas J. Higham",
  title =        "A {Schur--Parlett} Algorithm for Computing Matrix
                 Functions",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "25",
  number =       "2",
  pages =        "464--485",
  month =        apr,
  year =         "2003",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/S0895479802410815",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F30",
  MRnumber =     "MR2047429 (2004m:65056)",
  bibdate =      "Tue Sep 30 10:28:35 MDT 2003",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/25/2;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/41081",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:2003:BEM,
  author =       "Nicholas J. Higham and Fran{\c{c}}oise Tisseur",
  title =        "Bounds for eigenvalues of matrix polynomials",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "358",
  number =       "1--3",
  pages =        "5--22",
  day =          "1",
  month =        jan,
  year =         "2003",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/S0024-3795(01)00316-0",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A42 (15A18 65F15)",
  MRnumber =     "MR1942721 (2003k:15020)",
  MRreviewer =   "Ilse C. F. Ipsen",
  bibdate =      "Mon Apr 28 07:27:21 MDT 2003",
  bibsource =    "http://www.elsevier.com/locate/laa;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "Special issue on accurate solution of eigenvalue
                 problems (Hagen, 2000)",
  URL =          "http://www.elsevier.nl/gej-ng/10/30/19/207/25/27/abstract.html;
                 http://www.sciencedirect.com/science?_ob=GatewayURL&_origin=SOCJLA&_urlversion=4&_method=citationSearch&_version=1&_piikey=S0024379501003160&_volkey=00243795%23358%235&_refkey=Higham%232003%235%2322&md5=51223bc8229cca92374c1fcdbfa6b770",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Higham:2003:CMC,
  author =       "Nicholas J. Higham and Matthew I. Smith",
  title =        "Computing the Matrix Cosine",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "34",
  number =       "1",
  pages =        "13--26",
  month =        sep,
  year =         "2003",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1023/A:1026152731904",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65F30",
  MRnumber =     "MR2015575 (2004j:65053)",
  bibdate =      "Fri Oct 24 09:37:49 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://ipsapp008.kluweronline.com/content/getfile/5058/47/2/abstract.htm;
                 http://ipsapp008.kluweronline.com/content/getfile/5058/47/2/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Higham:2003:OMP,
  author =       "Nicholas J. Higham",
  title =        "{$J$}-Orthogonal Matrices: Properties and Generation",
  journal =      j-SIAM-REVIEW,
  volume =       "45",
  number =       "3",
  pages =        "504--519",
  month =        sep,
  year =         "2003",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/S0036144502414930",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65F25 (15A23 15A57)",
  MRnumber =     "MR2046506 (2004m:65054)",
  MRreviewer =   "Ilse C. F. Ipsen",
  bibdate =      "Sat Mar 29 09:56:44 MDT 2014",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/45/3;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/41493",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@Article{Higham:2003:SPS,
  author =       "Nicholas J. Higham",
  title =        "{SIAG/LA} Prizewinners Speed Up the {$ Q R $}
                 Algorithm",
  journal =      j-SIAM-NEWS,
  volume =       "36",
  number =       "9",
  pages =        "3",
  month =        nov,
  year =         "2003",
  ISSN =         "0036-1437",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-njh,
  created =      "1994.01.01",
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
  updated =      "1994.01.01",
}

@Article{Graham:2004:UAC,
  author =       "Ivan Graham and Nicholas J. Higham",
  title =        "{UKIE} Applied\slash Computational Mathematicians
                 Greet the Year in {Sheffield}, {Manchester}",
  journal =      j-SIAM-NEWS,
  volume =       "37",
  number =       "4",
  pages =        "12",
  month =        may,
  year =         "2004",
  ISSN =         "0036-1437",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-njh,
  created =      "1994.01.01",
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
  updated =      "1994.01.01",
}

@Article{Higham:2004:CPD,
  author =       "Nicholas J. Higham and D. Steven Mackey and Niloufer
                 Mackey and Fran{\c{c}}oise Tisseur",
  title =        "Computing the Polar Decomposition and the Matrix Sign
                 Decomposition in Matrix Groups",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "25",
  number =       "4",
  pages =        "1178--1192",
  month =        oct,
  year =         "2004",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/S0895479803426644",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "15A23",
  MRnumber =     "MR2081137",
  bibdate =      "Sat Apr 16 10:32:34 MDT 2005",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/25/4;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/42664",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:2004:NSB,
  author =       "Nicholas J. Higham",
  title =        "The numerical stability of barycentric {Lagrange}
                 interpolation",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "24",
  number =       "4",
  pages =        "547--556",
  month =        oct,
  year =         "2004",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/24.4.547",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65D05",
  MRnumber =     "MR2094569 (2005e:65007)",
  bibdate =      "Fri Jul 8 07:42:09 MDT 2005",
  bibsource =    "http://imanum.oxfordjournals.org/content/vol24/issue4/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://imanum.oupjournals.org/cgi/content/abstract/24/4/547;
                 http://imanum.oupjournals.org/cgi/reprint/24/4/547",
  abstract =     "The Lagrange representation of the interpolating
                 polynomial can be rewritten in two more computationally
                 attractive forms: a modified Lagrange form and a
                 barycentric form. We give an error analysis of the
                 evaluation of the interpolating polynomial using these
                 two forms. The modified Lagrange formula is shown to be
                 backward stable. The barycentric formula has a less
                 favourable error analysis, but is forward stable for
                 any set of interpolating points with a small Lebesgue
                 constant. Therefore the barycentric formula can be
                 significantly less accurate than the modified Lagrange
                 formula only for a poor choice of interpolating points.
                 This analysis provides further weight to the argument
                 of Berrut and Trefethen that barycentric Lagrange
                 interpolation should be the polynomial interpolation
                 method of choice.",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@Article{Bini:2005:AMR,
  author =       "Dario A. Bini and Nicholas J. Higham and Beatrice
                 Meini",
  title =        "Algorithms for the matrix $p$ th root",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "39",
  number =       "4",
  pages =        "349--378",
  month =        aug,
  year =         "2005",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-004-6709-8",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65F30",
  MRnumber =     "MR2134331 (2005m:65094)",
  MRreviewer =   "Jin Yun Yuan",
  bibdate =      "Sat May 14 09:10:05 MDT 2005",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=1017-1398;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@InProceedings{Davies:2005:CMF,
  author =       "Philip I. Davies and Nicholas J. Higham",
  editor =       "Artan Bori{\c{c}i} and others",
  booktitle =    "{QCD and numerical analysis III. Proceedings of the
                 third international workshop on numerical analysis and
                 lattice QCD, Edinburgh, UK, June 30--July 4, 2003}",
  title =        "Computing $ f({A})b $ for matrix functions $f$",
  volume =       "47",
  publisher =    pub-SPRINGER,
  address =      pub-SPRINGER:adr-NY,
  pages =        "15--24",
  year =         "2005",
  DOI =          "https://doi.org/10.1007/3-540-28504-0_2",
  MRclass =      "65F30 (15A99)",
  MRnumber =     "MR2180116",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  series =       "Lecture Notes in Computational Science and
                 Engineering",
  ZMnumber =     "1117.65319",
  abstract =     "For matrix functions $f$ we investigate how to compute
                 a matrix-vector product $ f(A)b $ without explicitly
                 computing $ f(A) $. A general method is described that
                 applies quadrature to the matrix version of the Cauchy
                 integral theorem. Methods specific to the logarithm,
                 based on quadrature, and fractional matrix powers,
                 based on solution of an ordinary differential equation
                 initial value problem, are also presented.",
  acknowledgement = ack-nhfb,
  classmath =    "65F30 (Other matrix algorithms); 15A54 (Matrices over
                 function rings)",
  keywords =     "Cauchy integral theorem; fractional matrix powers;
                 logarithm; matrix functions; matrix-vector product;
                 quadrature",
}

@Article{Hargreaves:2005:EAM,
  author =       "Gareth I. Hargreaves and Nicholas J. Higham",
  title =        "Efficient algorithms for the matrix cosine and sine",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "40",
  number =       "4",
  pages =        "383--400",
  year =         "2005",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-005-8141-0",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65F30",
  MRnumber =     "MR2191973 (2006h:65066)",
  bibdate =      "Wed May 19 16:29:32 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Higham:2005:BRS,
  author =       "Nicholas J. Higham",
  title =        "Book Review: {The SIAM 100-Digit Challenge: A Study in
                 High-Accuracy Numerical Computing. By Folkmar
                 Bornemann, Dirk Laurie, Stan Wagon, and J{\"o}rg
                 Waldvogel. SIAM, Philadelphia, 2004. \$57.00. xii + 306
                 pp., hardcover. ISBN 0-89871-561-X}",
  journal =      j-SIAM-REVIEW,
  volume =       "47",
  number =       "2",
  pages =        "382--383",
  month =        jun,
  year =         "2005",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri May 27 14:40:10 MDT 2005",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/47/2;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/97149",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@Article{Higham:2005:FPM,
  author =       "Nicholas J. Higham and D. Steven Mackey and Niloufer
                 Mackey and Fran{\c{c}}oise Tisseur",
  title =        "Functions Preserving Matrix Groups and Iterations for
                 the Matrix Square Root",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "26",
  number =       "3",
  pages =        "849--877",
  month =        jul,
  year =         "2005",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/S0895479804442218",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Sat Apr 16 10:32:41 MDT 2005",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/26/3;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/44221",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@TechReport{Higham:2005:IPLa,
  author =       "Nicholas J. Higham",
  title =        "An Interview with {Peter Lancaster}",
  type =         "Numerical Analysis Report",
  number =       "468",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  pages =        "10",
  month =        jun,
  year =         "2005",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-njh,
  created =      "2005.06.01",
  updated =      "2005.06.01",
}

@Article{Higham:2005:IPLb,
  author =       "Nicholas J. Higham",
  title =        "An Interview with {Peter Lancaster}",
  journal =      j-SIAM-NEWS,
  volume =       "38",
  number =       "6",
  pages =        "5--6",
  month =        jul # "/" # aug,
  year =         "2005",
  ISSN =         "0036-1437",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-njh,
  created =      "2005.08.12",
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
  updated =      "2005.08.12",
}

@Book{Higham:2005:MG,
  author =       "Desmond J. Higham and Nicholas J. Higham",
  title =        "{MATLAB} guide",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  edition =      "Second",
  pages =        "xxiv + 382",
  year =         "2005",
  ISBN =         "0-89871-578-4",
  ISBN-13 =      "978-0-89871-578-1",
  LCCN =         "QA297 .H5217 2005",
  MRclass =      "65-00 (00A20)",
  MRnumber =     "MR2135945",
  bibdate =      "Wed May 19 16:25:33 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
}

@Article{Higham:2005:SSM,
  author =       "Nicholas J. Higham",
  title =        "The Scaling and Squaring Method for the Matrix
                 Exponential Revisited",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "26",
  number =       "4",
  pages =        "1179--1193",
  month =        oct,
  year =         "2005",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/04061101X",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Thu Dec 29 16:33:50 MST 2005",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/26/4;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/61101",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Guo:2006:SNM,
  author =       "Chun-Hua Guo and Nicholas J. Higham",
  title =        "A {Schur--Newton} Method for the Matrix {\boldmath
                 $p$}th Root and its Inverse",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "28",
  number =       "3",
  pages =        "788--804",
  month =        jan,
  year =         "2006",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/050643374",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F30",
  MRnumber =     "MR2262981 (2007k:65071)",
  bibdate =      "Tue May 18 22:32:12 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:2006:CLM,
  author =       "Nicholas J. Higham and D. Steven Mackey and
                 Fran{\c{c}}oise Tisseur",
  title =        "The Conditioning of Linearizations of Matrix
                 Polynomials",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "28",
  number =       "4",
  pages =        "1005--1028",
  month =        jan,
  year =         "2006",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/050628283",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F15 (15A18)",
  MRnumber =     "MR2276551 (2008c:65103)",
  MRreviewer =   "Marc Van Barel",
  bibdate =      "Tue May 18 22:32:14 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:2006:RAJ,
  author =       "Nicholas J. Higham",
  title =        "Review of {``Alan J. Laub. \booktitle{Matrix Analysis
                 for Scientists and Engineers}''}",
  journal =      j-SIAM-REVIEW,
  volume =       "48",
  number =       "1",
  pages =        "170--171",
  month =        mar,
  year =         "2006",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/SIREAD000048000001000149000001",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Tue Feb 28 12:58:46 GMT 2006",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-njh,
  created =      "2006.02.28",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  updated =      "2014.07.26",
}

@Article{Higham:2006:RMC,
  author =       "Nicholas J. Higham",
  title =        "Review of {``Moody T. Chu and Gene H. Golub.
                 \booktitle{Inverse Eigenvalue Problems: Theory,
                 Algorithms, and Applications}''}",
  journal =      j-J-FLUID-MECH,
  volume =       "556",
  pages =        "442--443",
  year =         "2006",
  CODEN =        "JFLSA7",
  ISSN =         "0022-1120 (print), 1469-7645 (electronic)",
  ISSN-L =       "0022-1120",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  created =      "2006.05.11",
  fjournal =     "Journal of Fluid Mechanics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=FLM",
  updated =      "2006.05.11",
}

@Article{Higham:2006:SLM,
  author =       "Nicholas J. Higham and D. Steven Mackey and Niloufer
                 Mackey and Fran{\c{c}}oise Tisseur",
  title =        "Symmetric linearizations for matrix polynomials",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "29",
  number =       "1",
  pages =        "143--159",
  year =         "2006/2007",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/050646202",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F15 (15A18 15A22 93C05)",
  MRnumber =     "MR2288018 (2008e:65123)",
  MRreviewer =   "Rafikul Alam",
  bibdate =      "Wed May 19 16:25:33 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@InProceedings{Corless:2007:SEA,
  author =       "Robert M. Corless and Hui Ding and Nicholas J. Higham
                 and David J. Jeffrey",
  title =        "The solution of $ s \exp (s) = a $ is not always the
                 {Lambert} $ {W} $ function of $a$",
  crossref =     "Brown:2007:PIS",
  pages =        "116--121",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277565",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We study the solutions of the matrix equation $ S \exp
                 (S) = A $. Our motivation comes from the study of
                 systems of delay differential equations $ y'(t) = A y(t
                 - 1) $, which occur in some models of practical
                 interest, especially in mathematical biology. This
                 paper concentrates on the distinction between
                 evaluating a matrix function and solving a matrix
                 equation. In particular, it shows that the matrix
                 Lambert $W$ function evaluated at the matrix $A$ does
                 not represent all possible solutions of $ S \exp (S) =
                 A$. These results can easily be extended to more
                 general matrix equations.",
  acknowledgement = ack-nhfb,
  keywords =     "Lambert $W$ function; matrix function; nonlinear
                 matrix equation",
}

@Article{Guo:2007:ISN,
  author =       "Chun-Hua Guo and Nicholas J. Higham",
  title =        "Iterative Solution of a Nonsymmetric Algebraic
                 {Riccati} Equation",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "29",
  number =       "2",
  pages =        "396--412",
  month =        "????",
  year =         "2007",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/050647669",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "15A24 (15A48 65F30)",
  MRnumber =     "MR2318355 (2008b:15046)",
  MRreviewer =   "Ma. Isabel Garc{\'\i}a-Planas",
  bibdate =      "Tue May 18 22:32:18 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:2007:BEP,
  author =       "Nicholas J. Higham and Ren-Cang Li and Fran{\c{c}}oise
                 Tisseur",
  title =        "Backward error of polynomial eigenproblems solved by
                 linearization",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "29",
  number =       "4",
  pages =        "1218--1241",
  year =         "2007",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/060663738",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F15 (15A18)",
  MRnumber =     "MR2369292 (2009a:65092)",
  MRreviewer =   "Jens-Peter M. Zemke",
  bibdate =      "Wed May 19 16:25:33 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@InCollection{Higham:2007:FM,
  author =       "Nicholas J. Higham",
  title =        "Functions of matrices",
  crossref =     "Hogben:2007:HLA",
  pages =        "??--??",
  year =         "2007",
  bibdate =      "Mon Aug 23 07:45:17 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Higham:2007:MFA,
  author =       "Nicholas J. Higham",
  title =        "Matrix Factorizations and Applications: Commentary",
  crossref =     "Chan:2007:MMC",
  pages =        "??--??",
  year =         "2007",
  bibdate =      "Sat Apr 07 11:25:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
}

@Article{Higham:2007:RLT,
  author =       "Nicholas J. Higham",
  title =        "Review of {``Lloyd N. Trefethen and Mark Embree.
                 \booktitle{Spectra and Pseudospectra: The Behavior of
                 Nonnormal Matrices and Operators}''}",
  journal =      j-BULL-AMS,
  volume =       "44",
  number =       "2",
  pages =        "277--284",
  year =         "2007",
  CODEN =        "BAMOAD",
  ISSN =         "0002-9904 (print), 1936-881X (electronic)",
  ISSN-L =       "0002-9904",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  created =      "2007.03.21",
  fjournal =     "Bulletin of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/bull/",
  updated =      "2007.03.21",
}

@Article{Higham:2007:SLM,
  author =       "Nicholas J. Higham and D. Steven Mackey and Niloufer
                 Mackey and Fran{\c{c}}oise Tisseur",
  title =        "Symmetric Linearizations for Matrix Polynomials",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "29",
  number =       "1",
  pages =        "143--159",
  month =        "????",
  year =         "2007",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/050646202",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Tue May 18 22:32:16 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Al-Mohy:2008:CFD,
  author =       "Awad H. Al-Mohy and Nicholas J. Higham",
  title =        "Computing the {Fr{\'e}chet} derivative of the matrix
                 exponential, with an application to condition number
                 estimation",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "30",
  number =       "4",
  pages =        "1639--1657",
  year =         "2008",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/080716426",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F30 (65F35)",
  MRnumber =     "MR2486857 (2009m:65071)",
  MRreviewer =   "Dario Fasino",
  bibdate =      "Wed May 19 16:25:33 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Guo:2008:DSH,
  author =       "Chun-Hua Guo and Nicholas J. Higham and
                 Fran{\c{c}}oise Tisseur",
  title =        "Detecting and solving hyperbolic quadratic eigenvalue
                 problems",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "30",
  number =       "4",
  pages =        "1593--1613",
  year =         "2008",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/070704058",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "15A18 (15A24 65F30 65H17)",
  MRnumber =     "MR2486855 (2010b:15021)",
  MRreviewer =   "Mihai Cipu",
  bibdate =      "Wed May 19 16:25:33 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Hale:2008:CRM,
  author =       "Nicholas Hale and Nicholas J. Higham and Lloyd N.
                 Trefethen",
  title =        "Computing {$ {\bf A}^\alpha, \ \log ({\bf A}) $}, and
                 related matrix functions by contour integrals",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "46",
  number =       "5",
  pages =        "2505--2523",
  year =         "2008",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/070700607",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65F30",
  MRnumber =     "MR2421045 (2009e:65071)",
  MRreviewer =   "Raffaella Pavani",
  bibdate =      "Wed May 19 16:25:33 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}

