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@String{ack-nhfb = "Nelson H. F. Beebe,
Department of Mathematics,
University of Utah,
Salt Lake City, UT 84112, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|"}
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@MastersThesis{Trefethen:1977:CAP,
author = "Lloyd N. Trefethen",
title = "{Chebyshev} Approximation by Polynomials in the
Complex Plane",
type = "{Undergraduate} thesis",
school = "Harvard University",
address = "Cambridge, MA, USA",
month = may,
year = "1977",
bibdate = "Tue Jan 03 15:36:24 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Bolstad:1979:NAP,
author = "J. H. Bolstad and T. F. Chan and W. M. {Coughran, Jr.}
and W. D. Gropp and E. H. Grosse and M. T. Heath and R.
J. LeVeque and F. T. Luk and S. G. Nash and L. N.
Trefethen",
title = "Numerical Analysis Program Library User's Guide
{(NAPLUG)}",
type = "User Note",
number = "82",
institution = "SLAC Computing Services",
address = "Stanford, CA, USA",
year = "1979",
bibdate = "Wed Aug 24 16:01:44 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/coughran-william-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "First issued in 1976 by Chan, Coughran, Heath, and
Luk",
acknowledgement = ack-nhfb,
}
@InProceedings{Trefethen:1980:CAS,
author = "Lloyd N. Trefethen",
title = "Computation and application of {Schwarz--Christoffel}
transformations",
crossref = "Anonymous:1980:PAN",
volume = "3",
pages = "165--171",
year = "1980",
MRclass = "30C30 (65E05)",
MRnumber = "MR601632 (82d:30012)",
MRreviewer = "D. Gaier",
bibdate = "Sat Dec 9 12:43:58 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
ZMnumber = "0485.30007",
acknowledgement = ack-nhfb,
classmath = "*30C30 Numerical methods in conformal mapping theory
65E05 Numerical methods in complex analysis",
keywords = "applications to fluids and electrical problems;
computation and application of Schwarz--Christoffel
transformations; numerical conformal mapping",
}
@Article{Trefethen:1980:ENC,
author = "Lloyd N. Trefethen",
title = "Erratum: {``Numerical computation of the
Schwarz--Christoffel transformation''}",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "1",
number = "2",
pages = "302",
year = "1980",
CODEN = "SIJCD4",
ISSN = "0196-5204",
MRclass = "30C30 (65E05)",
MRnumber = "MR594762 (81g:30012b)",
MRreviewer = "N. Papamichael",
bibdate = "Sat Dec 9 12:44:53 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "See \cite{Trefethen:1980:NCS}.",
acknowledgement = ack-nhfb,
fjournal = "Society for Industrial and Applied Mathematics.
Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sjoce3",
}
@Article{Trefethen:1980:NCS,
author = "Lloyd N. Trefethen",
title = "Numerical computation of the {Schwarz--Christoffel}
transformation",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "1",
number = "1",
pages = "82--102",
year = "1980",
CODEN = "SIJCD4",
ISSN = "0196-5204",
MRclass = "30C30 (65E05)",
MRnumber = "MR572542 (81g:30012a)",
MRreviewer = "N. Papamichael",
bibdate = "Sat Dec 9 12:46:25 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "See erratum \cite{Trefethen:1980:ENC}.",
ZMnumber = "0451.30004",
acknowledgement = ack-nhfb,
fjournal = "Society for Industrial and Applied Mathematics.
Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sjoce3",
keywords = "conformal mapping of polygons; Schwarz--Christoffel
transformation",
}
@InProceedings{Trefethen:1981:CAS,
author = "Lloyd N. Trefethen",
title = "Computer application of the {Schwarz--Christoffel}
transformation",
crossref = "Butzer:1981:BCI",
pages = "263--274",
year = "1981",
MRclass = "65E05 (30C30 65F15 65H10 65L05)",
MRnumber = "MR661071 (83f:65036)",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
ZMnumber = "0476.30007",
classmath = "*30C30 Numerical methods in conformal mapping theory",
keywords = "numerical conformal mapping; Schwarz--Christoffel
transformation",
}
@Article{Trefethen:1981:NCC,
author = "Lloyd N. Trefethen",
title = "Near-circularity of the curve in complex {Chebyshev}
approximation",
journal = j-J-APPROX-THEORY,
volume = "31",
number = "4",
pages = "344--367",
year = "1981",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "41A10 (30E10 65E05)",
MRnumber = "MR628517 (83e:41011)",
MRreviewer = "Hans-Peter Blatt",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
xxtitle = "Near-circularity of the error curve in complex
{Chebyshev} approximation",
}
@Article{Trefethen:1981:NCE,
author = "Lloyd N. Trefethen",
title = "Near-circularity of the error curve in complex
{Chebyshev} approximation",