@Article{Higham:2008:BEP,
  author =       "Nicholas J. Higham and Ren-Cang Li and Fran{\c{c}}oise
                 Tisseur",
  title =        "Backward Error of Polynomial Eigenproblems Solved by
                 Linearization",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "29",
  number =       "4",
  pages =        "1218--1241",
  month =        "????",
  year =         "2008",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/060663738",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Tue May 18 22:32:22 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:2008:CSE,
  author =       "Nicholas J. Higham",
  title =        "{Cayley}, {Sylvester}, and early matrix theory",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "428",
  number =       "1",
  pages =        "39--43",
  year =         "2008",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2007.10.004",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15-03 (01A55)",
  MRnumber =     "MR2372584",
  bibdate =      "Wed May 19 16:25:33 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Book{Higham:2008:FMT,
  author =       "Nicholas J. Higham",
  title =        "Functions of Matrices: Theory and Computation",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xx + 425",
  year =         "2008",
  DOI =          "https://doi.org/10.1137/1.9780898717778",
  ISBN =         "0-89871-646-2",
  ISBN-13 =      "978-0-89871-646-7",
  MRclass =      "15-02 (93B40 93C05)",
  MRnumber =     "MR2396439 (2009b:15001)",
  MRreviewer =   "Daniel Kressner",
  bibdate =      "Wed May 19 16:25:33 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2000.bib",
  note =         "Theory and computation",
  acknowledgement = ack-nhfb,
}

@Article{Higham:2008:HOW,
  author =       "Nicholas J. Higham",
  title =        "In His Own Words [Interview with {Gene Golub}]",
  journal =      j-SIAM-NEWS,
  volume =       "41",
  number =       "1",
  pages =        "3",
  month =        jan # "/" # feb,
  year =         "2008",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "Extracts from \cite{high08-ghg}.",
  URL =          "https://www.siam.org/news/news.php?id=1290",
  acknowledgement = ack-njh,
  created =      "2013.11.28",
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
  updated =      "2013.11.28",
}

@TechReport{Higham:2008:IGG,
  author =       "Nicholas J. Higham",
  title =        "An Interview with {Gene Golub}",
  type =         "{MIMS EPrint}",
  number =       "2008.8",
  institution =  inst-MIMS,
  address =      inst-MIMS:adr,
  pages =        "13",
  month =        feb,
  year =         "2008",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-njh,
  created =      "2008.02.10",
  updated =      "2008.02.10",
}

@Misc{Higham:2008:MFT,
  author =       "Nicholas J. Higham",
  title =        "The {Matrix Function Toolbox}",
  year =         "2008",
  bibdate =      "Wed Sep 9 08:03:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://www.maths.manchester.ac.uk/~higham/mftoolbox",
  acknowledgement = ack-njh,
  created =      "2008.01.10",
  updated =      "2013.12.03",
}

@Article{Higham:2008:SSS,
  author =       "Nicholas J. Higham and D. Steven Mackey and
                 Fran{\c{c}}oise Tisseur and Seamus D. Garvey",
  title =        "Scaling, sensitivity and stability in the numerical
                 solution of quadratic eigenvalue problems",
  journal =      j-INT-J-NUMER-METHODS-ENG,
  volume =       "73",
  number =       "3",
  pages =        "344--360",
  year =         "2008",
  CODEN =        "IJNMBH",
  DOI =          "https://doi.org/10.1002/nme.2076",
  ISSN =         "0029-5981 (print), 1097-0207 (electronic)",
  ISSN-L =       "0029-5981",
  MRclass =      "65N25 (65F15 65H17 74H45 74K05)",
  MRnumber =     "MR2382048 (2009c:65288)",
  MRreviewer =   "Gh. Adam",
  bibdate =      "Wed May 19 16:25:33 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal for Numerical Methods in
                 Engineering",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
}

@Article{Al-Mohy:2009:CFD,
  author =       "Awad H. Al-Mohy and Nicholas J. Higham",
  title =        "Computing the {Fr{\'e}chet} Derivative of the Matrix
                 Exponential, with an Application to Condition Number
                 Estimation",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "30",
  number =       "4",
  pages =        "1639--1657",
  month =        "????",
  year =         "2009",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/080716426",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Tue May 18 22:32:31 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Al-Mohy:2009:NSS,
  author =       "Awad H. Al-Mohy and Nicholas J. Higham",
  title =        "A new scaling and squaring algorithm for the matrix
                 exponential",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "31",
  number =       "3",
  pages =        "970--989",
  year =         "2009",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/09074721X",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "15A16",
  MRnumber =     "MR2538661",
  bibdate =      "Wed May 19 16:25:33 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Guo:2009:DSH,
  author =       "Chun-Hua Guo and Nicholas J. Higham and
                 Fran{\c{c}}oise Tisseur",
  title =        "Detecting and Solving Hyperbolic Quadratic Eigenvalue
                 Problems",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "30",
  number =       "4",
  pages =        "1593--1613",
  month =        "????",
  year =         "2009",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/070704058",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Tue May 18 22:32:31 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Guo:2009:IAA,
  author =       "Chun-Hua Guo and Nicholas J. Higham and
                 Fran{\c{c}}oise Tisseur",
  title =        "An improved arc algorithm for detecting definite
                 {Hermitian} pairs",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "31",
  number =       "3",
  pages =        "1131--1151",
  year =         "2009",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/08074218X",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "15A18 (65F18)",
  MRnumber =     "MR2558816",
  bibdate =      "Wed May 19 16:25:33 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:2009:CGP,
  author =       "Nicholas J. Higham and Christian Mehl and
                 Fran{\c{c}}oise Tisseur",
  title =        "The canonical generalized polar decomposition",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "31",
  number =       "4",
  pages =        "2163--2180",
  year =         "2009/10",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/090765018",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "15A23",
  MRnumber =     "2678962 (2011i:15018)",
  MRreviewer =   "Marek Niezgoda",
  bibdate =      "Thu Mar 6 09:16:29 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:2009:DMP,
  author =       "Nicholas J. Higham and D. Steven Mackey and
                 Fran{\c{c}}oise Tisseur",
  title =        "Definite Matrix Polynomials and their Linearization by
                 Definite Pencils",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "31",
  number =       "2",
  pages =        "478--502",
  month =        "????",
  year =         "2009",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/080721406",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F15 (15A18)",
  MRnumber =     "MR2530260",
  MRreviewer =   "Miloud Sadkane",
  bibdate =      "Tue May 18 22:32:35 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:2009:SSM,
  author =       "Nicholas J. Higham",
  title =        "The Scaling and Squaring Method for the Matrix
                 Exponential Revisited",
  journal =      j-SIAM-REVIEW,
  volume =       "51",
  number =       "4",
  pages =        "747--764",
  month =        "????",
  year =         "2009",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/090768539",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65F60 (15A16)",
  MRnumber =     "MR2563832",
  bibdate =      "Mon May 17 17:56:49 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/51/4;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@Article{Trefethen:2009:DHP,
  author =       "Anne Trefethen and Nick Higham and Iain Duff and Peter
                 Coveney",
  title =        "Developing a High-Performance Computing\slash
                 Numerical Analysis Roadmap",
  journal =      j-IJHPCA,
  volume =       "23",
  number =       "4",
  pages =        "423--426",
  month =        nov,
  year =         "2009",
  CODEN =        "IHPCFL",
  DOI =          "https://doi.org/10.1177/1094342009347710",
  ISSN =         "1094-3420 (print), 1741-2846 (electronic)",
  ISSN-L =       "1094-3420",
  bibdate =      "Tue Aug 31 09:59:45 MDT 2010",
  bibsource =    "http://hpc.sagepub.com/content/23/4.toc;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://hpc.sagepub.com/content/23/4/423.full.pdf+html",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://hpc.sagepub.com/content/by/year",
}

@Article{Al-Mohy:2010:CSA,
  author =       "Awad H. Al-Mohy and Nicholas J. Higham",
  title =        "The complex step approximation to the {Fr{\'e}chet}
                 derivative of a matrix function",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "53",
  number =       "1",
  pages =        "133--148",
  month =        jan,
  year =         "2010",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-009-9323-y",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65F60",
  MRnumber =     "MR2566131",
  bibdate =      "Wed May 19 16:25:33 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=53&issue=1&spage=133",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Al-Mohy:2010:NSS,
  author =       "Awad H. Al-Mohy and Nicholas J. Higham",
  title =        "A New Scaling and Squaring Algorithm for the Matrix
                 Exponential",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "31",
  number =       "3",
  pages =        "970--989",
  month =        "????",
  year =         "2010",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/09074721X",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Tue May 18 22:32:37 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Borsdorf:2010:CNC,
  author =       "R{\"u}diger Borsdorf and Nicholas J. Higham and Marcos
                 Raydan",
  title =        "Computing a Nearest Correlation Matrix with Factor
                 Structure",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "31",
  number =       "5",
  pages =        "2603--2622",
  month =        "????",
  year =         "2010",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/090776718",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F30 (62H25 90C30 90C52)",
  MRnumber =     "2740623 (2011k:65061)",
  MRreviewer =   "Anders Linn{\'e}r",
  bibdate =      "Sun Nov 28 22:55:40 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/31/5;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Borsdorf:2010:PNA,
  author =       "R{\"u}diger Borsdorf and Nicholas J. Higham",
  title =        "A preconditioned {Newton} algorithm for the nearest
                 correlation matrix",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "30",
  number =       "1",
  pages =        "94--107",
  month =        jan,
  year =         "2010",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/drn085",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65F20 (62H20 65F25 65H10)",
  MRnumber =     "MR2580548",
  bibdate =      "Wed May 19 16:25:33 2010",
  bibsource =    "http://imanum.oxfordjournals.org/content/vol30/issue1/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://imajna.oxfordjournals.org/cgi/content/abstract/30/1/94;
                 http://imajna.oxfordjournals.org/cgi/reprint/30/1/94",
  abstract =     "Various methods have been developed for computing the
                 correlation matrix nearest in the Frobenius norm to a
                 given matrix. We focus on a quadratically convergent
                 Newton algorithm recently derived by Qi and Sun.
                 Various improvements to the efficiency and reliability
                 of the algorithm are introduced. Several of these
                 relate to the linear algebra: the Newton equations are
                 solved by minres instead of the conjugate gradient
                 method, as it more quickly satisfies the inexact Newton
                 condition; we apply a Jacobi preconditioner, which can
                 be computed efficiently even though the coefficient
                 matrix is not explicitly available; an efficient choice
                 of eigensolver is identified; and a final scaling step
                 is introduced to ensure that the returned matrix has
                 unit diagonal. Potential difficulties caused by
                 rounding errors in the Armijo line search are avoided
                 by altering the step selection strategy. These and
                 other improvements lead to a significant speed-up over
                 the original algorithm and allow the solution of
                 problems of dimension a few thousand in a few tens of
                 minutes.",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@Article{Guo:2010:IAA,
  author =       "Chun-Hua Guo and Nicholas J. Higham and
                 Fran{\c{c}}oise Tisseur",
  title =        "An Improved Arc Algorithm for Detecting Definite
                 {Hermitian} Pairs",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "31",
  number =       "3",
  pages =        "1131--1151",
  month =        "????",
  year =         "2010",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/08074218X",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Tue May 18 22:32:37 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:2010:CGP,
  author =       "Nicholas J. Higham and Christian Mehl and
                 Fran{\c{c}}oise Tisseur",
  title =        "The Canonical Generalized Polar Decomposition",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "31",
  number =       "4",
  pages =        "2163--2180",
  month =        "????",
  year =         "2010",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/090765018",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "15A23",
  MRnumber =     "2678962 (2011i:15018)",
  MRreviewer =   "Marek Niezgoda",
  bibdate =      "Sun Nov 28 22:55:37 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/31/4;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Higham:2010:CMF,
  author =       "Nicholas J. Higham and Awad H. Al-Mohy",
  title =        "Computing matrix functions",
  journal =      j-ACTA-NUMERICA,
  volume =       "19",
  pages =        "159--208",
  year =         "2010",
  CODEN =        "ANUMFU",
  DOI =          "https://doi.org/10.1017/S0962492910000036",
  ISBN =         "0-521-19284-6",
  ISBN-13 =      "978-0-521-19284-2",
  ISSN =         "0962-4929 (print), 1474-0508 (electronic)",
  ISSN-L =       "0962-4929",
  MRclass =      "65F60 (15A16)",
  MRnumber =     "2652782 (2011g:65073)",
  MRreviewer =   "Olexander S. Babanin",
  bibdate =      "Sat Sep 24 10:35:17 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Acta Numer.",
  fjournal =     "Acta Numerica",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANU",
  onlinedate =   "10 May 2010",
}

@Article{Al-Mohy:2011:CAM,
  author =       "Awad H. Al-Mohy and Nicholas J. Higham",
  title =        "Computing the Action of the Matrix Exponential, with
                 an Application to Exponential Integrators",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "33",
  number =       "2",
  pages =        "488--511",
  month =        "????",
  year =         "2011",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/100788860",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F60 (65P10)",
  MRnumber =     "2785959 (2012d:65082)",
  MRreviewer =   "Ross A. Lippert",
  bibdate =      "Fri Mar 4 09:58:54 MST 2011",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/33/2;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2015.bib",
  note =         "See \cite{Fischer:2017:AAM}.",
  URL =          "http://epubs.siam.org/sisc/resource/1/sjoce3/v33/i2/p488_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "March 01, 2011",
}

@Article{Grammont:2011:FAN,
  author =       "Laurence Grammont and Nicholas J. Higham and
                 Fran{\c{c}}oise Tisseur",
  title =        "A framework for analyzing nonlinear eigenproblems and
                 parametrized linear systems",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "435",
  number =       "3",
  pages =        "623--640",
  day =          "1",
  month =        aug,
  year =         "2011",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2009.12.038",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A18 (65F15 65F35)",
  MRnumber =     "2794594 (2012d:15022)",
  MRreviewer =   "Ilse C. F. Ipsen",
  bibdate =      "Mon Jun 13 18:34:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Higham:2011:RSM,
  author =       "Nicholas J. Higham and Lijing Lin",
  title =        "On $p$-th roots of stochastic matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "435",
  number =       "3",
  pages =        "448--463",
  day =          "1",
  month =        aug,
  year =         "2011",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2010.04.007",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15B51 (15A16 15B48 60J10)",
  MRnumber =     "2794585 (2012d:15062)",
  MRreviewer =   "Adolf Rhodius",
  bibdate =      "Sat Mar 23 18:05:45 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Higham:2011:SPA,
  author =       "Nicholas J. Higham and Lijing Lin",
  title =        "A {Schur--Pad{\'e}} Algorithm for Fractional Powers of
                 a Matrix",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "32",
  number =       "3",
  pages =        "1056--1078",
  month =        "????",
  year =         "2011",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/10081232X",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F60",
  MRnumber =     "2837592",
  MRreviewer =   "Jorge Sastre",
  bibdate =      "Thu Feb 9 08:15:43 MST 2012",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/32/3;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "September 29, 2011",
}

@Article{Al-Mohy:2012:IIS,
  author =       "Awad H. Al-Mohy and Nicholas J. Higham",
  title =        "Improved Inverse Scaling and Squaring Algorithms for
                 the Matrix Logarithm",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "34",
  number =       "4",
  pages =        "C153--C169",
  year =         "2012",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/110852553",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F30",
  MRnumber =     "2970418",
  bibdate =      "Tue Oct 30 14:49:05 MDT 2012",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/34/4;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2012",
}

@Article{Nakatsukasa:2012:BSI,
  author =       "Yuji Nakatsukasa and Nicholas J. Higham",
  title =        "Backward Stability of Iterations for Computing the
                 Polar Decomposition",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "33",
  number =       "2",
  pages =        "460--479",
  month =        "????",
  year =         "2012",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/110857544",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F30 (15A23 65F20 65F25 65F35 65G50)",
  MRnumber =     "2970215",
  MRreviewer =   "Ilse C. F. Ipsen",
  bibdate =      "Tue Oct 30 14:04:27 MDT 2012",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/33/2;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2012",
}

@Article{Al-Mohy:2013:CFD,
  author =       "Awad H. Al-Mohy and Nicholas J. Higham and Samuel D.
                 Relton",
  title =        "Computing the {Fr{\'e}chet} derivative of the matrix
                 logarithm and estimating the condition number",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "35",
  number =       "4",
  pages =        "C394--C410",
  year =         "2013",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/120885991",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F60 (65F35)",
  MRnumber =     "3080997",
  bibdate =      "Thu Mar 6 09:16:29 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@Article{Betcke:2013:NCN,
  author =       "Timo Betcke and Nicholas J. Higham and Volker Mehrmann
                 and Christian Schr{\"o}der and Fran{\c{c}}oise
                 Tisseur",
  title =        "{NLEVP}: a collection of nonlinear eigenvalue
                 problems",
  journal =      j-TOMS,
  volume =       "39",
  number =       "2",
  pages =        "Art. 7, 28",
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2427023.2427024",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H17 (65F10 65Y15)",
  MRnumber =     "3031626",
  bibdate =      "Thu Mar 6 09:16:29 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Dingle:2013:RIT,
  author =       "Nicholas J. Dingle and Nicholas J. Higham",
  title =        "Reducing the influence of tiny normwise relative
                 errors on performance profiles",
  journal =      j-TOMS,
  volume =       "39",
  number =       "4",
  pages =        "24:1--24:11",
  month =        jul,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2491491.2491494",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F35 (65G50 65Y20)",
  MRnumber =     "3092099",
  MRreviewer =   "Dario Fasino",
  bibdate =      "Fri Jul 19 17:20:56 MDT 2013",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "It is a widespread but little-noticed phenomenon that
                 the normwise relative error $ || x - y || / || x || $
                 of vectors $x$ and $y$ of floating point numbers of the
                 same precision, where $y$ is an approximation to x, can
                 be many orders of magnitude smaller than the unit
                 roundoff. We analyze this phenomenon and show that in
                 the $ \infty $-norm it happens precisely when $x$ has
                 components of widely varying magnitude and every
                 component of $x$ of largest magnitude agrees with the
                 corresponding component of $y$. Performance profiles
                 are a popular way to compare competing algorithms
                 according to particular measures of performance. We
                 show that performance profiles based on normwise
                 relative errors can give a misleading impression due to
                 the influence of zero or tiny normwise relative errors.
                 We propose a transformation that reduces the influence
                 of these extreme errors in a controlled manner, while
                 preserving the monotonicity of the underlying data and
                 leaving the performance profile unchanged at its left
                 end-point. Numerical examples with both artificial and
                 genuine data illustrate the benefits of the
                 transformation.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Higham:2013:ISP,
  author =       "Nicholas J. Higham and Lijing Lin",
  title =        "An improved {Schur--Pad{\'e}} algorithm for fractional
                 powers of a matrix and their {Fr{\'e}chet}
                 derivatives",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "34",
  number =       "3",
  pages =        "1341--1360",
  month =        "????",
  year =         "2013",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/130906118",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F60 (15A16)",
  MRnumber =     "3102571",
  bibdate =      "Tue Feb 11 12:44:41 MST 2014",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/34/3;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2013",
}