journal = j-J-APPROX-THEORY,
volume = "31",
number = "4",
pages = "344--367",
year = "1981",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Sat Dec 9 12:47:02 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
ZMnumber = "0462.41004",
acknowledgement = ack-nhfb,
classmath = "*41A10 Approximation by polynomials 30E10
Approximation in the complex domain 41A50 Best
approximation 41A20 Approximation by rational
functions",
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
keywords = "error curve; near-circularity phenomenon",
}
@Article{Trefethen:1981:RCA,
author = "Lloyd N. Trefethen",
title = "Rational {Chebyshev} approximation on the unit disk",
journal = j-NUM-MATH,
volume = "37",
number = "2",
pages = "297--320",
year = "1981",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "30E10 (41A50 65D15)",
MRnumber = "MR623046 (83c:30038)",
MRreviewer = "Volker Klotz",
bibdate = "Sat Dec 9 12:47:16 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
ZMnumber = "0443.30046",
acknowledgement = ack-nhfb,
classmath = "*30E10 Approximation in the complex domain 30D50
Blaschke products, etc. 41A50 Best approximation",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "rational Chebyshev approximation on unit disk",
}
@Article{Gutknecht:1982:RPC,
author = "Martin H. Gutknecht and Lloyd N. Trefethen",
title = "Real polynomial {Chebyshev} approximation by the
{Carath`eodory--Fej{\'e}r} method",
journal = j-SIAM-J-NUMER-ANAL,
volume = "19",
number = "2",
pages = "358--371",
month = apr,
year = "1982",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "41A10 (41A50)",
MRnumber = "MR650056 (83d:41006)",
MRreviewer = "Jean Tzimbalario",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
JSTOR database",
ZMnumber = "0491.41026",
acknowledgement = ack-nhfb,
classmath = "*41A50 Best approximation 41A10 Approximation by
polynomials",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "Caratheodory-Fejer theorem; complex Chebyshev
approximation; Hankel matrix of Taylor coefficients",
}
@Article{Trefethen:1982:GVF,
author = "Lloyd N. Trefethen",
title = "Group Velocity in Finite Difference Schemes",
journal = j-SIAM-REVIEW,
volume = "24",
number = "2",
pages = "113--136",
month = apr,
year = "1982",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1024038",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65P05 (76-08)",
MRnumber = "MR652463 (83b:65141)",
bibdate = "Sat Mar 29 09:53:27 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/24/2;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
ZMnumber = "0487.65055",
acknowledgement = ack-nhfb,
classmath = "*65N12 Stability and convergence of numerical methods
(BVP of PDE) 35L05 Wave equation 35L20 Second order
hyperbolic equations, boundary value problems 35L50
First order hyperbolic systems, boundary value problems
35L65 Conservation laws 65N06 Finite difference methods
(BVP of PDE) 76B15 Wave motions (fluid mechanics)",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "computational examples; group velocity; Lax- Wendroff;
motion of parasitic waves; nondissipative, linear
waves; numerically-induced anisotropy of waves; phase
velocity; propagation of pulses; stability theory",
onlinedate = "April 1982",
}
@PhdThesis{Trefethen:1982:WPS,
author = "Lloyd Nicholas Trefethen",
title = "Wave Propagation and Stability for Finite Difference
Schemes",
type = "{Ph.D.} thesis",
school = "Stanford University",
address = "Stanford, CA, USA",
pages = "208",
year = "1982",
bibdate = "Tue Jan 03 11:48:14 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Gutknecht:1983:CFM,
author = "Martin H. Gutknecht and Julius O. Smith and Lloyd N.
Trefethen",
title = "The {Carath{\'e}odory--Fej{\'e}r} method for recursive
digital filter design",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "31",
number = "6",
pages = "1417--1426",
month = "????",
year = "1983",
CODEN = "IETABA",
DOI = "https://doi.org/10.1109/TASSP.1983.1164242",
ISSN = "0096-3518",
bibdate = "Tue Mar 5 11:28:54 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1164242",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
}
@Article{Gutknecht:1983:NBR,
author = "Martin H. Gutknecht and Lloyd N. Trefethen",
title = "Nonuniqueness of best rational {Chebyshev}
approximations on the unit disk",
journal = j-J-APPROX-THEORY,
volume = "39",
number = "3",
pages = "275--288",
year = "1983",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "30E10 (41A20)",
MRnumber = "MR720942 (85d:30056)",
MRreviewer = "Hans-Peter Blatt",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
}
@Article{Gutknecht:1983:RCC,
author = "Martin H. Gutknecht and Lloyd N. Trefethen",
title = "Real and complex {Chebyshev} approximation on the unit
disk and interval",
journal = j-BULL-AMS-N-S,
volume = "8",
number = "3",
pages = "455--458",
year = "1983",
CODEN = "BAMOAD",
ISSN = "0273-0979 (print), 1088-9485 (electronic)",
ISSN-L = "0273-0979",
MRclass = "30E10 (41A20)",
MRnumber = "MR693961 (84d:30068)",
MRreviewer = "Jean Tzimbalario",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://projecteuclid.org/euclid.bams/1183550890",
fjournal = "American Mathematical Society. Bulletin. New Series",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
}
@InProceedings{Trefethen:1983:CAU,
author = "Lloyd N. Trefethen",
title = "{Chebyshev} approximation on the unit disk",
crossref = "Werner:1983:CAC",
pages = "309--323",
year = "1983",
MRclass = "65D15 (30E10)",
MRnumber = "MR712902 (84k:65017)",
bibdate = "Sat Dec 09 12:15:45 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Trefethen:1983:CEC,
author = "Lloyd N. Trefethen",
title = "Circularity of the error curve and sharpness of the
{CF} method in complex {Chebyshev} approximation",
journal = j-SIAM-J-NUMER-ANAL,
volume = "20",
number = "6",
pages = "1258--1263",
month = dec,
year = "1983",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "41A20 (30E10 65D15)",
MRnumber = "MR723844 (85f:41011)",
MRreviewer = "D. S. Lubinsky",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
JSTOR database",
ZMnumber = "0551.41042",
acknowledgement = ack-nhfb,
classmath = "*41A50 Best approximation 30E10 Approximation in the
complex domain",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "Carath{\'e}odory--Fej{\'e}r method; near-circularity;
rational Chebyshev approximation problem",
reviewer = "D. N. Zarnadze",
}
@Article{Trefethen:1983:CFM,
author = "Lloyd N. Trefethen and Martin H. Gutknecht",
title = "The {Carath{\'e}odory--Fej{\'e}r} method for real
rational approximation",
journal = j-SIAM-J-NUMER-ANAL,
volume = "20",
number = "2",
pages = "420--436",
month = apr,
year = "1983",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "41A20 (41A50)",
MRnumber = "MR694530 (85g:41024)",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Trefethen:1983:GVI,
author = "Lloyd N. Trefethen",
title = "Group velocity interpretation of the stability theory
of {Gustafsson}, {Kreiss}, and {Sundstr{\"o}m}",
journal = j-J-COMPUT-PHYS,
volume = "49",
number = "2",
pages = "199--217",
month = feb,
year = "1983",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(83)90123-7",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
MRclass = "65M10 (76-08)",
MRnumber = "MR699214 (84e:65096)",
bibdate = "Sun Jan 1 15:59:14 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999183901237",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Trefethen:1983:NBR,
author = "Lloyd N. Trefethen and M. H. Gutknecht",
title = "Nonuniqueness of best rational {Chebyshev}
approximations on the unit disk",
journal = j-J-APPROX-THEORY,
volume = "39",
number = "3",
pages = "275--288",
year = "1983",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Sat Dec 9 12:50:20 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
}
@Article{Trefethen:1983:RCCa,
author = "Lloyd N. Trefethen and M. H. Gutknecht",
title = "Real and complex {Chebyshev} approximation on the unit
disk and interval",
journal = j-BULL-AMS,
volume = "8",
number = "3",
pages = "455--458",
year = "1983",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Sat Dec 9 12:50:32 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
}
@InProceedings{Trefethen:1983:RCCb,
author = "Lloyd N. Trefethen and Martin H. Gutknecht",
title = "Real and complex {Chebyshev} approximation on the unit
disk and interval",
crossref = "Chui:1983:ATI",
pages = "712--722",
year = "1983",
MRclass = "41A50 (30E10)",
MRnumber = "MR754419",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
ZMnumber = "0557.41020",
classmath = "41A50 Best approximation; 30E10 Approximation in the
complex domain",
}
@Article{Trefethen:1983:RVC,
author = "Lloyd N. Trefethen and Martin H. Gutknecht",
title = "Real vs. complex rational {Chebyshev} approximation on
an interval",
journal = j-TRANS-AM-MATH-SOC,
volume = "280",
number = "2",
pages = "555--561",
year = "1983",
CODEN = "TAMTAM",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "41A25 (41A50)",
MRnumber = "MR716837 (85h:41045)",
bibdate = "Sat Dec 9 12:50:47 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
}
@Article{Duffy:1984:PSA,
author = "L. Richard Duffy and L. E. Mattics and Randall J.