@Article{Nakatsukasa:2013:SES,
  author =       "Yuji Nakatsukasa and Nicholas J. Higham",
  title =        "Stable and Efficient Spectral Divide and Conquer
                 Algorithms for the Symmetric Eigenvalue Decomposition
                 and the {SVD}",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "35",
  number =       "3",
  pages =        "A1325--A1349",
  month =        "????",
  year =         "2013",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/120876605",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F15",
  MRnumber =     "3054594",
  MRreviewer =   "Fatemeh Panjeh Ali Beik",
  bibdate =      "Fri Jul 19 07:43:53 MDT 2013",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/35/3;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  note =         "See \cite{Sukkari:2019:QBS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2013",
}

@Article{Aprahamian:2014:MUF,
  author =       "Mary Aprahamian and Nicholas J. Higham",
  title =        "The matrix unwinding function, with an application to
                 computing the matrix exponential",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "35",
  number =       "1",
  pages =        "88--109",
  month =        "????",
  year =         "2014",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/130920137",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F30 (15A24 65F60)",
  MRnumber =     "3159979",
  MRreviewer =   "Petko Petkov",
  bibdate =      "Mon Mar 31 06:45:43 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2014",
}

@Article{Bethune:2014:PAA,
  author =       "Iain Bethune and J. Mark Bull and Nicholas J. Dingle
                 and Nicholas J. Higham",
  title =        "Performance analysis of asynchronous {Jacobi}'s method
                 implemented in {MPI}, {SHMEM} and {OpenMP}",
  journal =      j-IJHPCA,
  volume =       "28",
  number =       "1",
  pages =        "97--111",
  month =        feb,
  year =         "2014",
  CODEN =        "IHPCFL",
  DOI =          "https://doi.org/10.1177/1094342013493123",
  ISSN =         "1094-3420 (print), 1741-2846 (electronic)",
  ISSN-L =       "1094-3420",
  bibdate =      "Fri Mar 14 15:39:59 MDT 2014",
  bibsource =    "http://hpc.sagepub.com/content/28/1.toc;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijsa.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib",
  URL =          "http://hpc.sagepub.com/content/28/1/97.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of High Performance Computing
                 Applications",
  journal-URL =  "http://hpc.sagepub.com/content/by/year",
  onlinedate =   "July 11, 2013",
}

@Article{Higham:2014:ECN,
  author =       "Nicholas J. Higham and Samuel D. Relton",
  title =        "Estimating the condition number of the {Fr{\'e}chet}
                 derivative of a matrix function",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "36",
  number =       "6",
  pages =        "C617--C634",
  year =         "2014",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/130950082",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F35 (65F60)",
  MRnumber =     "3281285",
  MRreviewer =   "A. Bultheel",
  bibdate =      "Wed Sep 9 06:09:29 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  ZMnumber =     "06409885",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@Article{Higham:2014:HOF,
  author =       "Nicholas J. Higham and Samuel D. Relton",
  title =        "Higher Order {Fr{\'e}chet} Derivatives of Matrix
                 Functions and the Level-$2$ Condition Number",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "35",
  number =       "3",
  pages =        "1019--1037",
  month =        "????",
  year =         "2014",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/130945259",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F35 (15A16 65F60)",
  MRnumber =     "3233937",
  MRreviewer =   "Boyan G. Zlatanov",
  bibdate =      "Sat Sep 13 12:06:59 MDT 2014",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/35/3;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2014",
}

@Article{Higham:2014:SIA,
  author =       "Nicholas J. Higham",
  title =        "{Sylvester}'s influence on applied mathematics",
  journal =      j-MATH-TODAY,
  volume =       "50",
  number =       "4",
  pages =        "202--206",
  year =         "2014",
  ISSN =         "1361-2042",
  ISSN-L =       "1361-2042",
  MRclass =      "01A70",
  MRnumber =     "3241571",
  bibdate =      "Wed Sep 9 06:09:29 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Today",
  journal-URL =  "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
}

@Article{Lin:2014:CSR,
  author =       "Lijing Lin and Nicholas J. Higham and Jianxin Pan",
  title =        "Covariance structure regularization via entropy loss
                 function",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "72",
  pages =        "315--327",
  year =         "2014",
  CODEN =        "CSDADW",
  DOI =          "https://doi.org/10.1016/j.csda.2013.10.004",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  MRclass =      "Preliminary Data",
  MRnumber =     "3139365",
  bibdate =      "Thu Mar 6 09:16:29 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
}

@Article{Al-Mohy:2015:NAC,
  author =       "Awad H. Al-Mohy and Nicholas J. Higham and Samuel D.
                 Relton",
  title =        "New algorithms for computing the matrix sine and
                 cosine separately or simultaneously",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "37",
  number =       "1",
  pages =        "A456--A487",
  year =         "2015",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/140973979",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F60",
  MRnumber =     "3311875",
  MRreviewer =   "Petko Petkov",
  bibdate =      "Wed Sep 9 06:09:29 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  ZMnumber =     "1315.65045",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@Article{Fasi:2015:AML,
  author =       "Massimiliano Fasi and Nicholas J. Higham and Bruno
                 Iannazzo",
  title =        "An algorithm for the matrix {Lambert} {$W$} function",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "36",
  number =       "2",
  pages =        "669--685",
  month =        "????",
  year =         "2015",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/140997610",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F60 (15A15)",
  MRnumber =     "3354997",
  MRreviewer =   "Thomas Mach",
  bibdate =      "Fri Aug 7 16:43:51 MDT 2015",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/36/2;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  ZMnumber =     "1317.65116",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2015",
}

@Misc{Higham:2015:MCT,
  author =       "Nicholas J. Higham",
  title =        "Matrix Computation Toolbox",
  howpublished = "Web site.",
  year =         "2015",
  bibdate =      "Sat Apr 01 08:14:19 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  URL =          "http://www.ma.man.ac.uk/~higham/mctoolbox",
  abstract =     "The Matrix Computation Toolbox is a collection of
                 MATLAB M-files containing functions for constructing
                 test matrices, computing matrix factorizations,
                 visualizing matrices, and carrying out direct search
                 optimization. Various other miscellaneous functions are
                 also included. This toolbox supersedes the author's
                 earlier Test Matrix Toolbox (final release
                 1995).\par

                 The toolbox was developed in conjunction with the book
                 Accuracy and Stability of Numerical Algorithms (SIAM,
                 Second edition, August 2002, xxx + 680 pp.). That book
                 is the primary documentation for the toolbox: it
                 describes much of the underlying mathematics and many
                 of the algorithms and matrices (it also describes many
                 of the matrices provided by MATLAB's gallery
                 function).",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; MATLAB",
}

@InCollection{Higham:2015:MFS,
  author =       "Nicholas J. Higham and Lijing Lin",
  editor =       "Zhaojun Bai and Weiguo Gao and Yangfeng Su",
  booktitle =    "Matrix Functions and Matrix Equations",
  title =        "Matrix Functions: a Short Course",
  volume =       "19",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  bookpages =    "vii + 137",
  pages =        "1--27",
  year =         "2015",
  ISBN =         "981-4675-76-8 (hardcover), 981-4675-77-6 (e-book),
                 981-4675-78-4 (e-book)",
  ISBN-13 =      "978-981-4675-76-5 (hardcover), 978-981-4675-77-2
                 (e-book), 978-981-4675-78-9 (e-book)",
  LCCN =         "QA184.2 .M39 2015",
  MRclass =      "15-01",
  MRnumber =     "3445562",
  bibdate =      "Sat Aug 26 17:36:15 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  series =       "Ser. Contemp. Appl. Math. CAM",
  URL =          "http://www.worldscientific.com/worldscibooks/10.1142/9590",
  acknowledgement = ack-nhfb,
  tableofcontents = "Matrix Functions: A Short Course / Nicholas J.
                 Higham and Lijing Lin / 1 \\
                 A Short Course on Exponential Integrators / Marlis
                 Hochbruck / 28 \\
                 Matrix Equations and Model Reduction / Peter Benner,
                 Tobias Breiten and Lihong Feng / 50 \\
                 Rayleigh Quotient Based Optimization Methods for
                 Eigenvalue Problems / Ren-Cang Li / 76 \\
                 Factorization-Based Sparse Solvers and Preconditioners
                 / Xiaoye Sherry Li / 109",
  xxaddress =    "Beijing, China",
  xxpublisher =  "Higher Education Press",
}

@Article{Aprahamian:2016:MEB,
  author =       "Mary Aprahamian and Desmond J. Higham and Nicholas J.
                 Higham",
  title =        "Matching exponential-based and resolvent-based
                 centrality measures",
  journal =      j-J-COMPLEX-NETWORKS,
  volume =       "4",
  number =       "2",
  pages =        "157--176",
  year =         "2016",
  DOI =          "https://doi.org/10.1093/comnet/cnv016",
  ISSN =         "2051-1310 (print), 2051-1329 (electronic)",
  ISSN-L =       "2051-1310",
  MRclass =      "05C82",
  MRnumber =     "3605538",
  bibdate =      "Sat Aug 26 17:36:42 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Complex Netw.",
  fjournal =     "Journal of Complex Networks",
  journal-URL =  "http://www.comnet.oxfordjournals.org",
}

@Article{Aprahamian:2016:MIT,
  author =       "Mary Aprahamian and Nicholas J. Higham",
  title =        "Matrix Inverse Trigonometric and Inverse Hyperbolic
                 Functions: Theory and Algorithms",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "37",
  number =       "4",
  pages =        "1453--1477",
  month =        "????",
  year =         "2016",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/16M1057577",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "15A24 (65F60)",
  MRnumber =     "3556068",
  MRreviewer =   "Mustapha Rachidi",
  bibdate =      "Fri Aug 25 09:01:43 MDT 2017",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/37/4;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2016",
}

@Article{Deadman:2016:TMF,
  author =       "Edvin Deadman and Nicholas J. Higham",
  title =        "Testing Matrix Function Algorithms Using Identities",
  journal =      j-TOMS,
  volume =       "42",
  number =       "1",
  pages =        "4:1--4:15",
  month =        feb,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2723157",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F60",
  MRnumber =     "3472420",
  bibdate =      "Tue Mar 1 17:07:56 MST 2016",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Algorithms for computing matrix functions are
                 typically tested by comparing the forward error with
                 the product of the condition number and the unit
                 roundoff. The forward error is computed with the aid of
                 a reference solution, typically computed at high
                 precision. An alternative approach is to use functional
                 identities such as the ``round-trip tests'' $ e^{\log
                 A} = A $ and $ (A^{1 / p})^p = A $, as are currently
                 employed in a SciPy test module. We show how a
                 linearized perturbation analysis for a functional
                 identity allows the determination of a maximum residual
                 consistent with backward stability of the constituent
                 matrix function evaluations. Comparison of this maximum
                 residual with a computed residual provides a necessary
                 test for backward stability. We also show how the
                 actual linearized backward error for these relations
                 can be computed. Our approach makes use of Fr{\'e}chet
                 derivatives and estimates of their norms. Numerical
                 experiments show that the proposed approaches are able
                 both to detect instability and to confirm stability.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Higham:2016:AAA,
  author =       "Nicholas J. Higham and Nata{\v{s}}a Strabi{\'c}",
  title =        "{Anderson} acceleration of the alternating projections
                 method for computing the nearest correlation matrix",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "72",
  number =       "4",
  pages =        "1021--1042",
  month =        aug,
  year =         "2016",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-015-0078-3",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65F30 (15B57)",
  MRnumber =     "3529831",
  MRreviewer =   "Hassane Abbas",
  bibdate =      "Tue Sep 20 10:57:47 MDT 2016",
  bibsource =    "http://link.springer.com/journal/11075/72/4;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/s11075-015-0078-3.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Higham:2016:ACP,
  author =       "Nicholas J. Higham and Vanni Noferini",
  title =        "An algorithm to compute the polar decomposition of a $
                 3 \times 3 $ matrix",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "73",
  number =       "2",
  pages =        "349--369",
  month =        oct,
  year =         "2016",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-016-0098-7",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65F99 (15A21)",
  MRnumber =     "3549082",
  bibdate =      "Tue Sep 20 10:57:48 MDT 2016",
  bibsource =    "http://link.springer.com/journal/11075/73/2;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/s11075-016-0098-7.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "$3 \times 3$ matrix; Numerical stability; Polar
                 decomposition; Quaternions; Singular value
                 decomposition",
}

@Article{Higham:2016:BDN,
  author =       "Nicholas J. Higham and Natasa Strabi{\'c}",
  title =        "Bounds for the Distance to the Nearest Correlation
                 Matrix",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "37",
  number =       "3",
  pages =        "1088--1102",
  month =        "????",
  year =         "2016",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/15M1052007",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "15A45 (65F05 65F30)",
  MRnumber =     "3537883",
  MRreviewer =   "Antonio Cicone",
  bibdate =      "Tue Nov 8 08:41:57 MST 2016",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/37/3;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2016",
}

@Article{Higham:2016:ELE,
  author =       "Nicholas J. Higham and Samuel D. Relton",
  title =        "Estimating the Largest Elements of a Matrix",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "38",
  number =       "5",
  pages =        "C584--C601",
  month =        "????",
  year =         "2016",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/15M1053645",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F99 (65F35)",
  MRnumber =     "3561776",
  MRreviewer =   "Jo\~ao Ribeiro Cardoso",
  bibdate =      "Sun Mar 12 07:28:39 MDT 2017",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/38/5;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2016",
}

@Article{Higham:2016:KGS,
  author =       "Nicholas J. Higham",
  title =        "{Knuth} Gives Satisfaction in {SIAM von Neumann
                 Lecture}",
  journal =      j-SIAM-NEWS,
  volume =       "49",
  number =       "6",
  pages =        "??--??",
  month =        jul # "\slash " # aug,
  year =         "2016",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Fri Sep 30 15:20:42 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "https://sinews.siam.org/DetailsPage/TabId/900/ArtMID/2243/ArticleID/820/Knuth-Gives-Satisfaction-in-SIAM-von-Neumann-Lecture.aspx",
  acknowledgement = ack-nhfb,
  keywords =     "2016 SIAM John von Neumann lecture prize; Art of
                 Computer Programming; Donald E. Knuth; Satisfiability
                 and Combinatorics",
}

@Article{Higham:2016:MWP,
  author =       "Nicholas J. Higham",
  title =        "Mathematical Word Processing: Historical Snippets",
  journal =      j-SIAM-NEWS,
  volume =       "49",
  number =       "6",
  pages =        "??--??",
  month =        jul # "\slash " # aug,
  year =         "2016",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Fri Sep 30 12:32:57 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "https://sinews.siam.org/DetailsPage/TabId/900/ArtMID/2243/ArticleID/1655/Mathematical-Word-Processing-Historical-Snippets.aspx",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@Article{Higham:2016:RDS,
  author =       "Nicholas J. Higham and Nata{\v{s}}a Strabi{\'c} and
                 Vedran {\v{S}}ego",
  title =        "Restoring Definiteness via Shrinking, with an
                 Application to Correlation Matrices with a Fixed
                 Block",
  journal =      j-SIAM-REVIEW,
  volume =       "58",
  number =       "2",
  pages =        "245--263",
  month =        "????",
  year =         "2016",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/140996112",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "15B57 (65F30)",
  MRnumber =     "3493945",
  MRreviewer =   "Yang Cao",
  bibdate =      "Fri May 27 07:15:57 MDT 2016",
  bibsource =    "http://epubs.siam.org/toc/siread/58/2;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 2016",
}

@Article{Carson:2017:NAI,
  author =       "Erin Carson and Nicholas J. Higham",
  title =        "A new analysis of iterative refinement and its
                 application to accurate solution of ill-conditioned
                 sparse linear systems",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "39",
  number =       "6",
  pages =        "A2834--A2856",
  year =         "2017",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/17M1122918",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65G50 (65F10 65F35 65F50)",
  MRnumber =     "3732948",
  bibdate =      "Tue May 8 08:38:21 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  URL =          "http://eprints.maths.manchester.ac.uk/2537/",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@Article{Fischer:2017:AAM,
  author =       "Thomas M. Fischer",
  title =        "On the algorithm by {Al-Mohy} and {Higham} for
                 computing the action of the matrix exponential: a
                 posteriori roundoff error estimation",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "531",
  number =       "??",
  pages =        "141--168",
  day =          "15",
  month =        oct,
  year =         "2017",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2017.05.042",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Sat Aug 26 17:24:35 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2015.bib",
  note =         "See \cite{Al-Mohy:2011:CAM}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379517303427",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Higham:2017:CAT,
  author =       "Nicholas J. Higham and Peter Kandolf",
  title =        "Computing the Action of Trigonometric and Hyperbolic
                 Matrix Functions",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "39",
  number =       "2",
  pages =        "A613--A627",
  month =        "????",
  year =         "2017",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/16M1084225",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F60 (15A16)",
  MRnumber =     "3636536",
  MRreviewer =   "Ralf Zimmermann",
  bibdate =      "Fri Aug 25 09:17:35 MDT 2017",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/39/2;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2017",
}