LeVeque and Lloyd N. Trefethen",
title = "Problems and Solutions: Advanced Problems:
6460--6462",
journal = j-AMER-MATH-MONTHLY,
volume = "91",
number = "6",
pages = "371--371",
month = jun # "\slash " # jul,
year = "1984",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:35 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
JSTOR database",
note = "See also
\cite{Duffy:1985:PSS,LeVeque:1985:PSS,Mattics:1985:APS}.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@InProceedings{Gutknecht:1984:RVC,
author = "Martin H. Gutknecht and Lloyd N. Trefethen",
title = "Real vs. complex rational {Chebyshev} approximation on
complex domains",
crossref = "Collatz:1984:WNM",
pages = "87--97",
year = "1984",
MRclass = "41A50",
MRnumber = "MR757011 (85h:41067)",
MRreviewer = "Jean Tzimbalario",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
}
@Article{LeVeque:1984:RCK,
author = "Randall J. LeVeque and Lloyd N. Trefethen",
title = "On the resolvent condition in the {Kreiss Matrix
Theorem}",
journal = j-BIT,
volume = "24",
number = "4",
pages = "584--591",
year = "1984",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "39A11 (15A45 30A10 65F30)",
MRnumber = "MR764830 (86c:39004)",
MRreviewer = "Thomas H. Foregger",
bibdate = "Fri Nov 13 11:51:59 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
ZMnumber = "0559.15018",
acknowledgement = ack-nhfb,
classmath = "*15A60 Appl. of functional analysis to matrix theory
65F35 Matrix norms, etc. (numerical linear algebra)
15A45 Miscellaneous inequalities involving matrices",
fjournal = "BIT. Nordisk Tidskrift for Informationsbehandling
(BIT)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "Kreiss matrix theorem; matrix exponentials; matrix
norm; power boundedness; resolvent condition; resolvent
estimate",
ZMreviewer = "F. J. Gaines",
}
@Article{Trefethen:1984:AAR,
author = "Lloyd N. Trefethen",
title = "The asymptotic accuracy of rational best
approximations to $ e^z $ on a disk",
journal = j-J-APPROX-THEORY,
volume = "40",
number = "4",
pages = "380--383",
year = "1984",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "41A20 (30E10 41A21)",
MRnumber = "MR740651 (85j:41031)",
MRreviewer = "A. J. Rodrigues",
bibdate = "Sat Dec 9 12:51:07 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
}
@Article{Trefethen:1984:ADP,
author = "Lloyd N. Trefethen and Z. Angew",
title = "Analysis and design of polygonal resistors by
conformal mapping",
journal = j-Z-ANGE-MATH-PHYS,
volume = "35",
number = "5",
pages = "692--704",
year = "1984",
CODEN = "AZMPA8",
ISSN = "0044-2275 (print), 1420-9039 (electronic)",
ISSN-L = "0044-2275",
MRclass = "78A55",
MRnumber = "MR767435 (86b:78025)",
bibdate = "Sat Dec 9 12:51:42 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Zeitschrift f{\"u}r Angewandte Mathematik und Physik.
ZAMP. Journal of Applied Mathematics and Physics.
Journal de Math\'ematiques et de Physique
Appliqu\'ees",
journal-URL = "http://link.springer.com/journal/33",
}
@Article{Trefethen:1984:BRF,
author = "Lloyd N. Trefethen",
title = "Book Review: {{\booktitle{Fourier Analysis of
Numerical Approximations of Hyperbolic Equations}} (R.
Vichnevetsky and J. B. Bowles)}",
journal = j-SIAM-REVIEW,
volume = "26",
number = "3",
pages = "439--441",
month = "????",
year = "1984",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1026089",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:53:48 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/26/3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.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 = "July 1984",
}
@InProceedings{Trefethen:1984:IDD,
author = "Lloyd N. Trefethen",
title = "On $ \ell^p $-instability and dispersion at
discontinuities in finite difference schemes",
crossref = "Vichnevetsky:1984:ACM",
pages = "??--??",
year = "1984",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
}
@Article{Trefethen:1984:IDM,
author = "Lloyd N. Trefethen",
title = "Instability of difference models for hyperbolic
initial-boundary value problems",
journal = j-COMM-PURE-APPL-MATH,
volume = "37",
number = "3",
pages = "329--367",
year = "1984",
CODEN = "CPAMAT",
ISSN = "0010-3640 (print), 1097-0312 (electronic)",
ISSN-L = "0010-3640",
MRclass = "65M10",
MRnumber = "MR739924 (86f:65162)",
MRreviewer = "Bonita Bowman",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "Communications on Pure and Applied Mathematics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
}
@Article{Trefethen:1984:IFD,
author = "Lloyd N. Trefethen",
title = "Instability of finite difference models for hyperbolic
initial boundary value problems",
journal = j-COMM-PURE-APPL-MATH,
volume = "24",
number = "3",
pages = "329--367",
year = "1984",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640 (print), 1097-0312 (electronic)",
ISSN-L = "0010-3640",
bibdate = "Sat Dec 9 12:52:08 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications on Pure and Applied Mathematics (New
York)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
}
@Article{Trefethen:1984:PSA,
author = "Lloyd N. Trefethen and Randall J. LeVeque and L. E.
Mattics and L. Richard Duffy",
title = "Problems and Solutions: Advanced Problems:
6460--6462",
journal = j-AMER-MATH-MONTHLY,
volume = "91",
number = "6",
pages = "371",
year = "1984",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "Contributed Item",
MRnumber = "MR1540454",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "The American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@InProceedings{Trefethen:1984:RVC,
author = "Lloyd N. Trefethen and M. H. Gutknecht",
title = "Real vs. complex rational {Chebyshev} approximation on
complex domains",
crossref = "Collatz:1982:WNM",
pages = "87--97",
year = "1984",
bibdate = "Sat Dec 09 12:52:56 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Trefethen:1984:SBE,
author = "Lloyd N. Trefethen",
title = "Square blocks and equioscillation in the {Pad{\'e}},
{Walsh}, and {CF} tables",
journal = j-LECT-NOTES-MATH,
volume = "1105",
pages = "170--181",
year = "1984",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0072410",
ISBN = "3-540-13899-4 (print), 3-540-39113-4 (e-book)",
ISBN-13 = "978-3-540-13899-0 (print), 978-3-540-39113-5
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
MRclass = "41A21",
MRnumber = "783272 (86e:41030)",
MRreviewer = "A. Bultheel",
bibdate = "Fri May 9 19:07:44 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1980.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0072410/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0072395",
book-URL = "http://www.springerlink.com/content/978-3-540-39113-5",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Trefethen:1985:CDR,
author = "Lloyd N. Trefethen and Martin H. Gutknecht",
title = "On convergence and degeneracy in rational {Pad{\'e}}
and {Chebyshev} approximation",
journal = j-SIAM-J-MATH-ANA,
volume = "16",
number = "1",
pages = "198--210",
month = jan,
year = "1985",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "41A21 (30E10 41A50)",
MRnumber = "MR772879 (86e:41031)",
MRreviewer = "A. Magnus",
bibdate = "Sat Dec 5 18:14:13 MST 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Trefethen:1985:PSS,
author = "Lloyd N. Trefethen and James C. Smith and J. LeVeque",
title = "Problems and Solutions: Solutions of Advanced
Problems: 6462",
journal = j-AMER-MATH-MONTHLY,
volume = "92",
number = "10",
pages = "740--741",
year = "1985",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "Contributed Item",
MRnumber = "MR1540768",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "The American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Trefethen:1985:SFD,
author = "Lloyd N. Trefethen",
title = "Stability of finite-difference models containing two
boundaries or interfaces",
journal = j-MATH-COMPUT,
volume = "45",
number = "172",
pages = "279--300",
month = oct,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65M10",
MRnumber = "MR804924 (87h:65158)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comp.",
classcodes = "B0290P (Differential equations); C4170 (Differential
equations)",
corpsource = "Inst. for Comput. Applications in Sci. and Eng., NASA
Langley Res. Center, Hampton, VA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "boundary; convergence of numerical methods; difference
equations; dissipativity; finite-difference models;
GKS; GKS-stability; hyperbolic initial-boundary value;
hyperbolic partial differential equations; infinite
numerical reflection coefficient; initial value
problems; instabilities; instability; internal
interface; P-stability; parasitic waves; partial
differential equations; problems; propagation;
reflection; trapped; wave packets",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Trefethen:1985:SHF,
author = "Lloyd N. Trefethen",
title = "Stability of hyperbolic finite-difference models with
one or two boundaries",
crossref = "Engquist:1985:LSC",
pages = "311--326",
year = "1985",
MRclass = "65M10",
MRnumber = "MR818794 (87b:65151)",
bibdate = "Sat Dec 09 12:29:05 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
}
@Article{Trefethen:1985:TMG,
author = "Lloyd N. Trefethen",
title = "Three mysteries of {Gaussian} elimination",
journal = j-SIGNUM,
volume = "20",
number = "4",
pages = "2--5",
month = oct,
year = "1985",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Sat Aug 13 17:16:02 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
keywords = "algorithms",
subject = "G.1.5 Mathematics of Computing, NUMERICAL ANALYSIS,
Roots of Nonlinear Equations, Systems of equations \\
G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Linear systems (direct and
iterative methods)",
}
@Article{Elcrat:1986:CFS,
author = "Alan R. Elcrat and Lloyd N. Trefethen",
title = "Classical free-streamline flow over a polygonal
obstacle",
journal = j-J-COMPUT-APPL-MATH,
volume = "14",
number = "1--2",
pages = "251--265",
month = feb,
year = "1986",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(86)90142-1",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "76B10 (65E05 76-08)",
MRnumber = "MR829042 (87d:76021)",
bibdate = "Sat Feb 25 12:10:36 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042786901421",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
remark = "Special issue on numerical conformal mapping.",
}
@Article{Trefethen:1986:CMS,