@Article{Higham:2017:CHB,
  author =       "Nicholas J. Higham and Neville J. Ford",
  title =        "{Christopher T. H. Baker} (1939--2017)",
  journal =      j-MATH-TODAY,
  volume =       "53",
  number =       "6",
  pages =        "257",
  year =         "2017",
  ISSN =         "1361-2042",
  ISSN-L =       "1361-2042",
  MRclass =      "01A70",
  MRnumber =     "3702305",
  bibdate =      "Tue May 8 08:39:11 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Today",
  journal-URL =  "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
}

@Book{Higham:2017:MG,
  author =       "Desmond J. Higham and Nicholas J. Higham",
  title =        "{MATLAB} guide",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xxvi + 476",
  year =         "2017",
  ISBN =         "1-61197-465-8",
  ISBN-13 =      "978-1-61197-465-2",
  MRclass =      "65-00 (00A20)",
  MRnumber =     "3601107",
  bibdate =      "Sat Aug 26 17:40:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
  abstract =     "MATLAB is an interactive system for numerical
                 computation that is widely used for teaching and
                 research in industry and academia. It provides a modern
                 programming language and problem solving environment,
                 with powerful data structures, customizable graphics,
                 and easy-to-use editing and debugging tools. This third
                 edition of MATLAB Guide completely revises and updates
                 the best-selling second edition and is more than 25
                 percent longer. The book remains a lively, concise
                 introduction to the most popular and important features
                 of MATLAB and the Symbolic Math Toolbox. Key features
                 are a tutorial in Chapter 1 that gives a hands-on
                 overview of MATLAB, a thorough treatment of MATLAB
                 mathematics, including the linear algebra and numerical
                 analysis functions and the differential equation
                 solvers, and a web page that provides a link to example
                 program files, updates, and links to MATLAB resources.
                 The new edition contains color figures throughout,
                 includes pithy discussions of related topics in new
                 `Asides' boxes that augment the text, has new chapters
                 on the Parallel Computing Toolbox, object-oriented
                 programming, graphs, and large data sets, covers
                 important new MATLAB data types such as categorical
                 arrays, string arrays, tall arrays, tables, and
                 timetables, contains more on MATLAB workflow, including
                 the Live Editor and unit tests, and fully reflects
                 major updates to the MATLAB graphics system.",
  acknowledgement = ack-nhfb,
  remark =       "Third edition of
                 \cite{Higham:2000:MG,Higham:2005:MG}.",
  subject =      "MATLAB (logiciel).; Analyse num{\'e}rique; Logiciels.;
                 Numerical analysis; Data processing; Data processing.",
  tableofcontents = "1: A Brief Tutorial \\
                 2: Basics \\
                 3: Distinctive Features of MATLAB \\
                 4: Arithmetic \\
                 5: Matrices \\
                 6: Operators and Flow Control \\
                 7: Program Files \\
                 8: Graphics \\
                 9: Linear Algebra \\
                 10: More on Functions \\
                 11: Numerical Methods: Part I \\
                 12: Numerical Methods: Part II \\
                 13: Input and Output \\
                 14: Troubleshooting \\
                 15: Sparse Matrices \\
                 16: More on Coding \\
                 17: Advanced Graphics \\
                 18: Other Data Types and Multidimensional Arrays \\
                 19: Object-Oriented Programming \\
                 20: The Symbolic Math Toolbox \\
                 21: Graphs \\
                 22: Large Data Sets \\
                 23: Optimizing Codes \\
                 24: Tricks and Tips \\
                 25: The Parallel Computing Toolbox \\
                 26: Case Studies",
}

@InProceedings{Higham:2017:RMA,
  author =       "N. J. Higham",
  title =        "The Rise of Multiprecision Arithmetic",
  crossref =     "Burgess:2017:ISC",
  pages =        "1--1",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.24",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "There is a growing demand for and availability of
                 multiprecision arithmetic: floating point arithmetic
                 supporting multiple, possibly arbitrary, precisions.
                 For an increasing body of applications, including in
                 supernova simulations, electromagnetic scattering
                 theory, and computational number theory, double
                 precision arithmetic is insufficient to provide results
                 of the required accuracy. On the other hand, for
                 climate modelling and deep learning half precision
                 (about four significant decimal digits) has been shown
                 to be sufficient in some studies. We discuss a number
                 of topics involving multiprecision arithmetic,
                 including: The need for, availability of, and ways to
                 exploit, higher precision arithmetic (e.g., quadruple
                 precision arithmetic). How to derive linear algebra
                 algorithms that will run in any precision, as opposed
                 to be being optimized (as some key algorithms are) for
                 double precision. For solving linear systems with the
                 use of iterative refinement, the benefits of suitably
                 combining three different precisions of arithmetic
                 (say, half, single, and double). How a new form of
                 preconditioned iterative refinement can be used to
                 solve very ill conditioned sparse linear systems to
                 high accuracy.",
  acknowledgement = ack-nhfb,
  keywords =     "climate modelling; Computational modeling; deep
                 learning half precision; Digital arithmetic; double
                 precision arithmetic; Electromagnetic scattering;
                 floating point arithmetic; Floating-point arithmetic;
                 iterative methods; iterative refinement; linear
                 algebra; linear algebra algorithms; linear systems;
                 Linear systems; Mathematical model; multiprecision
                 arithmetic; sparse linear systems",
}

@Article{Carson:2018:ASL,
  author =       "Erin Carson and Nicholas J. Higham",
  title =        "Accelerating the Solution of Linear Systems by
                 Iterative Refinement in Three Precisions",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "40",
  number =       "2",
  pages =        "A817--A847",
  month =        "????",
  year =         "2018",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/17M1140819",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F10 (65F05 65F35 65G50)",
  MRnumber =     "3775138",
  MRreviewer =   "Dimitrios Christou",
  bibdate =      "Tue May 8 15:57:34 MDT 2018",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/40/2;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2018",
}

@Article{Fasi:2018:MAC,
  author =       "Massimiliano Fasi and Nicholas J. Higham",
  title =        "Multiprecision algorithms for computing the matrix
                 logarithm",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "39",
  number =       "1",
  pages =        "472--491",
  year =         "2018",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/17M1129866",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F60 (15A16 15A60)",
  MRnumber =     "3775134",
  MRreviewer =   "Javier Pastor",
  bibdate =      "Tue May 8 08:39:52 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Freeman:2018:JWF,
  author =       "T. L. Freeman and Nicholas J. Higham",
  title =        "{Joan E. Walsh FIMA} (1932--2017)",
  journal =      j-MATH-TODAY,
  volume =       "54",
  number =       "3",
  pages =        "89",
  year =         "2018",
  ISSN =         "1361-2042",
  ISSN-L =       "1361-2042",
  MRclass =      "01A70",
  MRnumber =     "3820884",
  bibdate =      "Sat Oct 6 15:34:30 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Today",
  journal-URL =  "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
}

@Article{Georgescu:2018:ESC,
  author =       "Dan I. Georgescu and Nicholas J. Higham and Gareth W.
                 Peters",
  title =        "Explicit solutions to correlation matrix completion
                 problems, with an application to risk management and
                 insurance",
  journal =      j-R-SOC-OPEN-SCI,
  volume =       "5",
  number =       "3",
  pages =        "172348:1--172348:11",
  month =        mar,
  year =         "2018",
  CODEN =        "RSOSAV",
  DOI =          "https://doi.org/10.1098/rsos.172348",
  ISSN =         "2054-5703",
  ISSN-L =       "2054-5703",
  MRclass =      "65F99 (15A83 91B30)",
  MRnumber =     "3815440",
  bibdate =      "Sat Oct 6 15:34:30 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "R. Soc. Open Sci.",
  fjournal =     "Royal Society Open Science",
  journal-URL =  "http://rsos.royalsocietypublishing.org/",
}

@InProceedings{Haidar:2018:HGT,
  author =       "Azzam Haidar and Stanimire Tomov and Jack Dongarra and
                 Nicholas J. Higham",
  editor =       "{IEEE}",
  booktitle =    "{SC '18 Proceedings of the International Conference
                 for High Performance Computing, Networking, Storage,
                 and Analysis, Dallas, Texas, November 11--16, 2018}",
  title =        "Harnessing {GPU} tensor cores for fast {FP16}
                 arithmetic to speed up mixed-precision iterative
                 refinement solvers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "47:1--47:11",
  year =         "2018",
  ISBN =         "1-5386-8384-9",
  ISBN-13 =      "978-1-5386-8384-2",
  LCCN =         "????",
  bibdate =      "Sat Jan 19 18:51:19 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3291656.3291719",
  abstract =     "Low-precision floating-point arithmetic is a powerful
                 tool for accelerating scientific computing
                 applications, especially those in artificial
                 intelligence. Here, we present an investigation showing
                 that other high-performance computing (HPC)
                 applications can also harness this power. Specifically,
                 we use the general HPC problem, Ax = b, where A is a
                 large dense matrix, and a double precision (FP64)
                 solution is needed for accuracy. Our approach is based
                 on mixed-precision (FP16 $ \to $ FP64) iterative
                 refinement, and we generalize and extend prior advances
                 into a framework, for which we develop
                 architecture-specific algorithms and highly tuned
                 implementations. These new methods show how using
                 half-precision Tensor Cores (FP16-TC) for the
                 arithmetic can provide up to 4X speedup. This is due to
                 the performance boost that the FP16-TC provide as well
                 as to the improved accuracy over the classical FP16
                 arithmetic that is obtained because the GEMM
                 accumulation occurs in FP32 arithmetic.",
  acknowledgement = ack-nhfb,
}

@Article{Higham:2018:DD,
  author =       "Nicholas Higham",
  title =        "Differentiation with(out) a difference",
  journal =      j-SIAM-NEWS,
  volume =       "51",
  number =       "5",
  pages =        "2",
  year =         "2018",
  ISSN =         "1557-9573",
  ISSN-L =       "1557-9573",
  MRclass =      "65D25 (41A80 65G50)",
  MRnumber =     "3823048",
  bibdate =      "Tue Jan 22 15:10:07 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@Misc{Higham:2018:HPA,
  author =       "Nicholas J. Higham",
  title =        "Half Precision Arithmetic: fp16 Versus bfloat16",
  howpublished = "Web site.",
  day =          "3",
  month =        dec,
  year =         "2018",
  bibdate =      "Sat Jan 19 18:43:15 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://nickhigham.wordpress.com/2018/12/03/half-precision-arithmetic-fp16-versus-bfloat16/",
  abstract =     "The 2008 revision of the IEEE Standard for
                 Floating-Point Arithmetic introduced a half precision
                 16-bit floating point format, known as fp16, as a
                 storage format. Various manufacturers have adopted fp16
                 for computation, using the obvious extension of the
                 rules for the fp32 (single precision) and fp64 (double
                 precision) formats. For example, fp16 is supported by
                 the NVIDIA P100 and V100 GPUs and the AMD Radeon
                 Instinct MI25 GPU, as well as the A64FX Arm processor
                 that will power the Fujitsu Post-K exascale computer.",
  acknowledgement = ack-nhfb,
}

@Article{Higham:2018:RAB,
  author =       "Nicholas Higham",
  title =        "Rhapsodizing about {Bohemian} matrices",
  journal =      j-SIAM-NEWS,
  volume =       "51",
  number =       "10",
  pages =        "2",
  year =         "2018",
  ISSN =         "1557-9573",
  ISSN-L =       "1557-9573",
  MRclass =      "15B34",
  MRnumber =     "3929646",
  bibdate =      "Fri Jul 9 15:09:12 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@Article{Higham:2018:SS,
  author =       "Nicholas Higham",
  title =        "Snap to structure",
  journal =      j-SIAM-NEWS,
  volume =       "51",
  number =       "1",
  pages =        "2",
  year =         "2018",
  ISSN =         "1557-9573",
  ISSN-L =       "1557-9573",
  MRclass =      "65G99 (68W30)",
  MRnumber =     "3823054",
  bibdate =      "Tue Jan 22 15:10:07 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@Article{Higham:2018:TFD,
  author =       "Nicholas Higham",
  title =        "A timely focus on data science",
  journal =      j-SIAM-NEWS,
  volume =       "51",
  number =       "9",
  pages =        "2",
  year =         "2018",
  ISSN =         "1557-9573",
  ISSN-L =       "1557-9573",
  MRclass =      "68T01",
  MRnumber =     "3889491",
  bibdate =      "Fri Jul 9 15:09:43 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@Article{Higham:2018:UN,
  author =       "Nicholas J. Higham",
  title =        "The Unwinding Number",
  journal =      j-SIAM-NEWS,
  volume =       "51",
  number =       "8",
  pages =        "2--2",
  month =        oct,
  year =         "2018",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  MRclass =      "65E05 (68N15)",
  MRnumber =     "3823081",
  bibdate =      "Sat Oct 06 08:46:15 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://sinews.siam.org/Details-Page/the-unwinding-number",
  abstract =     "While Fortran 66 had a complex data type, this was not
                 true of most other early programming languages, such as
                 Algol 60. As a result, programmers had to write their
                 own procedures to implement complex arithmetic and
                 transcendental functions in terms of separately stored
                 real and imaginary parts. They quickly realized that
                 this is not a trivial task; in the early 1960s, it took
                 five published attempts over three years to obtain a
                 correct implementation of the complex logarithm in
                 Algol 60.",
  acknowledgement = ack-nhfb,
}

@Article{Nadukandi:2018:CWK,
  author =       "Prashanth Nadukandi and Nicholas J. Higham",
  title =        "Computing the Wave-Kernel Matrix Functions",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "40",
  number =       "6",
  pages =        "A4060--A4082",
  month =        "????",
  year =         "2018",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/18M1170352",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F60 (15A60 41A21)",
  MRnumber =     "3884228",
  MRreviewer =   "Fazlollah Soleymani",
  bibdate =      "Tue Jan 22 15:10:07 2019",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/40/6;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2018",
}

@Article{Anzt:2019:APB,
  author =       "Hartwig Anzt and Jack Dongarra and Goran Flegar and
                 Nicholas J. Higham and Enrique S. Quintana-Ort{\'\i}",
  title =        "Adaptive precision in block-{Jacobi} preconditioning
                 for iterative sparse linear system solvers",
  journal =      j-CCPE,
  volume =       "31",
  number =       "6",
  pages =        "e4460:1--e4460:??",
  day =          "25",
  month =        mar,
  year =         "2019",
  CODEN =        "CCPEBO",
  DOI =          "https://doi.org/10.1002/cpe.4460",
  ISSN =         "1532-0626 (print), 1532-0634 (electronic)",
  ISSN-L =       "1532-0626",
  bibdate =      "Thu Mar 28 08:07:56 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/ccpe.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Concurrency and Computation: Practice and Experience",
  journal-URL =  "http://www.interscience.wiley.com/jpages/1532-0626",
  onlinedate =   "12 March 2018",
}

@TechReport{Blanchard:2019:MPB,
  author =       "Pierre Blanchard and Nicholas J. Higham and Florent
                 Lopez and Theo Mary and Srikara Pranesh",
  title =        "Mixed Precision Block Fused Multiply-Add: Error
                 Analysis and Application to {GPU} Tensor Cores",
  type =         "MIMS EPrint",
  number =       "2019.18",
  institution =  "Manchester Institute for Mathematical Sciences, School
                 of Mathematics, The University of Manchester",
  address =      "Manchester, UK",
  day =          "24",
  month =        sep,
  year =         "2019",
  ISSN =         "1749-9097",
  bibdate =      "Thu Dec 05 10:14:37 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://eprints.maths.manchester.ac.uk/2733/;
                 https://en.wikipedia.org/wiki/Bfloat16 floating-point
                 format",
  abstract =     "Computing units that carry out a fused multiply-add
                 (FMA) operation with matrix arguments, referred to as
                 tensor units by some vendors, have great potential for
                 use in scientific computing. However, these units are
                 inherently mixed precision and existing rounding error
                 analyses do not support them. We consider a mixed
                 precision block FMA that generalizes both the usual
                 scalar FMA and existing tensor units. We describe how
                 to exploit such a block FMA in the numerical linear
                 algebra kernels of matrix multiplication and LU
                 factorization and give rounding error analyses of both
                 kernels. An important application is to GMRES-based
                 iterative refinement with block FMAs, for which our
                 analysis provides new insight. Our framework is
                 applicable to the tensor core units in the NVIDIA Volta
                 and Turing GPUs. For these we compare matrix
                 multiplication and LU factorization with TC16 and TC32
                 forms of FMA, which differ in the precision used for
                 the output of the tensor cores. Our experiments on an
                 NVDIA V100 GPU confirm the predictions of the analysis
                 that the TC32 variant is much more accurate than the
                 TC16 one, while achieving almost the same
                 performance.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; fused multiply-add; LU
                 factorization; matrix multiplication; rounding error
                 analysis, NVIDIA GPU; tensor cores",
}

@Article{Fasi:2019:APS,
  author =       "Massimiliano Fasi and Nicholas J. Higham",
  title =        "An arbitrary precision scaling and squaring algorithm
                 for the matrix exponential",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "40",
  number =       "4",
  pages =        "1233--1256",
  year =         "2019",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/18M1228876",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F60 (15A16)",
  MRnumber =     "4014393",
  MRreviewer =   "Ralf Zimmermann",
  bibdate =      "Fri Jul 9 15:12:06 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Hammarling:2019:CJH,
  author =       "Sven J. Hammarling and Nicholas J. Higham",
  title =        "Celebrating {James Hardy Wilkinson}",
  journal =      j-MATH-TODAY,
  volume =       "55",
  number =       "4",
  pages =        "131--131",
  year =         "2019",
  ISSN =         "1361-2042",
  MRclass =      "01A70",
  MRnumber =     "3967944",
  bibdate =      "Fri Jul 9 15:12:06 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Today",
  journal-URL =  "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
}

@Article{Higham:2019:NAP,
  author =       "Nicholas J. Higham and Theo Mary",
  title =        "A New Approach to Probabilistic Rounding Error
                 Analysis",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "41",
  number =       "5",
  pages =        "A2815--A2835",
  month =        "????",
  year =         "2019",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/18M1226312",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65G50 (60E15 65F05)",
  MRnumber =     "4002728",
  MRreviewer =   "A. Bultheel",
  bibdate =      "Tue Nov 5 05:24:19 MST 2019",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/41/5;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "floating-point arithmetic; MATLAB; numerical linear
                 algebra; rounding error analysis",
  onlinedate =   "January 2019",
}

@Article{Higham:2019:NPE,
  author =       "Nicholas J. Higham and Theo Mary",
  title =        "A New Preconditioner that Exploits Low-Rank
                 Approximations to Factorization Error",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "41",
  number =       "1",
  pages =        "A59--A82",
  month =        "????",
  year =         "2019",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/18M1182802",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F22 (65F05 65F08 65F10 68W20)",
  MRnumber =     "3895124",
  bibdate =      "Thu Oct 10 06:58:01 MDT 2019",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/41/1;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2019",
}

@Article{Higham:2019:SLP,
  author =       "Nicholas J. Higham and Srikara Pranesh",
  title =        "Simulating Low Precision Floating-Point Arithmetic",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "41",
  number =       "5",
  pages =        "C585--C602",
  month =        "????",
  year =         "2019",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/19M1251308",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F05 (65G50 65Y04)",
  MRnumber =     "4024753",
  MRreviewer =   "Jin Yun Yuan",
  bibdate =      "Tue Nov 5 05:24:19 MST 2019",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/41/5;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "bfloat16; bit flips; directed rounding; floating-point
                 arithmetic; fp16; half precision; IEEE arithmetic; low
                 precision; MATLAB; mixed precision; round to nearest;
                 rounding error analysis; simulation; stochastic
                 rounding; subnormal numbers",
  onlinedate =   "January 2019",
}

@Article{Higham:2019:SMH,
  author =       "Nicholas J. Higham and Srikara Pranesh and Mawussi
                 Zounon",
  title =        "Squeezing a Matrix into Half Precision, with an
                 Application to Solving Linear Systems",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "41",
  number =       "4",
  pages =        "A2536--A2551",
  month =        "????",
  year =         "2019",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/18M1229511",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F35 (65F05 65F08 65F10 65G50)",
  MRnumber =     "3987532",
  MRreviewer =   "A. Bultheel",
  bibdate =      "Thu Oct 10 06:58:08 MDT 2019",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/41/4;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "diagonal scaling; fp16; GMRES; half precision
                 arithmetic; iterative refinement; linear system;
                 MATLAB; mixed precision; overflow; preconditioning;
                 subnormal numbers; underflow",
  onlinedate =   "January 2019",
}

@Article{Blanchard:2020:CFA,
  author =       "Pierre Blanchard and Nicholas J. Higham and Theo
                 Mary",
  title =        "A Class of Fast and Accurate Summation Algorithms",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "42",
  number =       "3",
  pages =        "A1541--A1557",
  month =        "????",
  year =         "2020",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/19M1257780",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65B10 (65F05 65G50)",
  MRnumber =     "4094754",
  MRreviewer =   "S. Hitotumatu",
  bibdate =      "Fri Mar 12 11:39:57 MST 2021",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/42/3;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  abstract =     "The need to sum floating-point numbers is ubiquitous
                 in scientific computing. Standard recursive summation
                 of $n$ summands, often implemented in a blocked form,
                 has a backward error bound proportional to $ n u$,
                 where $u$ is the unit roundoff. With the growing
                 interest in low precision floating-point arithmetic and
                 ever increasing $n$ in applications, computed sums are
                 more likely to have insufficient accuracy. We propose a
                 class of summation algorithms called FABsum (for fast
                 and accurate block summation'') that applies a fast
                 summation algorithm (such as recursive summation)
                 blockwise and then sums the partial sums using an
                 accurate summation algorithm (such as compensated
                 summation, or recursive summation in higher precision).
                 We give a rounding error analysis to show that FABsum
                 with a fixed block size $b$ has a backward error bound
                 $ (b + 1)u + O(u^2)$, which is independent of $n$ to
                 first order. Our computational experiments show that
                 with a suitable choice of $b$ (independent of $n$)
                 FABsum can deliver substantially more accurate results
                 than blocked recursive summation, with only a modest
                 drop in performance. FABsum is especially attractive
                 for low precisions, where it can provide correct digits
                 for much larger $n$ than recursive summation.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic; rounding errors",
  onlinedate =   "January 2020",
}

@Article{Blanchard:2020:MPB,
  author =       "Pierre Blanchard and Nicholas J. Higham and Florent
                 Lopez and Theo Mary and Srikara Pranesh",
  title =        "Mixed precision block fused multiply-add: error
                 analysis and application to {GPU} tensor cores",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "42",
  number =       "3",
  pages =        "C124--C141",
  year =         "2020",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/19M1289546",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F05 (65G50 65Y04 68M07)",
  MRnumber =     "4103291",
  bibdate =      "Fri Jul 9 15:12:06 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@Article{Carson:2020:TPG,
  author =       "Erin Carson and Nicholas J. Higham and Srikara
                 Pranesh",
  title =        "Three-precision {GMRES}-based iterative refinement for
                 least squares problems",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "42",
  number =       "6",
  pages =        "A4063--A4083",
  year =         "2020",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/20M1316822",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F05 (65F08 65F20)",
  MRnumber =     "4188846",
  bibdate =      "Fri Jul 9 15:12:06 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@Article{Dongarra:2020:NAH,
  author =       "Jack Dongarra and Laura Grigori and Nicholas J.
                 Higham",
  title =        "Numerical algorithms for high-performance
                 computational science",
  journal =      j-PHILOS-TRANS-R-SOC-LOND-SER-A,
  volume =       "378",
  number =       "2166",
  pages =        "20190066:1--20190066:18",
  year =         "2020",
  DOI =          "https://doi.org/10.1098/rsta.2019.0066",
  ISSN =         "1364-503X (print), 1471-2962 (electronic)",
  MRclass =      "65Y10",
  MRnumber =     "4072450",
  bibdate =      "Fri Jul 9 15:12:06 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Philos. Trans. Roy. Soc. A",
  fjournal =     "Philosophical Transactions of the Royal Society A.
                 Mathematical, Physical and Engineering Sciences",
}

@Article{Haidar:2020:MPI,
  author =       "Azzam Haidar and Harun Bayraktar and Stanimire Tomov
                 and Jack Dongarra and Nicholas J. Higham",
  title =        "Mixed-precision iterative refinement using tensor
                 cores on {GPUs} to accelerate solution of linear
                 systems",
  journal =      j-PROC-R-SOC-LOND-SER-A,
  volume =       "476",
  number =       "2243",
  pages =        "20200110:1--2020011030",
  year =         "2020",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.2020.0110",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  MRclass =      "65F10 (65Y10)",
  MRnumber =     "4187936",
  bibdate =      "Fri Jul 9 15:12:06 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society of London. Series A",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
}

@Book{Higham:2020:HWM,
  author =       "Nicholas J. Higham",
  title =        "Handbook of Writing for the Mathematical Sciences",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xxi + 353",
  year =         "2020",
  DOI =          "https://doi.org/10.1137/1.9781611976106",
  ISBN =         "91-611-9760-9-X (paperback), 1-61197-610-3 (e-book)",
  ISBN-13 =      "91-611-9760-9-X (paperback), 978-1-61197-610-6
                 (e-book)",
  LCCN =         "QA42 .H54 2020",
  MRclass =      "00A20",
  MRnumber =     "4050520",
  bibdate =      "Fri Jul 9 15:12:06 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  abstract =     "{{\booktitle{Handbook of Writing for the Mathematical
                 Sciences}}} provides advice on all aspects of
                 scientific writing, with a particular focus on writing
                 mathematics. Its readable style and handy format,
                 coupled with an extensive bibliography and
                 comprehensive index, make it useful for everyone from
                 undergraduates to seasoned professionals. This third
                 edition revises, updates, and expands the best-selling
                 second edition to reflect modern writing and publishing
                 practices and builds on the author's extensive
                 experience in writing and speaking about mathematics.
                 Key features are coverage of fundamentals of writing,
                 including English usage, revising a draft, and writing
                 when your first language is not English; thorough
                 treatment of mathematical writing, including how to
                 choose notation, how to choose between words and
                 symbols, and how to format equations; many tips for
                 exploiting \LaTeX{} and \BibTeX{}; advice on how to
                 write and publish a paper, covering the entire
                 publication process; and anecdotes, quotes, and unusual
                 facts that enliven the presentation. The new edition
                 has been reorganized to make the book easier to use for
                 reference; treats modern developments in publishing
                 such as open access, DOIs, and ORCID; has a new chapter
                 on workflow covering text editors, markup languages,
                 version control, and much more; has a new chapter that
                 discusses the principles of indexing and how to prepare
                 an index in \LaTeX; has a new chapter on reviewing a
                 paper, book proposal, or book; has a new chapter
                 ``Writing a Book'' that includes advice on choosing a
                 publisher and \LaTeX tips particular to books; contains
                 more on poster design, and discusses e-posters and the
                 poster blitz; and has a new chapter giving advice on
                 writing a blog post.",
  acknowledgement = ack-nhfb,
  remark =       "Third edition of \cite{Higham:1998:HWM} (MR1223778).",
  tableofcontents = "General principles \\
                 Mathematical writing \\
                 English usage \\
                 The writer's bookshelf \\
                 When English is a foreign language \\
                 Writing a paper \\
                 Revising a draft \\
                 \TeX{}, \LaTeX{}, and \BibTeX{} \\
                 Workflow \\
                 Publishing a paper \\
                 Refereeing and reviewing \\
                 Writing a talk \\
                 Giving a talk \\
                 Preparing a poster \\
                 Writing and defending a thesis \\
                 Writing a book \\
                 Preparing an index \\
                 Writing a blog post \\
                 Information sources",
}

@Article{Higham:2020:SPB,
  author =       "Nicholas J. Higham and Theo Mary",
  title =        "Sharper probabilistic backward error analysis for
                 basic linear algebra kernels with random data",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "42",
  number =       "5",
  pages =        "A3427--A3446",
  year =         "2020",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/20M1314355",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F35 (60E15 65F05 65G50)",
  MRnumber =     "4165945",
  bibdate =      "Fri Jul 9 15:12:06 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@Article{Abdelfattah:2021:SBB,
  author =       "Ahmad Abdelfattah and Timothy Costa and Jack Dongarra
                 and Mark Gates and Azzam Haidar and Sven Hammarling and
                 Nicholas J. Higham and Jakub Kurzak and Piotr Luszczek
                 and Stanimire Tomov and Mawussi Zounon",
  title =        "A Set of Batched Basic Linear Algebra Subprograms and
                 {LAPACK} Routines",
  journal =      j-TOMS,
  volume =       "47",
  number =       "3",
  pages =        "21:1--21:23",
  month =        jun,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3431921",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Jun 27 07:42:02 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3431921",
  abstract =     "This article describes a standard API for a set of
                 Batched Basic Linear Algebra Subprograms (Batched BLAS
                 or BBLAS). The focus is on many independent BLAS
                 operations on small matrices that are grouped together
                 and processed by a single routine, called a Batched
                 BLAS routine. The matrices are grouped together in
                 uniformly sized groups, with just one group if all the
                 matrices are of equal size. The aim is to provide more
                 efficient, but portable, implementations of algorithms
                 on high-performance many-core platforms. These include
                 multicore and many-core CPU processors, GPUs and
                 coprocessors, and other hardware accelerators with
                 floating-point compute facility. As well as the
                 standard types of single and double precision, we also
                 include half and quadruple precision in the standard.
                 In particular, half precision is used in many very
                 large scale applications, such as those associated with
                 machine learning.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Blanchard:2021:ACL,
  author =       "Pierre Blanchard and Desmond J. Higham and Nicholas J.
                 Higham",
  title =        "Accurately computing the log-sum-exp and softmax
                 functions",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "41",
  number =       "4",
  pages =        "2311--2330",
  month =        oct,
  year =         "2021",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/draa038",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  bibdate =      "Sat Oct 23 16:14:21 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib",
  URL =          "http://academic.oup.com/imajna/article/41/4/2311/5893596",
  abstract =     "Evaluating the log-sum-exp function or the softmax
                 function is a key step in many modern data science
                 algorithms, notably in inference and classification.
                 Because of the exponentials that these functions
                 contain, the evaluation is prone to overflow and
                 underflow, especially in low-precision arithmetic.
                 Software implementations commonly use alternative
                 formulas that avoid overflow and reduce the chance of
                 harmful underflow, employing a shift or another
                 rewriting. Although mathematically equivalent, these
                 variants behave differently in floating-point
                 arithmetic and shifting can introduce subtractive
                 cancellation. We give rounding error analyses of
                 different evaluation algorithms and interpret the error
                 bounds using condition numbers for the functions. We
                 conclude, based on the analysis and numerical
                 experiments, that the shifted formulas are of similar
                 accuracy to the unshifted ones, so can safely be used,
                 but that a division-free variant of softmax can suffer
                 from loss of accuracy.",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@Article{Connolly:2021:SRP,
  author =       "Michael P. Connolly and Nicholas J. Higham and Theo
                 Mary",
  title =        "Stochastic rounding and its probabilistic backward
                 error analysis",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "43",
  number =       "1",
  pages =        "A566--A585",
  year =         "2021",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/20M1334796",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65G50 (60G42 65F35)",
  MRnumber =     "4214365",
  bibdate =      "Fri Jul 9 15:12:06 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@Article{Fasi:2021:GES,
  author =       "Massimiliano Fasi and Nicholas J. Higham",
  title =        "Generating extreme-scale matrices with specified
                 singular values or condition number",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "43",
  number =       "1",
  pages =        "A663--A684",
  year =         "2021",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/20M1327938",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F18 (65F35 65Y05)",
  MRnumber =     "4218408",
  bibdate =      "Fri Jul 9 15:12:06 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@Article{Fasi:2021:MTI,
  author =       "Massimiliano Fasi and Nicholas J. Higham",
  title =        "Matrices with Tunable Infinity-Norm Condition Number
                 and No Need for Pivoting in {$ L U $} Factorization",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "42",
  number =       "1",
  pages =        "417--435",
  month =        "????",
  year =         "2021",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/20M1357238",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F35 (65Y05)",
  MRnumber =     "4232450",
  bibdate =      "Fri Jul 9 15:12:06 2021",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/42/1;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2021",
}

@Article{Higham:2021:ELP,
  author =       "Nicholas J. Higham and Srikara Pranesh",
  title =        "Exploiting lower precision arithmetic in solving
                 symmetric positive definite linear systems and least
                 squares problems",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "43",
  number =       "1",
  pages =        "A258--A277",
  year =         "2021",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/19M1298263",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F05 (65F08 65F10 65F35)",
  MRnumber =     "4201445",
  bibdate =      "Fri Jul 9 15:12:06 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@Article{Higham:2021:IMF,
  author =       "Nicholas J. Higham and Matthew C. Lettington and Karl
                 Michael Schmidt",
  title =        "Integer matrix factorisations, superalgebras and the
                 quadratic form obstruction",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "622",
  pages =        "250--267",
  year =         "2021",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2021.03.028",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15B36 (05B15 11E12 15A15 15A23 15A30)",
  MRnumber =     "4241259",
  bibdate =      "Fri Jul 9 15:12:06 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Higham:2021:MDF,
  author =       "Nicholas J. Higham and Xiaobo Liu",
  title =        "A Multiprecision Derivative-Free {Schur--Parlett}
                 Algorithm for Computing Matrix Functions",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "42",
  number =       "3",
  pages =        "1401--1422",
  month =        "????",
  year =         "2021",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/20M1365326",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F60",
  MRnumber =     "4313845",
  bibdate =      "Tue Jan 18 10:51:55 MST 2022",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/42/3;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2021",
}

@Article{Higham:2021:RMG,
  author =       "Desmond J. Higham and Nicholas J. Higham and Srikara
                 Pranesh",
  title =        "Random Matrices Generating Large Growth in {$ L U $}
                 Factorization with Pivoting",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "42",
  number =       "1",
  pages =        "185--201",
  month =        "????",
  year =         "2021",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/20M1338149",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F05 (15B52 65F35)",
  MRnumber =     "4207902",
  bibdate =      "Fri Jul 9 15:12:06 2021",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/42/1;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2021",
}

@Article{Hammarling:2022:ICJ,
  author =       "Sven Hammarling and Nicholas J. Higham",
  title =        "The Influence and Contribution of {Jack Dongarra} to
                 Numerical Linear Algebra",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "24",
  number =       "4",
  month =        jul # "\slash " # aug,
  pages =        "6--11",
  year =         "2022",
  CODEN =        "CSENFA",
  DOI =          "https://doi.org/10.1109/MCSE.2022.3198330",
  ISSN =         "1521-9615 (print), 1558-366X (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Fri Mar 3 06:06:17 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/computscieng.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}

@Article{Higham:2022:AEM,
  author =       "Nicholas J. Higham and Mantas Mikaitis",
  title =        "\pkg{Anymatrix}: an extensible {MATLAB} matrix
                 collection",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "90",
  number =       "3",
  pages =        "1175--1196",
  month =        jul,
  year =         "2022",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-021-01226-2",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Thu Jun 9 09:50:52 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-021-01226-2",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Higham:2022:MPA,
  author =       "Nicholas J. Higham and Theo Mary",
  title =        "Mixed precision algorithms in numerical linear
                 algebra",
  journal =      j-ACTA-NUMERICA,
  volume =       "31",
  pages =        "347--414",
  month =        may,
  year =         "2022",
  CODEN =        "ANUMFU",
  DOI =          "https://doi.org/10.1017/S0962492922000022",
  ISSN =         "0962-4929 (print), 1474-0508 (electronic)",
  ISSN-L =       "0962-4929",
  bibdate =      "Wed Jun 15 09:10:34 MDT 2022",
  bibsource =    "http://journals.cambridge.org/action/displayIssue?jid=ANU&volumeId=31&issueId=00;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
  URL =          "https://www.cambridge.org/core/journals/acta-numerica/article/mixed-precision-algorithms-in-numerical-linear-algebra/43CA701BA29251B5790C653E66F46197",
  acknowledgement = ack-nhfb,
  ajournal =     "Acta Numer.",
  fjournal =     "Acta Numerica",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANU",
  onlinedate =   "09 June 2022",
}

@Article{Higham:2022:SBL,
  author =       "Nicholas J. Higham and Theo Mary",
  title =        "Solving block low-rank linear systems by {$ L U $}
                 factorization is numerically stable",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "42",
  number =       "2",
  pages =        "951--980",
  month =        apr,
  year =         "2022",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/drab020",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  bibdate =      "Sat Apr 23 13:25:36 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib",
  URL =          "http://academic.oup.com/imajna/article/42/2/951/6238550",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