author = "Lloyd N. Trefethen and Ruth J. Williams",
title = "Conformal mapping solution of {Laplace}'s equation on
a polygon with oblique derivative boundary conditions",
journal = j-J-COMPUT-APPL-MATH,
volume = "14",
number = "1--2",
pages = "227--249",
month = feb,
year = "1986",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "30C30 (35J25 65E05)",
MRnumber = "MR829041 (87f:30019)",
MRreviewer = "D. Gaier",
bibdate = "Sat Feb 25 12:10:36 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037704278690141X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
remark = "Special issue on numerical conformal mapping.",
}
@InProceedings{Trefethen:1986:DDS,
author = "Lloyd N. Trefethen",
title = "Dispersion, dissipation, and stability",
crossref = "Griffiths:1986:NA",
pages = "200--219",
year = "1986",
MRclass = "65N10 (65-02)",
MRnumber = "MR873111 (87m:65159)",
bibdate = "Mon Jul 11 13:19:59 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
}
@InProceedings{Trefethen:1986:MPC,
author = "Lloyd N. Trefethen",
title = "{MATLAB} programs for {CF} approximation",
crossref = "Chui:1986:ATV",
pages = "??--??",
year = "1986",
bibdate = "Sat Dec 09 12:31:17 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
}
@Book{Trefethen:1986:NCM,
editor = "Lloyd N. Trefethen",
title = "Numerical Conformal Mapping",
publisher = pub-NH,
address = pub-NH:adr,
pages = "iv + 269",
year = "1986",
ISBN = "0-444-87855-6",
ISBN-13 = "978-0-444-87855-7",
LCCN = "QA1.J54",
MRclass = "30C30",
MRnumber = "MR874989 (87m:30013)",
bibdate = "Sat Dec 09 12:55:23 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "Reprint of J. Comput.\ Appl.\ Math.\ {\bf 14} (1986),
no.\ 1--2.",
acknowledgement = ack-nhfb,
}
@Article{Trefethen:1986:P,
author = "Lloyd N. Trefethen",
title = "Preface",
journal = j-J-COMPUT-APPL-MATH,
volume = "14",
number = "1--2",
pages = "1--6",
month = feb,
year = "1986",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(86)90127-5",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:10:36 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042786901275",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Book{Trefethen:1986:SIN,
editor = "Lloyd N. Trefethen",
title = "Special issue on numerical conformal mapping",
volume = "14(1--2)",
publisher = pub-ELS,
address = pub-ELS:adr,
pages = "viii + 269",
year = "1986",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
MRclass = "30C30 (30-06 65-06 65E05)",
MRnumber = "MR829027 (86m:30010)",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
series = j-J-COMPUT-APPL-MATH,
}
@Article{Trefethen:1986:WPA,
author = "Lloyd N. Trefethen and L. Halpern",
title = "Well-posedness of absorbing boundary conditions and
one-way wave equations",
journal = j-MATH-COMPUT,
volume = "47",
number = "176",
pages = "421--435",
year = "1986",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Sat Dec 9 12:57:56 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Trefethen:1986:WPO,
author = "Lloyd N. Trefethen and Laurence Halpern",
title = "Well-posedness of one-way wave equations and absorbing
boundary conditions",
journal = j-MATH-COMPUT,
volume = "47",
number = "176",
pages = "421--435",
year = "1986",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65N99 (65D05 65M05)",
MRnumber = "MR856695 (88b:65148)",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Dias:1987:IJF,
author = "Fr{\'e}d{\'e}ric Dias and Alan R. Elcrat and Lloyd N.
Trefethen",
title = "Ideal jet flow in two dimensions",
journal = j-FLUID-MECH,
volume = "185",
pages = "275--288",
year = "1987",
CODEN = "JFLSA7",
ISSN = "0022-1120 (print), 1469-7645 (electronic)",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
ZMnumber = "0633.76013",
classmath = "*76B10 Free-streamline theory and appl. 76T99 None of
the above, but in this section 76M99 Basic methods in
fluid mechanics",
keywords = "jet flow; nozzle geometries; polygonal nozzle",
xxauthor = "Lloyd N. Trefethen and F. Dias and A. R. Elcrat",
}
@TechReport{Trefethen:1987:ACS,
author = "L. N. Trefethen and R. S. Schreiber",
title = "Average Case Stability of {Gaussian} Elimination",
number = "88-3",
institution = "Numerical Analysis, Department of Mathematics, MIT",
address = "Cambridge, MA, USA",
year = "1987",
bibdate = "Tue Sep 6 16:42:43 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Trefethen:1987:IPS,
author = "Lloyd N. Trefethen and Manfred R. Trummer",
title = "An Instability Phenomenon in Spectral Methods",
journal = j-SIAM-J-NUMER-ANAL,
volume = "24",
number = "5",
pages = "1008--1023",
month = oct,
year = "1987",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65M10 (65D25 65F15 65G05)",
MRnumber = "MR909061 (89a:65139)",
MRreviewer = "V. L. Makarov",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@InProceedings{Trefethen:1987:PSP,
author = "Lloyd N. Trefethen and M. H. H. Gutknecht",
title = "{Pad{\'e}}, stable {Pad{\'e}}, and
{Chebyshev--Pad{\'e}} approximation",
crossref = "Mason:1987:AAB",
pages = "227--264",
year = "1987",
MRclass = "41A21 (65D15)",
MRnumber = "MR911316 (89g:41011)",
bibdate = "Sat Dec 09 12:32:00 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
}
@Article{Halpern:1988:WAO,
author = "Laurence Halpern and Lloyd N. Trefethen",
title = "Wide-angle one-way wave equations",