%%% ====================================================================
%%% Cross-referenced entries must come last:
@Proceedings{Iserles:1987:SAN,
  editor =       "A. Iserles and M. J. D. Powell",
  booktitle =    "{State of the Art in Numerical Analysis. Proceedings
                 of the Joint IMA\slash SIAM Conference held at the
                 University of Birmingham, 14--18 April 1986}",
  title =        "{State of the Art in Numerical Analysis. Proceedings
                 of the Joint IMA\slash SIAM Conference held at the
                 University of Birmingham, 14--18 April 1986}",
  volume =       "9",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "x + 719",
  year =         "1987",
  ISBN =         "0-19-853614-3",
  ISBN-13 =      "978-0-19-853614-7",
  LCCN =         "QA297.J65 1986",
  bibdate =      "Mon Sep 9 14:56:14 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "The Institute of Mathematics and Its Applications
                 conference series; new series",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht002967923.pdf;
                 http://zbmath.org/?q=an:0611.00024",
  ZMnumber =     "0611.00024",
  acknowledgement = ack-nhfb,
  confdate =     "14--18 April 1986",
  conflocation = "Birmingham, UK",
  confsponsor =  "Inst. Math. Appl.; SIAM",
  pubcountry =   "UK",
  tableofcontents = "Contributors / / xiii \\
                 1. Eigenvalue problems / J. H. Wilkinson / 1 \\
                 2. Numerical linear algebra in statistical computing /
                 N. J. Higham and G. W. Stewart / 41 \\
                 3. Sparse matrices / J. K. Reid / 59 \\
                 4. Multivariate approximation / Carl de Boor / 87 \\
                 5. Data approximation by splines in one and two
                 independent variables / M. G. Cox / 111 \\
                 6. Methods for best approximation and regression
                 problems / G. A. Watson / 139 \\
                 7. Branch cuts for complex elementary functions / W.
                 Kahan / 165 \\
                 8. Recent developments in linear and quadratic
                 programming / R. Fletcher / 213 \\
                 9. Solving systems of nonlinear equations by tensor
                 methods / R. B. Schnabel and P. D. Frank / 245 \\
                 10. Numerical methods for bifurcation problems / A. D.
                 Jepson and A. Spence / 273 \\
                 11. On the iterative solution of differential and
                 integral equations using secant updating techniques /
                 A. Griewank / 299 \\
                 12. Methods for nonlinear constraints in optimization
                 calculations / M. J. D. Powell / 325 \\
                 13. The influence of vector and parallel processors on
                 numerical analysis / I. S. Duff / 359 \\
                 14. Developments in stability theory for ordinary
                 differential equations / J. D. Lambert / 409 \\
                 15. Stiff ODE initial value problems and their solution
                 / A. R. Curtis / 433 \\
                 16. Order stars and stability / G. Wanner / 451 \\
                 17. The state of the art in the numerical treatment of
                 integral equations / C. T. H. Baker / 473 \\
                 18. Strongly elliptic boundary integral equations / W.
                 L. Wendland / 511 \\
                 19. Collocation methods for one-dimensional Fredholm
                 and Volterra integral equations / H. Brunner / 563 \\
                 20. Numerical methods for free and moving boundary
                 problems / C. W. Cryer / 601 \\
                 21. Multigrid methods for elliptic equations / J. Walsh
                 / 623 \\
                 22. Galerkin finite element methods and their
                 generalizations / K. W. Morton / 645 \\
                 23. Recent developments in the numerical solution of
                 nonlinear conservation laws / S. Osher and P. K. Sweby
                 / 681 \\
                 Index / 701",
}

@Article{Dongarra:1990:ASL,
  author =       "Jack J. Dongarra and Jeremy {Du Croz} and Sven
                 Hammarling and Iain Duff",
  title =        "{Algorithm 679}: {A} Set of {Level 3 Basic Linear
                 Algebra Subprograms}: Model Implementation and Test
                 Programs",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "18--28",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77627",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Mar 22 15:39:54 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "See also
                 \cite{Higham:1990:EFM,Demmel:1992:SBA,Dayde:1994:PBI}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p18-dongarra/;
                 http://www.netlib.org/utk/people/JackDongarra/PAPERS/ALGORITHM-679-A-Set-of-Level-3-BLAS.pdf",
  acknowledgement = ack-nhfb,
  classcodes =   "C4140 (Linear algebra); C7310 (Mathematics)",
  corpsource =   "Oak Ridge Nat. Lab., TN, USA",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
  keywords =     "computers; Fortran 77; high-performance; level 3 basic
                 linear algebra subprograms; mathematics computing;
                 matrix algebra; matrix-matrix operations; portable;
                 program testing; subroutines; test programs",
  treatment =    "P Practical",
}

@Proceedings{Meyer:1993:LAM,
  editor =       "C. D. (Carl Dean) Meyer and Robert J. Plemmons",
  booktitle =    "{Linear algebra, Markov chains, and queueing models:
                 [\ldots{} some of the lectures given at the Workshop
                 Linear Algebra, Markov Chains, and Queueing Models held
                 January 13--17, 1992, as part of the Year of Applied
                 Linear Algebra at the Institute for Mathematics and its
                 Applications]}",
  title =        "{Linear algebra, Markov chains, and queueing models:
                 [\ldots{} some of the lectures given at the Workshop
                 Linear Algebra, Markov Chains, and Queueing Models held
                 January 13--17, 1992, as part of the Year of Applied
                 Linear Algebra at the Institute for Mathematics and its
                 Applications]}",
  volume =       "48",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 294",
  year =         "1993",
  ISBN =         "0-387-94085-5 (New York), 3-540-94085-5 (Berlin)",
  ISBN-13 =      "978-0-387-94085-4 (New York), 978-3-540-94085-2
                 (Berlin)",
  LCCN =         "QA184 .L545 1993",
  bibdate =      "Wed May 28 17:58:34 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "The IMA volumes in mathematics and its applications",
  URL =          "http://catalog.hathitrust.org/api/volumes/oclc/28182134.html;
                 http://www.gbv.de/dms/ilmenau/toc/126000387.PDF;
                 http://www.zentralblatt-math.org/zmath/en/search/?an=0779.00020",
  acknowledgement = ack-nhfb,
  subject =      "Algebras, Linear; Congresses; Markov processes;
                 Queuing theory",
  tableofcontents = "Error bounds for the computation of null vectors
                 with applications to Markov chains / Jesse L. Barlow
                 \\
                 The influence of nonnormality on matrix computations /
                 Fran{\c{c}}oise Chatelin \\
                 Componentwise error analysis for stationary iterative
                 methods / Nicholas J. Higham and Philip A. Knight \\
                 The character of a finite Markov chain / Carl D. Meyer
                 \\
                 Gaussian elimination, perturbation theory, and Markov
                 chains / G. W. Stewart \\
                 Algorithms for periodic Markov chains / Fran{\c{c}}ois
                 Bonhoure, Yves Dallery, and William J. Stewart \\
                 Iterative methods for queueing networks with irregular
                 state-spaces / Raymond H. Chan \\
                 Analysis of $p$-cyclic iterations for Markov chains /
                 Apostolos Hadjidimos and Robert J. Plemmons \\
                 Iterative methods for finding the stationary vector for
                 Markov chains / Dianne P. O'Leary \\
                 Local convergence of (exact and inexact) iterative
                 aggregation / Daniel B. Szyld \\
                 Automated generation and analysis of Markov reward
                 models using stochastic reward nets / Gianfranco Ciardo
                 \ldots{} [et al.] \\
                 Means and variances in Markov reward systems / Winfried
                 K. Grassman \\
                 A direct algorithm for computing the stationary
                 distribution of a $p$-cyclic Markov chain / Daniel P.
                 Heyman \\
                 Approximate analysis of a discrete-time queueing model
                 of the shared buffer ATM switch / S. Hong, H. G.
                 Perros, and H. Yamashita \\
                 Algorithms for infinite Markov chains with repeating
                 columms / Guy Latouche \\
                 Cray-2 memory organization and interprocessor memory
                 contention / Robert W. Numrich",
}

@Proceedings{Moonen:1993:LAL,
  editor =       "Marc S. Moonen and Gene H. Golub and Bart L. R. {De
                 Moor}",
  booktitle =    "{Linear Algebra for Large Scale and Real-Time
                 Applications: Proceedings of the NATO Advanced Study
                 Institute, Leuven, Belgium, August 3--14, 1992}",
  title =        "{Linear Algebra for Large Scale and Real-Time
                 Applications: Proceedings of the NATO Advanced Study
                 Institute, Leuven, Belgium, August 3--14, 1992}",
  volume =       "232",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "ix + 435",
  year =         "1993",
  ISBN =         "0-7923-2151-0",
  ISBN-13 =      "978-0-7923-2151-4",
  LCCN =         "QA185.D37 L56 1993",
  MRclass =      "65-06 (65Fxx 65Y05)",
  MRnumber =     "94e:65009",
  bibdate =      "Mon Jan 15 17:53:04 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib",
  series =       "NATO ASI series. Series E, Applied sciences",
  URL =          "http://catdir.loc.gov/catdir/enhancements/fy0823/92046135-d.html;
                 http://www.gbv.de/dms/hbz/toc/ht004938330.pdf;
                 http://zbmath.org/?q=an:0810.00029",
  ZMnumber =     "0810.00029",
  abstract =     "In recent years there has been great interest in large
                 scale and real-time matrix computations; these
                 computations arise in a variety of fields, such as
                 computer graphics, imaging, speech and image
                 processing, telecommunication, biomedical signal
                 processing, optimization and so on. This volume, which
                 is an outgrowth of a NATO ASI, held at Leuven, Belgium,
                 August 1992, gives an account of recent research
                 advances in numerical techniques used in large scale
                 and real-time computations and their implementation on
                 high performance computers.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface / / xi \\
                 Invited Lectures / / 1 \\
                 Large scale structural analysis on massively parallel
                 computers / P. E. Bj{\o}rstad and J. Cook / 3 \\
                 Data-parallel BLAS as a basis for LAPACK on massively
                 parallel computers / P. E. Bj{\o}rstad and T.
                 S{\o}revik / 13 \\
                 a Large-scale nonlinear constrained optimization / A.
                 R. Conn, N. Gould and Ph. L. Toint / 21 \\
                 Trading off parallelism and numerical stability / J. W.
                 Demmel / 49 \\
                 Subband filtering: CORDIC modulation and systolic
                 quadrature mirror filter tree / E. F. Deprettere / 69
                 \\
                 A parallel image rendering algorithm and architecture
                 based on ray tracing and radiosity shading / E. F.
                 Deprettere and L.-S. Shen / 91 \\
                 Reduction and approximation of linear computational
                 circuits / P. Dewilde and A.-J. van der Veen / 109 \\
                 The look-ahead Lanczos process for large nonsymmetric
                 matrices and related algorithms / R. W. Freund / 137
                 \\
                 Case studies of real-time processing in robotics / W.
                 M. Gentleman / 165 \\
                 Adaptive signal processing with emphasis on QRD-least
                 squares lattice / S. Haykin / 183 \\
                 A direct method for reordering eigenvalues in the
                 generalized real Schur form of a regular matrix pair
                 (A, B) / B. K{\aa}gstr{\"o}m / 195 \\
                 Block shift invariance and efficient system
                 identification algorithms / N. Kalouptsidis / 219 \\
                 Computing the singular value decomposition on a
                 fat-tree architecture / T. J. Lee, F. T. Luk and D. L.
                 Boley / 231 \\
                 A new matrix decomposition for signal processing / F.
                 T. Luk and S. Qiao / 241 \\
                 The linear algebra of perfect reconstruction filtering
                 / M. Stewart and G. Cybenko / 249 \\
                 Determining rank in the presence of error / G. W.
                 Stewart / 275 \\
                 Approximation with Kronecker products / C. F. Van Loan
                 and N. Pitsianis / 293 \\
                 Some linear algebra issues in large-scale optimization
                 / M. H. Wright / 315 \\
                 Contributed Lectures / / 339 \\
                 Direct and inverse unitary eigenproblems in signal
                 processing: an overview / G. S. Ammar, W. B. Gragg and
                 L. Reichel / 341 \\
                 Block implementations of the symmetric QR and Jacobi
                 algorithms / P. Arbenz and M. Oettli / 345 \\
                 Linear algebra for large-scale information retrieval
                 applications / M. W. Berry / 347 \\
                 Matched filter vs. least-squares approximation / L. H.
                 J. Bierens / 349 \\
                 Reordering diagonal blocks in real Schur form / A. W.
                 Bojanczyk and P. Van Dooren / 351 \\
                 Placing zeroes and the Kronecker canonical form / D. L.
                 Boley and P. Van Dooren / 353 \\
                 Analysis of the recursive least squares lattice
                 algorithm / J. R. Bunch and R. C. LeBorne / 355 \\
                 Adaptive Chebyshev iteration based on modified moments
                 / D. Calvetti, G. H. Golub and L. Reichel / 357 \\
                 Continuous realization methods and their applications /
                 M. T. Chu / 359 \\
                 Asymptotic behavior of orthogonal polynomials / T. Dehn
                 / 361 \\
                 CADCS and parallel computing / F. Dumortier, A. Van
                 Cauwenberghe and L. Boullart / 363 \\
                 Eigenvalue roulette and random test matrices / A.
                 Edelman / 365 \\
                 On numerical methods for unitary eigenvalue problems /
                 H. Fa{\sas}bender / 369 \\
                 Accurate singular values and differential qd algorithms
                 / K. V. Fernando and B. N. Parlett / 371 \\
                 Orthogonal projection and total least squares / R. D.
                 Fierro and J. R. Bunch / 375 \\
                 Gauss quadratures associated with the Arnoldi process
                 and the Lanczos algorithm / R. W. Freund and M.
                 Hochbruck / 377 \\
                 An implementation of the QMR method based on coupled
                 two-term recurrences / R. W. Freund and N. M. Nachtigal
                 / 381 \\
                 Computationally efficient homotopies for the H 2 model
                 order reduction problem / Y. Ge, L. T. Watson, E. G.
                 Collins, Jr. and L. D. Davis / 385 \\
                 A fast algorithm for QR decomposition of Toeplitz
                 matrices / G. O. Glentis / 387 \\
                 Unitary Hessenberg methods for Toeplitz approximations
                 and applications / Ch. He and A. Bunse-Gerstner / 389
                 \\
                 Perturbation theory and backward error for $A X - X B =
                 C$ / N. J. Higham / 391 \\
                 Fast transforms and elliptic problems / T. Huckle / 393
                 \\
                 An interior-point method for minimizing the maximum
                 eigenvalue of a linear combination of matrices / F.
                 Jarre / 395 \\
                 The lattice-ladder with generalized forgetting / J.
                 Kadlec / 397 \\
                 Solving a least squares problem with boundary
                 constraints / L. Kaufman / 399 \\
                 Estimating the extremal eigenvalues and condition
                 number by the Lanczos algorithm with a random start /
                 J. Kuczy{\'n}ski and H. Wo{\'z}niakowski / 401 \\
                 A generalized ADI iterative method / N. Levenberg and
                 L. Reichel / 403 \\
                 Quaternions and the symmetric eigenvalue problem / N.
                 Mackey / 405 \\
                 Application of the Gauss-Seidel iteration to the RLS
                 algorithm / {\"O}. Morg{\"u}l and A. Mala{\c{s}} / 407
                 \\
                 Ranks of submatrices of a matrix and its inverse / C.
                 C. Paige and M. Wei / 409 \\
                 A QRD-based least-squares algorithm for multipulse
                 antenna array signal processing / I. K. Proudler / 411
                 \\
                 On displacement structures for covariance matrices and
                 lossless functions / P. A. Regalia and F. Desbouvries /
                 413 \\
                 Application of vector extrapolation and conjugate
                 gradient type methods to the semiconductor device
                 problem / W. H. A. Schilders / 415 \\
                 Accurate symmetric eigenreduction by a Jacobi method /
                 I. Slapni{\v{c}}ar / 417 \\
                 The order-recursive Chandrasekhar equations for fast
                 square-root Kalman filtering / D. T. M. Slock / 419 \\
                 Hybrid iterative methods based on Faber polynomials /
                 G. Starke / 421 \\
                 Aspects of implementing a 'C' matrix library / D. E.
                 Stewart / 423 \\
                 Intermediate fill-in in sparse QR decomposition / M.
                 T{\r{u}}ma / 425 \\
                 Shifting strategies for the parallel QR algorithm / D.
                 S. Watkins / 427 \\
                 List of Participants / / 429 \\
                 Authors Index / / 437",
}

@Article{Dayde:1994:PBI,
  author =       "Michael J. Dayd{\'e} and Iain S. Duff and Antoine
                 Petitet",
  title =        "A Parallel Block Implementation of Level-3 {BLAS} for
                 {MIMD} Vector Processors",
  journal =      j-TOMS,
  volume =       "20",
  number =       "2",
  pages =        "178--193",
  month =        jun,
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 09 13:52:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "See
                 \cite{Dongarra:1990:ASL,Higham:1990:EFM,Demmel:1992:SBA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
  keywords =     "algorithms; Level-3 BLAS; matrix-matrix kernels;
                 measurement; parallelization; performance;
                 vectorization",
  subject =      "F.2.1 [Analysis of Algorithms and Problem Complexity]:
                 Numerical Algorithms and Problems--computations on
                 matrices; G.1.0 [Numerical Analysis]:
                 General--numerical algorithms; G.1.3 [Numerical
                 Analysis]: Numerical Linear Algebra--linear systems
                 (direct and iterative methods); G.4 [Mathematics of
                 Computing]: Mathematical Software--certification and
                 testing; efficiency; portability; reliability and
                 robustness; verification",
}

@Proceedings{Duff:1997:SAN,
  editor =       "Iain S. Duff and G. Alistair Watson",
  booktitle =    "The state of the art in numerical analysis",
  title =        "The state of the art in numerical analysis",
  volume =       "63",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xiv + 562",
  year =         "1997",
  ISBN =         "0-19-850014-9",
  ISBN-13 =      "978-0-19-850014-8",
  LCCN =         "QA297.S775 1997",
  MRclass =      "65-06 (00B25)",
  MRnumber =     "MR1628339 (99a:65008)",
  bibdate =      "Thu Sep 16 11:59:48 1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/gould-nicholas-ian.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
  note =         "Based on the proceedings of a conference on the state
                 of the art in numerical analysis. Organized by the
                 Institute of Mathematics and Its Applications and held
                 at York University in April 1996.",
  series =       "The Institute of Mathematics and Its Applications
                 conference series: new series",
  URL =          "https://global.oup.com/academic/product/the-state-of-the-art-in-numerical-analysis-9780198500148",
  acknowledgement = ack-nhfb,
  tableofcontents = "1. Recent Developments in Dense Numerical Linear
                 Algebra / N. J. Higham \\
                 2. Sparse Numerical Linear Algebra: Direct Methods and
                 Preconditioning / I. S. Duff \\
                 3. Closer to the Solution: Iterative Linear Solvers /
                 G. H. Golub and H. A. van der Vorst \\
                 4. 150 Years Old and Still Alive: Eigenproblems / H. A.
                 van der Vorst and G. H. Golub \\
                 5. Geometric Integration / J. M. Sanz-Serna \\
                 6. Convergence and Stability in the Numerical
                 Approximation of Dynamical Systems / A. Stuart \\
                 7. Beyond the Classical Theory of Computational
                 Ordinary Differential Equations / A. Iserles \\
                 8. Numerical Analysis of Volterra Functional and
                 Integral Equations / C. T. H. Baker \\
                 9. The Numerical Solution of Boundary Integral
                 Equations / K. E. Atkinson \\
                 10. Aspects of Approximation with Emphasis on the
                 Univariate Case / G. A. Watson \\
                 11. A Review of Methods for Multivariable Interpolation
                 at Scattered Data Points / M. J. D. Powell \\
                 12. Large Scale Unconstrained Optimization / J. Nocedal
                 \\
                 13. Interior Point Methods for Linear and Nonlinear
                 Programming / D. F. Shanno and E. M. Simantiraki \\
                 14. Methods for Nonlinear Constraints in Optimization
                 Calculations / A. R. Conn, N. I. M. Gould and Ph. L.
                 Toint \\
                 15. Stabilization Techniques and Subgrid Scales
                 Capturing, F. Brezzi, L. P. Franca / T. J. R. Hughes
                 and A. Russo \\
                 16. Approximation of Curvature Dependent Interface
                 Motion / C. M. Elliott \\
                 17. Finite Element Methods for Hyperbolic Problems: a
                 Posteriori Error Analysis and Adaptivity / E. S{\"u}li
                 and P. Houston \\
                 18. Approximation of Multidimensional Hyperbolic
                 Partial Differential Equations / K. W. Morton \\
                 19. Algorithms in Tomography / F. Natterer \\
                 20. Partial Differential Equations and Image Iterative
                 Filtering / F. Guichard and J.-M. Morel",
}

@Book{Ainsworth:1999:GSG,
  editor =       "Mark Ainsworth and Jeremy Levesley and Marco
                 Marletta",
  title =        "The Graduate Student's Guide to Numerical Analysis
                 '98: Lecture Notes from the {VIII EPSRC Summer School
                 in Numerical Analysis}",
  volume =       "26",
  publisher =    pub-SPRINGER,
  address =      pub-SPRINGER:adr-B,
  pages =        "x + 250",
  year =         "1999",
  ISBN =         "3-540-65752-5 (hardcover)",
  ISBN-13 =      "978-3-540-65752-1 (hardcover)",
  ISSN =         "0179-3632",
  LCCN =         "QA 297 G67 1999",
  bibdate =      "Wed Nov 3 09:30:14 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "The Eighth EPSRC Numerical Analysis Summer School was
                 held at the University of Leicester from the 5th to the
                 17th of July, 1998.",
  series =       "Springer series in computational mathematics",
  acknowledgement = ack-nhfb,
  keywords =     "numerical analysis",
}

@Proceedings{Higham:1998:NAP,
  editor =       "D. J. (Desmond J.) Higham and G. A. Watson and D. F.
                 (David Francis) Griffiths",
  booktitle =    "{Numerical analysis 1997: Proceedings of the 17th
                 Dundee Biennial Conference, June 24--27, 1997}",
  title =        "{Numerical analysis 1997: proceedings of the 17th
                 Dundee Biennial Conference, June 24--27, 1997}",
  volume =       "380",
  publisher =    pub-LONGMAN-ST,
  address =      pub-LONGMAN-ST:adr,
  pages =        "254",
  year =         "1998",
  ISBN =         "0-582-31261-2 (paperback)",
  ISBN-13 =      "978-0-582-31261-6 (paperback)",
  ISSN =         "0269-3674",
  LCCN =         "QA297 .D85 1997",
  bibdate =      "Tue Jan 3 15:19:05 MST 2006",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "Pitman Research Notes in Mathematics",
  acknowledgement = ack-nhfb,
  meetingname =  "Dundee Conference on Numerical Analysis (17th: 1997)",
  subject =      "Numerical analysis; Congresses",
}

@Proceedings{Higham:2001:PEC,
  editor =       "Nicholas J. Higham and Roger Horn and Thomas J.
                 Laffey",
  booktitle =    "Proceedings of the {Eighth Conference of the
                 International Linear Algebra Society}",
  title =        "Proceedings of the {Eighth Conference of the
                 International Linear Algebra Society}",
  publisher =    pub-ELS,
  address =      pub-ELS:adr,
  pages =        "x--xii + 1--609",
  year =         "2001",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  MRclass =      "00B25 (15-06)",
  MRnumber =     "MR1839422",
  bibdate =      "Sat Apr 16 17:55:00 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
  note =         "Held at the Universitat Politecnica de Catalunya,
                 Barcelona, July 19--22, 1999, Linear Algebra Appl. {\bf
                 332/334} (2001)",
  acknowledgement = ack-nhfb,
}

@Proceedings{Brown:2007:PIS,
  editor =       "C. W. Brown",
  booktitle =    "{Proceedings of the 2007 International Symposium on
                 Symbolic and Algebraic Computation, July 29--August 1,
                 2007, University of Waterloo, Waterloo, Ontario,
                 Canada}",
  title =        "{Proceedings of the 2007 International Symposium on
                 Symbolic and Algebraic Computation, July 29--August 1,
                 2007, University of Waterloo, Waterloo, Ontario,
                 Canada}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "????",
  year =         "2007",
  ISBN =         "1-59593-743-9 (print), 1-59593-742-0 (CD-ROM)",
  ISBN-13 =      "978-1-59593-743-8 (print), 978-1-59593-742-1
                 (CD-ROM)",
  LCCN =         "QA76.5 S98 2007",
  bibdate =      "Fri Jun 20 08:53:37 2008",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/axiom.bib;
                 https://www.math.utah.edu/pub/tex/bib/issac.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  note =         "ACM order number 505070.",
  acknowledgement = ack-nhfb,
}

@Book{Chan:2007:MMC,
  editor =       "Raymond H. Chan and Chen Greif and Dianne P. O'Leary",
  booktitle =    "Milestones in Matrix Computation: the Selected Works
                 of {Gene H. Golub} with Commentaries",
  title =        "Milestones in Matrix Computation: the Selected Works
                 of {Gene H. Golub} with Commentaries",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xi + 565 + 3",
  year =         "2007",
  ISBN =         "0-19-920681-3",
  ISBN-13 =      "978-0-19-920681-0",
  LCCN =         "QA188 .G67 2007",
  MRclass =      "65-06 (01A75 65Fxx)",
  MRnumber =     "MR2281939 (2008b:65004)",
  MRreviewer =   "David Scott Watkins",
  bibdate =      "Sat Apr 07 10:23:33 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib;
                 https://www.math.utah.edu/pub/tex/bib/technometrics1970.bib",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0737/2007276086-d.html",
  abstract =     "The text presents and discusses some of the most
                 influential papers in Matrix Computation authored by
                 Gene H. Golub, one of the founding fathers of the
                 field. The collection of 21 papers in divided into five
                 main areas: iterative methods for linear systems,
                 solution of least squares problems, matrix
                 factorizations and applications, orthogonal polynomials
                 and quadrature, and eigenvalue problems an commentaries
                 for each area are provided by leading experts: Anne
                 Greenbaum, {\AA}ke Bj{\"o}rck, Nicholas Higham, Walter
                 Gautschi, and G. W. (Pete) Stewart. Comments on each
                 paper are also provided by the original authors,
                 providing the reader with historical information on how
                 the paper came to be written and under what
                 circumstances the collaboration was undertaken.
                 Including a brief biography and facsimiles of the
                 original papers, this text will be of great interest to
                 students and researchers in numerical analysis and
                 scientific computation.",
  acknowledgement = ack-nhfb,
  tableofcontents = "List of Plates / x \\
                 I: Gene H. Golub \\
                 1 Gene H. Golub Biography, by Chen Greif / 3 \\
                 2 Publications of Gene H. Golub / 13 \\
                 3 Major Awards / 30 \\
                 4 Students of Gene H. Golub / 32 \\
                 II: Iterative Methods for Linear Systems \\
                 5 Commentary, by Anne Greenbaum / 35 \\
                 References / 43 \\
                 6 Chebyshev semi-iterative methods, successive
                 over-relaxation iterative methods, and second-order
                 Richardson iterative methods, Parts I and II (with R.
                 S. Varga) / 45 \\
                 7 A generalized conjugate gradient method for
                 non-symmetric systems of linear equations (with Paul
                 Concus) / 68 \\
                 8 A generalized conjugate gradient method for the
                 numerical solution of elliptic partial differential
                 equations (with Paul Concus and Dianne P. O'Leary) / 79
                 \\
                 9 Hermitian and Skew-Hermitian Splitting Methods for
                 Non-Hermitian Positive Definite Linear Systems (with
                 Zhong-Zhi Bai and Michael K. Ng) / 102 \\
                 III: Solution of Least Squares Problems \\
                 10 Commentary, by {\AA}ke Bj{\"o}rck / 129 \\
                 References / 141 \\
                 11 Numerical methods for solving linear least squares
                 problems / 148 \\
                 12 Singular value decomposition and least squares
                 solutions (with C. Reinsch) / 160 \\
                 13 The differentiation of pseudo-inverses and
                 non-linear least squares problems whose variables
                 separate (with V. Pereyra) / 181 \\
                 14 Generalized cross-validation as a method for
                 choosing a good ridge parameter (with M. Heath and G.
                 Wahba) / 202 \\
                 15 An analysis of the total least squares problem (with
                 C. Van Loan) / 213 \\
                 IV: Matrix Factorizations and Applications \\
                 16 Commentary, by Nicholas Higham / 227 \\
                 References / 233 \\
                 17 Calculating the singular values and pseudo-inverse
                 of a matrix (with W. Kahan) / 236 \\
                 18 The simplex method of linear programming using $ L U
                 $ decomposition (with R. H. Bartels) / 257 \\
                 19 On direct methods for solving Poisson's equation
                 (with B. L. Buzbee and C. W. Nielson) / 261 \\
                 20 Numerical methods for computing angles between
                 linear subspaces (with {\AA}. Bj{\"o}rck) / 292 \\
                 21 Methods for modifying matrix factorizations (with P.
                 E. Gill, W. Murray and M. A. Saunders) / 309 \\
                 V: Orthogonal Polynomials and Quadrature \\
                 22 Commentary, by Walter Gautschi / 345 \\
                 References / 354 \\
                 23 Calculation of Gauss quadrature rules (with J. H.
                 Welsch) / 359 \\
                 24 Matrices, moments, and quadrature (with G{\'e}rard
                 Meurant) / 380 \\
                 25 Computation of Gauss--Kronrod Quadrature Rules (with
                 D. Calvetti, W. B. Gragg and L. Reichel) / 434 \\
                 VI: Eigenvalue Problems \\
                 26 Commentary, by G. W. Stewart / 457 \\
                 References / 465 \\
                 27 Some modified matrix eigenvalue problems / 467 \\
                 28 Ill-conditioned eigensystems and the computation of
                 the Jordan canonical form (with J. H. Wilkinson) / 485
                 \\
                 29 The block Lanczos method for computing eigenvalues
                 (with R. Underwood) / 528 \\
                 30 The numerically stable reconstruction of a Jacobi
                 matrix from spectral data (with C. de Boor) / 546 Index
                 / 563",
}

@Book{Hogben:2007:HLA,
  editor =       "Leslie Hogben",
  booktitle =    "Handbook of Linear Algebra",
  title =        "Handbook of Linear Algebra",
  publisher =    pub-CHAPMAN-HALL-CRC,
  address =      pub-CHAPMAN-HALL-CRC:adr,
  pages =        "xxx + 1370",
  year =         "2007",
  ISBN =         "1-58488-510-6 (hardcover), 1-4200-1057-3 (e-book)",
  ISBN-13 =      "978-1-58488-510-8 (hardcover), 978-1-4200-1057-2
                 (e-book)",
  LCCN =         "QA184.2 .H36 2007",
  MRclass =      "15-00 (00A20)",
  MRnumber =     "2279160 (2007j:15001)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2000.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Associate editors: Richard Brualdi, Anne Greenbaum and
                 Roy Mathias.",
  series =       "Discrete Mathematics and its Applications (Boca
                 Raton)",
  URL =          "http://www.crcnetbase.com/isbn/9781420010572;
                 http://www.crcnetbase.com/isbn/9781584885108;
                 http://www.loc.gov/catdir/enhancements/fy0647/2006045491-d.html",
  abstract =     "\booktitle{Handbook of Linear Algebra} covers all
                 aspects of linear algebra, including fundamentals,
                 numerical linear algebra, software packages for
                 computation in linear algebra, and various
                 applications, such as quantum computing, control
                 theory, image compression, and computational biology.
                 The author addresses combinatorial Matrix theory and
                 features Matrix notation throughout the text. The book
                 includes a chapter on software that provides extensive
                 coverage of MATLAB, Maple, and Mathematica and contains
                 details of Fortran subroutines available for linear
                 algebra such as LAPACK and ARPACK. Rather than
                 presenting long mathematical proofs, the text provides
                 numerous references for additional information.",
  acknowledgement = ack-nhfb # " and " # ack-rah,
  keywords =     "Maple",
  remark =       "Associate editors: Richard Brualdi, Anne Greenbaum,
                 and Roy Mathias.",
  subject =      "Algebras, Linear",
  tableofcontents = "Preliminaries \\
                 I. Linear algebra \\
                 1: Vectors, matrices and systems of linear equations /
                 Jane Day \\
                 2: Linear independence, span, and bases / Mark Mills
                 \\
                 3: Linear transformations / Francesco Barioli \\
                 4: Determinants and eigenvalues / Luz M. DeAlba \\
                 5: Inner product spaces, orthogonal projection, least
                 squares and singular value decomposition / Lixing Han
                 and Michael Neumann \\
                 6: Canonical forms / Leslie Hogben \\
                 7: Unitary similarity, normal matrices, and spectral
                 theory / Helene Shapiro \\
                 8: Hermitian and positive definite matrices / Wayne
                 Barrett \\
                 9: Nonnegative and stochastic matrices / Uriel G.
                 Rothblum \\
                 10: Partitioned matrices / Robert Reams \\
                 11: Functions of matrices / Nicholas J. Higham \\
                 12: Quadratic, bilinear and sesquilinear forms /
                 Raphael Lowey \\
                 13: Multilinear algebra / J. A. Dias de Silva and
                 Armando Machado \\
                 14: Matrix equalities and inequalities / Michael
                 Tsatsomeros \\
                 15: Matrix perturbation theory / Ren-Cang Li \\
                 16: Pseudospectra / Mark Embree \\
                 17: Singular values and singular value inequalities /
                 Roy Mathias \\
                 18: Numerical range / Chi-Kwong Li \\
                 19: Matrix stability and inertia / Daniel Hershkowitz
                 \\
                 20: Inverse eigenvalue problems / Alberto Borobia \\
                 21: Totally positive and totally negative matrices /
                 Shaun M. Fallat \\
                 22: Linear preserver problems / Peter \v Semrl \\
                 23: Matrices over integral domains / Shmuel Friedland
                 \\
                 24: Similarities of families of matrices / Shmuel
                 Friedland \\
                 25: Max-plus algebra / Marianne Akian, Ravindra Bapat,
                 St{\'e}phane Gaubert \\
                 26: Matrices leaving a cone invariant / Bit-Shun Tam
                 and Hans Schneider \\
                 II. Combinatorial matrix theory and graphs \\
                 27: Combinatorial matrix theory / Richard A. Brualdi
                 \\
                 28: Matrices and graphs / Willem H. Haemers \\
                 29: Digraphs and matrices / Jeffrey L. Stuart \\
                 30: Bipartite graphs and matrices / Bryan L. Shader \\
                 31: Permanents / Ian M. Wanless \\
                 32: D-optimal designs / Michael G. Neubauer and William
                 Watkins \\
                 33: Sign pattern matrices / Frank J. Hall and Zhongshan
                 Li \\
                 34: Multiplicity lists for the eigenvalues of symmetric
                 matrices with a given graph / Charles R. Johnson,
                 Ant{\'o}nio Leal Duarte, and Carlos M. Saiago \\
                 35: Matrix completion problems / Leslie Hogben and Amy
                 Wangsness \\
                 36: Algebraic connectivity / Steve Kirkland \\
                 III. Numerical methods \\
                 37: Vector and matrix norms, error analysis, efficiency
                 and stability / Ralph Byers and Biswa Nath Datta \\
                 38: Matrix factorizations, and direct solution of
                 linear systems / Christopher Beattie \\
                 39: Least squares solution of linear systems / Per
                 Christian Hansen and Hans Bruun Nielsen \\
                 40: Sparse matrix methods / Esmond G. Ng \\
                 41: Iterative solution methods for linear systems /
                 Anne Greenbaum \\
                 42: Symmetric matrix eigenvalue techniques / Ivan
                 Slapni\v car \\
                 43: Unsymmetric matrix eigenvalue techniques / David S.
                 Watkins \\
                 44: The implicitly restarted Arnoldi method / D. C.
                 Sorensen \\
                 45: Computation of the singular value decomposition /
                 Alan Kaylor Cline and Inderjit S. Dhillon \\
                 46: Computing eigenvalues and singular values to high
                 relative accuracy / Zlatko Drma{\v{c}} \\
                 47: Fast matrix multiplication / Dario A. Bini \\
                 48: Structured matrix computations / Michael Ng \\
                 49: Large-scale matrix computations / Roland W. Freund
                 \\
                 IV. Applications \\
                 50: Linear programming / Leonid S. Vaserstein \\
                 51: Semidefinite programming / Henry Wolkowicz \\
                 52: Random vectors and linear statistical models / Simo
                 Puntanen and George P. H. Styan \\
                 53: Multivariate statistical analysis / Simo Puntanen,
                 George A. F. Seber, and George P. H. Styan \\
                 54: Markov chains / Beatrice Meini \\
                 55: Differential equations and stability / Volker
                 Mehrmann and Tatjana Stykel \\
                 56: Dynamical systems and linear algebra / Fritz
                 Colonius and Wolfgang Kliemann \\
                 57: Control theory / Peter Benner \\
                 58: Fourier analysis / Kenneth Howell \\
                 59: Linear algebra and mathematical physics / Lorenzo
                 Sadun \\
                 60: Linear algebra in biomolecular modeling / Zhijun Wu
                 \\
                 61: Coding theory / Joachim Rosenthal and Paul Weiner
                 \\
                 62: Quantum computation / Zijian Diao \\
                 63: Information retrieval and web search / Amy
                 Langville and Carl Meyer \\
                 64: Signal processing / Michael Stewart \\
                 65: Geometry / Mark Hunacek \\
                 66: Some applications of matrices and graphs in
                 Euclidean geometry / Miroslav Fiedler \\
                 67: Matrix groups / Peter J. Cameron \\
                 68: Group representations / Randall Holmes and T. Y.
                 Tam \\
                 69: Nonassociative algebras / Murray R. Bremner, Lucia
                 I. Muakami and Ivan P. Shestakov \\
                 70: Lie algebras / Robert Wilson \\
                 V. Computational software \\
                 71: METLAB / Steven J. Leon \\
                 72: Linear algebra in Maple / David J. Jeffrey and
                 Robert M. Corless \\
                 73: Mathematica / Heikki Ruskeep{\"a}{\"a} \\
                 74: BLAS / Jack Dongarra, Victor Eijkhout, and Julien
                 Langou \\
                 75: LAPACK / Zhaojun Bai \\
                 76: Use of ARPACK and EIGS / D. C. Sorensen \\
                 77: Summary of Software for Linear Algebra Freely
                 Available on the Web / Jack Dongarra, Victor Eijkhout,
                 Julien Langou \\
                 G-1: Glossary \\
                 H-1: Notation Index",
}

@Book{Higham:2015:PCA,
  editor =       "Nicholas J. Higham and Mark R. Dennis and Paul
                 Glendinning and Paul A. Martin and Fadil Santosa and
                 Jared Tanner",
  booktitle =    "The {Princeton} Companion to Applied Mathematics",
  title =        "The {Princeton} Companion to Applied Mathematics",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "xvii + 3 + 994 + 16",
  year =         "2015",
  ISBN =         "0-691-15039-7 (hardcover)",
  ISBN-13 =      "978-0-691-15039-0 (hardcover)",
  LCCN =         "QA155 .P75 2015",
  bibdate =      "Wed Sep 9 05:32:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/companion-applied-mathematics.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://press.princeton.edu/titles/10592.html",
  abstract =     "This is the most authoritative and accessible
                 single-volume reference book on applied mathematics.
                 Featuring numerous entries by leading experts and
                 organized thematically, it introduces readers to
                 applied mathematics and its uses; explains key
                 concepts; describes important questions, laws, and
                 functions; looks at exciting areas of research; covers
                 modeling and simulation; explores areas of application;
                 and more. Modeled on the popular Princeton Companion to
                 Mathematics, this volume is an indispensable resource
                 for undergraduate and graduate students, researchers,
                 and practitioners in other disciplines seeking a
                 user-friendly reference book on applied mathematics.",
  acknowledgement = ack-njh,
  subject =      "Algebra; Mathematics; Mathematical models",
  tableofcontents = "Preface / ix \\
                 Contributors / xiii \\
                 Part I: Introduction to Applied Mathematics \\
                 I.1 What Is Applied Mathematics? / 1 \\
                 I.2 The Language of Applied Mathematics / 8 \\
                 I.3 Methods of Solution / 27 \\
                 I.4 Algorithms / 40 \\
                 I.5 Goals of Applied Mathematical Research / 48 \\
                 I.6 The History of Applied Mathematics / 55 \\
                 Part II: Concepts \\
                 II.1 Asymptotics / 81 \\
                 II.2 Boundary Layer / 82 \\
                 II.3 Chaos and Ergodicity / 82 \\
                 II.4 Complex Systems / 83 \\
                 II.5 Conformal Mapping / 84 \\
                 II.6 Conservation Laws / 86 \\
                 II.7 Control / 88 \\
                 II.8 Convexity / 89 \\
                 II.9 Dimensional Analysis and Scaling / 90 \\
                 II.10 The Fast Fourier Transform / 94 \\
                 II.11 Finite Differences / 95 \\
                 II.12 The Finite-Element Method / 96 \\
                 II.13 Floating-Point Arithmetic / 96 \\
                 II.14 Functions of Matrices / 97 \\
                 II.15 Function Spaces / 99 \\
                 II.16 Graph Theory / 101 \\
                 II.17 Homogenization / 103 \\
                 II.18 Hybrid Systems / 103 \\
                 II.19 Integral Transforms and Convolution / 104 \\
                 II.20 Interval Analysis / 105 \\
                 II.21 Invariants and Conservation Laws / 106 \\
                 II.22 The Jordan Canonical Form / 112 \\
                 II.23 Krylov Subspaces / 113 \\
                 II.24 The Level Set Method / 114 \\
                 II.25 Markov Chains / 116 \\
                 II.26 Model Reduction / 117 \\
                 II.27 Multiscale Modeling / 119 \\
                 II.28 Nonlinear Equations and Newton's Method / 120 \\
                 II.29 Orthogonal Polynomials / 122 \\
                 II.30 Shocks / 122 \\
                 II.31 Singularities / 124 \\
                 II.32 The Singular Value Decomposition / 126 \\
                 II.33 Tensors and Manifolds / 127 \\
                 II.34 Uncertainty Quantification / 131 \\
                 II.35 Variational Principle / 134 \\
                 II.36 Wave Phenomena / 134 \\
                 Part III: Equations, Laws, and Functions of Applied
                 Mathematics \\
                 III.1 Benford's Law / 135 \\
                 III.2 Bessel Functions / 137 \\
                 III.3 The Black--Scholes Equation / 137 \\
                 III.4 The Burgers Equation / 138 \\
                 III.5 The Cahn--Hilliard Equation / 138 \\
                 III.6 The Cauchy--Riemann Equations / 139 \\
                 III.7 The Delta Function and Generalized Functions /
                 139 \\
                 III.8 The Diffusion Equation / 142 \\
                 III.9 The Dirac Equation / 142 \\
                 III.10 Einstein's Field Equations / 144 \\
                 III.11 The Euler Equations / 146 \\
                 III.12 The Euler--Lagrange Equations / 147 \\
                 III.13 The Gamma Function / 148 \\
                 III.14 The Ginzburg--Landau Equation / 148 \\
                 III.15 Hooke's Law / 149 \\
                 III.16 The Korteweg--de Vries Equation / 150 \\
                 III.17 The Lambert $W$ Function / 151 \\
                 III.18 Laplace's Equation / 155 \\
                 III.19 The Logistic Equation / 156 \\
                 III.20 The Lorenz Equations / 158 \\
                 III.21 Mathieu Functions / 159 \\
                 III.22 Maxwell's Equations / 160 \\
                 III.23 The Navier--Stokes Equations / 162 \\
                 III.24 The Painlev{\'e} Equations / 163 \\
                 III.25 The Riccati Equation / 165 \\
                 III.26 Schr{\"o}dinger's Equation / 167 \\
                 III.27 The Shallow-Water Equations / 167 \\
                 III.28 The Sylvester and Lyapunov Equations / 168 \\
                 III.29 The Thin-Film Equation / 169 \\
                 III.30 The Tricomi Equation / 170 \\
                 III.31 The Wave Equation / 171 \\
                 Part IV: Areas of Applied Mathematics \\
                 IV.1 Complex Analysis / 173 \\
                 IV.2 Ordinary Differential Equations / 181 \\
                 IV.3 Partial Differential Equations / 190 \\
                 IV.4 Integral Equations / 200 \\
                 IV.5 Perturbation Theory and Asymptotics / 208 \\
                 IV.6 Calculus of Variations / 218 \\
                 IV.7 Special Functions / 227 \\
                 IV.8 Spectral Theory / 236 \\
                 IV.9 Approximation Theory / 248 \\
                 IV.10 Numerical Linear Algebra and Matrix Analysis /
                 263 \\
                 IV.11 Continuous Optimization (Nonlinear and Linear
                 Programming) / 281 \\
                 IV.12 Numerical Solution of Ordinary Differential
                 Equations / 293 \\
                 IV.13 Numerical Solution of Partial Differential
                 Equations / 306 \\
                 IV.14 Applications of Stochastic Analysis / 319 \\
                 IV.15 Inverse Problems / 327 \\
                 IV.16 Computational Science / 335 \\
                 IV.17 Data Mining and Analysis / 350 \\
                 IV.18 Network Analysis / 360 \\
                 IV.19 Classical Mechanics / 374 \\
                 IV.20 Dynamical Systems / 383 \\
                 IV.21 Bifurcation Theory / 393 \\
                 IV.22 Symmetry in Applied Mathematics / 402 \\
                 IV.23 Quantum Mechanics / 411 \\
                 IV.24 Random-Matrix Theory / 419 \\
                 IV.25 Kinetic Theory / 428 \\
                 IV.26 Continuum Mechanics / 446 \\
                 IV.27 Pattern Formation / 458 \\
                 IV.28 Fluid Dynamics / 467 \\
                 IV.29 Magnetohydrodynamics / 476 \\
                 IV.30 Earth System Dynamics / 485 \\
                 IV.31 Effective Medium Theories / 500 \\
                 IV.32 Mechanics of Solids / 505 \\
                 IV.33 Soft Matter / 516 \\
                 IV.34 Control Theory / 523 \\
                 IV.35 Signal Processing / 533 \\
                 IV.36 Information Theory / 545 \\
                 IV.37 Applied Combinatorics and Graph Theory / 552 \\
                 IV.38 Combinatorial Optimization / 564 \\
                 IV.39 Algebraic Geometry / 570 \\
                 IV.40 General Relativity and Cosmology / 579 \\
                 Part V: Modeling \\
                 V.1 The Mathematics of Adaptation (Or the Ten Avatars
                 of Vishnu) / 591 \\
                 V.2 Sport / 598 \\
                 V.3 Inerters / 604 \\
                 V.4 Mathematical Biomechanics / 609 \\
                 V.5 Mathematical Physiology / 616 \\
                 V.6 Cardiac Modeling / 623 \\
                 V.7 Chemical Reactions / 627 \\
                 V.8 Divergent Series: Taming the Tails / 634 \\
                 V.9 Financial Mathematics / 640 \\
                 V.10 Portfolio Theory / 648 \\
                 V.11 Bayesian Inference in Applied Mathematics / 658
                 \\
                 V.12 A Symmetric Framework with Many Applications / 661
                 \\
                 V.13 Granular Flows / 665 \\
                 V.14 Modern Optics / 673 \\
                 V.15 Numerical Relativity / 680 \\
                 V.16 The Spread of Infectious Diseases / 687 \\
                 V.17 The Mathematics of Sea Ice / 694 \\
                 V.18 Numerical Weather Prediction / 705 \\
                 V.19 Tsunami Modeling / 712 \\
                 V.20 Shock Waves / 720 \\
                 V.21 Turbulence / 724 \\
                 Part VI: Example Problems \\
                 VI.1 Cloaking / 733 \\
                 VI.2 Bubbles / 735 \\
                 VI.3 Foams / 737 \\
                 VI.4 Inverted Pendulums / 741 \\
                 VI.5 Insect Flight / 743 \\
                 VI.6 The Flight of a Golf Ball / 746 \\
                 VI.7 Automatic Differentiation / 749 \\
                 VI.8 Knotting and Linking of Macromolecules / 752 \\
                 VI.9 Ranking Web Pages / 755 \\
                 VI.10 Searching a Graph / 757 \\
                 VI.11 Evaluating Elementary Functions / 759 \\
                 VI.12 Random Number Generation / 761 \\
                 VI.13 Optimal Sensor Location in the Control of
                 Energy-Efficient Buildings / 763 \\
                 VI.14 Robotics / 767 \\
                 VI.15 Slipping, Sliding, Rattling, and Impact:
                 Nonsmooth Dynamics and Its Applications / 769 \\
                 VI.16 From the $N$-Body Problem to Astronomy and Dark
                 Matter / 771 \\
                 VI.17 The $N$-Body Problem and the Fast Multipole
                 Method / 775 \\
                 VI.18 The Traveling Salesman Problem / 778 \\
                 Part VII: Application Areas \\
                 VII.1 Aircraft Noise / 783 \\
                 VII.2 A Hybrid Symbolic--Numeric Approach to Geometry
                 Processing and Modeling / 787 \\
                 VII.3 Computer-Aided Proofs via Interval Analysis / 790
                 \\
                 VII.4 Applications of Max-Plus Algebra / 795 \\
                 VII.5 Evolving Social Networks, Attitudes, and Beliefs
                 --- and Counterterrorism / 800 \\
                 VII.6 Chip Design / 804 \\
                 VII.7 Color Spaces and Digital Imaging / 808 \\
                 VII.8 Mathematical Image Processing / 813 \\
                 VII.9 Medical Imaging / 816 \\
                 VII.10 Compressed Sensing / 823 \\
                 VII.11 Programming Languages: An Applied Mathematics
                 View / 828 \\
                 VII.12 High-Performance Computing / 839 \\
                 VII.13 Visualization / 843 \\
                 VII.14 Electronic Structure Calculations (Solid State
                 Physics) / 847 \\
                 VII.15 Flame Propagation / 852 \\
                 VII.16 Imaging the Earth Using Green's Theorem / 857
                 \\
                 VII.17 Radar Imaging / 860 \\
                 VII.18 Modeling a Pregnancy Testing Kit / 864 \\
                 VII.19 Airport Baggage Screening with X-Ray Tomography
                 / 866 \\
                 VII.20 Mathematical Economics / 868 \\
                 VII.21 Mathematical Neuroscience / 873 \\
                 VII.22 Systems Biology / 879 \\
                 VII.23 Communication Networks / 883 \\
                 VII.24 Text Mining / 887 \\
                 VII.25 Voting Systems / 891 \\
                 Part VIII: Final Perspectives \\
                 VIII.1 Mathematical Writing / 897 \\
                 VIII.2 How to Read and Understand a Paper / 903 \\
                 VIII.3 How to Write a General Interest Mathematics Book
                 / 906 \\
                 VIII.4 Workflow / 912 \\
                 VIII.5 Reproducible Research in the Mathematical
                 Sciences / 916 \\
                 VIII.6 Experimental Applied Mathematics / 925 \\
                 VIII.7 Teaching Applied Mathematics / 933 \\
                 VIII.8 Mediated Mathematics: Representations of
                 Mathematics in Popular Culture and Why These Matter /
                 943 \\
                 VIII.9 Mathematics and Policy / 953 \\
                 Index / 963",
}

@Proceedings{Burgess:2017:ISC,
  editor =       "Neil Burgess and Javier Bruguera and Florent de
                 Dinechin",
  booktitle =    "{24th IEEE Symposium on Computer Arithmetic (ARITH
                 24), London, UK, 24--26 July 2017}",
  title =        "{2017 IEEE 24th Symposium on Computer Arithmetic
                 (ARITH 24), London, UK, 24--26 July 2017}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 198",
  year =         "2017",
  ISBN =         "1-5386-1966-0 (print), 1-5386-1965-2, 1-5386-1964-4",
  ISBN-13 =      "978-1-5386-1966-7 (print), 978-1-5386-1965-0,
                 978-1-5386-1964-3",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 2017",
  bibdate =      "Fri Nov 17 10:14:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib",
  URL =          "http://ieeexplore.ieee.org/servlet/opac?punumber=8019911",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic units; correctness proofs;
                 cryptography; domain specific designs; error analysis;
                 exascale computing; floating point arithmetic;
                 floating-point error analysis; formal verification;
                 function approximation; modular arithmetic; theorem
                 proving; verification",
}

@Article{Sukkari:2019:QBS,
  author =       "Dalal Sukkari and Hatem Ltaief and Aniello Esposito
                 and David Keyes",
  title =        "A {QDWH}-based {SVD} Software Framework on
                 Distributed-memory Manycore Systems",
  journal =      j-TOMS,
  volume =       "45",
  number =       "2",
  pages =        "18:1--18:21",
  month =        apr,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3309548",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Nakatsukasa:2013:SES}.",
  URL =          "https://dl.acm.org/citation.cfm?id=3309548",
  abstract =     "This article presents a high-performance software
                 framework for computing a dense SVD on
                 distributed-memory manycore systems. Originally
                 introduced by Nakatsukasa et al. (2010) and Nakatsukasa
                 and Higham (2013), the SVD solver relies on the polar
                 decomposition using the QR Dynamically Weighted Halley
                 algorithm (QDWH). Although the QDWH-based SVD algorithm
                 performs a significant amount of extra floating-point
                 operations compared to the traditional SVD with the
                 one-stage bidiagonal reduction, the inherent high level
                 of concurrency associated with Level 3 BLAS
                 compute-bound kernels ultimately compensates for the
                 arithmetic complexity overhead. Using the ScaLAPACK
                 two-dimensional block cyclic data distribution with a
                 rectangular processor topology, the resulting QDWH-SVD
                 further reduces excessive communications during the
                 panel factorization, while increasing the degree of
                 parallelism during the update of the trailing
                 submatrix, as opposed to relying on the default square
                 processor grid. After detailing the algorithmic
                 complexity and the memory footprint of the algorithm,
                 we conduct a thorough performance analysis and study
                 the impact of the grid topology on the performance by
                 looking at the communication and computation profiling
                 trade-offs. We report performance results against
                 state-of-the-art existing QDWH software implementations
                 (e.g., Elemental) and their SVD extensions on
                 large-scale distributed-memory manycore systems based
                 on commodity Intel x86 Haswell processors and Knights
                 Landing (KNL) architecture. The QDWH-SVD framework
                 achieves up to 3/8-fold speedups on the
                 Haswell/KNL-based platforms, respectively, against
                 ScaLAPACK PDGESVD and turns out to be a competitive
                 alternative for well- and ill-conditioned matrices. We
                 finally come up herein with a performance model based
                 on these empirical results. Our QDWH-based polar
                 decomposition and its SVD extension are freely
                 available at https://github.com/ecrc/qdwh.git and
                 https://github.com/ecrc/ksvd.git, respectively, and
                 have been integrated into the Cray Scientific numerical
                 library LibSci v17.11.1.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

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