journal = j-J-ACOUST-SOC-AM,
volume = "84",
number = "4",
pages = "1397--1404",
month = oct,
year = "1988",
CODEN = "JASMAN",
DOI = "https://doi.org/10.1121/1.396586",
ISSN = "0001-4966",
ISSN-L = "0001-4966",
MRclass = "76Q05 (35L05 76-08)",
MRnumber = "MR965847 (89j:76076)",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "Acoustical Society of America. Journal",
journal-URL = "http://scitation.aip.org/content/asa/journal/jasa",
}
@Article{LeVeque:1988:FAS,
author = "Randall J. LeVeque and Lloyd N. Trefethen",
title = "{Fourier} analysis of the {SOR} iteration",
journal = j-IMA-J-NUMER-ANAL,
volume = "8",
number = "3",
pages = "273--279",
year = "1988",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/8.3.273",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65F10",
MRnumber = "MR968092 (89i:65036)",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
MathSciNet database",
ZMnumber = "0648.65028",
abstract = "The SOR iteration for solving linear systems of
equations depends upon an overrelaxation factor. We
show that, for the standard model problem of Poisson's
equation on a rectangle, the optimal and corresponding
convergence rate can be obtained rigorously by Fourier
analysis. The trick is to tilt the space-time grid so
that the SOR stencil becomes symmetrical. The tilted
grid also gives new insight into the relationships
between the Gauss--Seidel and Jacobi iterations and
between the lexicographic and red-black orderings, and
into the modified equation analysis of Garabedian.",
acknowledgement = ack-nhfb,
classmath = "*65F10 Iterative methods for linear systems 65N22
Solution of discretized equations (BVP of PDE) 35J05
Laplace equation, etc",
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "Fourier analysis; optimal relaxation parameter;
Poisson's equation; successive overrelaxation",
ZMreviewer = "H.Hollatz",
}
@Article{Trefethen:1988:IPA,
author = "Lloyd N. Trefethen and L. H. Howell",
title = "Ill-posedness of absorbing boundary conditions for
migration",
journal = j-GEOPHYSICS,
volume = "53",
pages = "593--603",
year = "1988",
CODEN = "GPYSA7",
ISSN = "0016-8033 (print), 1942-2156 (electronic)",
ISSN-L = "0016-8033",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "Geophysics",
journal-URL = "http://library.seg.org/loi/gpysa7",
}
@InProceedings{Trefethen:1988:LSV,
author = "Lloyd N. Trefethen",
title = "{Lax}-stability vs. eigenvalue stability of spectral
methods",
crossref = "Morton:1988:NMF",
pages = "237--253",
year = "1988",
MRclass = "65N99 (76M25)",
MRnumber = "MR989156 (91a:65241)",
MRreviewer = "J. Mikl{\'\i}{\v{c}}ek",
bibdate = "Sat Dec 09 13:00:11 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
series = "Inst. Math. Appl. Conf. Ser. New Ser.",
acknowledgement = ack-nhfb,
}
@Article{Weideman:1988:ESO,
author = "J. A. C. Weideman and Lloyd N. Trefethen",
title = "The eigenvalues of second-order spectral
differentiation matrices",
journal = j-SIAM-J-NUMER-ANAL,
volume = "25",
number = "6",
pages = "1279--1298",
month = dec,
year = "1988",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65N25 (65F15)",
MRnumber = "MR972454 (90a:65228)",
MRreviewer = "Aur{\'e}l Gal{\'a}ntai",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@TechReport{Trefethen:1989:SCM,
author = "Lloyd N. Trefethen",
title = "{Schwarz--Christoffel} mapping in the 1980's",
type = "Numerical Analysis Report",
number = "89-1",
institution = inst-MATH-MIT,
address = inst-math-mit:adr,
year = "1989",
bibdate = "Mon Jul 11 13:19:59 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
}
@TechReport{Trefethen:1989:SUG,
author = "Lloyd N. Trefethen",
title = "{SCPACK} User's Guide",
type = "Numerical Analysis Report",
number = "89-2",
institution = inst-MATH-MIT,
address = inst-math-mit:adr,
year = "1989",
bibdate = "Mon Jul 11 13:19:59 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "(An earlier edition appeared as an ICASE internal
report in 1983.)",
}
@Article{Hayashi:1990:CT,
author = "Eric Hayashi and Lloyd N. Trefethen and Martin H.
Gutknecht",
title = "The {CF} table",
journal = j-CONST-APPROX,
volume = "6",
number = "2",
pages = "195--223",
year = "1990",
ISSN = "0176-4276 (print), 1432-0940 (electronic)",
ISSN-L = "0176-4276",
MRclass = "41A20 (30E10 41A50 47A57 65D15)",
MRnumber = "MR1036609 (91e:41014)",
MRreviewer = "Olav Nj{\aa}stad",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "Constructive Approximation. An International Journal
for Approximations and Expansions",
journal-URL = "http://link.springer.com/journal/365",
}
@Article{Howell:1990:MSC,
author = "Louis H. Howell and Lloyd N. Trefethen",
title = "A modified {Schwarz--Christoffel} transformation for
elongated regions",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "11",
number = "5",
pages = "928--949",
month = sep,
year = "1990",
CODEN = "SIJCD4",
ISSN = "0196-5204",
MRclass = "30C20 (30C30 65D30)",
MRnumber = "MR1057148 (92j:30006)",
MRreviewer = "G. Opfer",
bibdate = "Tue Apr 29 19:18:28 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
classification = "B0290R (Integral equations); C4180 (Integral
equations); C7310 (Mathematics)",
corpsource = "Lawrence Livermore Lab., CA, USA",
fjournal = "Society for Industrial and Applied Mathematics.
Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sjoce3",
keywords = "arbitrary polygonal channel; conformal map; elongated
regions; integral equations; mathematics computing;
modified Schwarz--Christoffel transformation; numerical
integration",
treatment = "T Theoretical or Mathematical",
}
@Article{Reddy:1990:LSF,
author = "Satish C. Reddy and Lloyd N. Trefethen",
title = "{Lax-stability} of fully discrete spectral methods via
stability regions and pseudo-eigenvalues",
journal = j-COMPUT-METH-APPL-MECH-ENG,
volume = "80",
number = "1--3",
pages = "147--164",
year = "1990",
CODEN = "CMMECC",
ISSN = "0045-7825, 0374-2830",
ISSN-L = "0045-7825",
MRclass = "65J10 (65L05 65P05); 65M12 (65M20 65M70)",
MRnumber = "MR1067947 (91j:65102); MR1180554 (93e:65115)",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "Spectral and high order methods for partial
differential equations (Como, 1989)",
ZMnumber = "0735.65070",
classmath = "*65M70 Spectral, collocation and related methods (IVP
of PDE) 65M20 Method of lines (IVP of PDE) 65M12
Stability and convergence of numerical methods (IVP of
PDE) 65L20 Stability of numerical methods for ODE",
fjournal = "Computer Methods in Applied Mechanics and
Engineering",
journal-URL = "http://www.sciencedirect.com/science/journal/00457825",
keywords = "Chebyshev collocation; Lax-stability; method of lines;
pseudo-eigenvalues; spectral methods; stability
region",
ZMreviewer = "V.Subba Rao",
}
@Article{Trefethen:1990:ACS,
author = "Lloyd N. Trefethen and Robert S. Schreiber",
title = "Average-Case Stability of {Gaussian} Elimination",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "11",
number = "3",
pages = "335--360",
month = jul,
year = "1990",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F05",
MRnumber = "MR1054179 (91g:65062)",
bibdate = "Tue Jan 21 08:54:30 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Trefethen:1990:ATN,
author = "Lloyd N. Trefethen",
title = "Approximation theory and numerical linear algebra",
crossref = "Mason:1990:AAI",
pages = "336--360",
year = "1990",
MRclass = "65F10 (41A10 41A20)",
MRnumber = "MR1071991 (91j:65063)",
MRreviewer = "K. Jetter",
bibdate = "Sat Dec 09 12:32:52 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
}
@Article{Trefethen:1990:CT,
author = "Lloyd N. Trefethen and E. Hayashi and M. H.
Gutknecht",
title = "The {CF} table",
journal = j-CONST-APPROX,
volume = "6",
number = "2",
pages = "195--223",
year = "1990",
ISSN = "0176-4276 (print), 1432-0940 (electronic)",
ISSN-L = "0176-4276",
bibdate = "Sat Dec 9 13:01:14 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Constructive Approximation",
journal-URL = "http://link.springer.com/journal/365",
}
@Article{Trefethen:1990:SUQ,
author = "Lloyd M. Trefethen and Ronald L. Panton",
title = "Some unanswered questions in fluid mechanics",
journal = j-APPL-MECH-REV,
volume = "43",
number = "8",
pages = "153--170",
year = "1990",
CODEN = "AMREAD",
ISSN = "0003-6900 (print), 1088-8535 (electronic)",
ISSN-L = "0003-6900",
MRclass = "76-06",
MRnumber = "MR1066082 (91j:76001)",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "Applied Mechanics Reviews",
journal-URL = "http://appliedmechanicsreviews.asmedigitalcollection.asme.org/issues.aspx",
}
@Article{Trefethen:1991:TRP,
author = "Lloyd N. Trefethen and J. A. C. Weideman",
title = "Two results on polynomial interpolation in equally
spaced points",
journal = j-J-APPROX-THEORY,
volume = "65",
number = "3",
pages = "247--260",
year = "1991",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "41A05 (41A10)",
MRnumber = "MR1109406 (92e:41007)",
MRreviewer = "Allan Pinkus",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
}
@Article{Nachtigal:1992:HFN,
author = "No{\"e}l M. Nachtigal and Satish C. Reddy and Lloyd N.
Trefethen",
title = "How Fast Are Nonsymmetric Matrix Iterations?",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "3",
pages = "778--795",
month = jul,
year = "1992",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F10 (65Y10)",
MRnumber = "MR1168079 (93a:65039)",
bibdate = "Tue Jan 21 08:54:30 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "Iterative methods in numerical linear algebra (Copper
Mountain, CO, 1990).",
ZMnumber = "0754.65036",
acknowledgement = ack-nhfb,
classmath = "*65F10 Iterative methods for linear systems 65Y20
Complexity and performance of numerical algorithms",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "biconjugate gradient iteration; biorthogonalization
algorithm; CGN; CGS; conjugate gradient iteration;
convergence; GMRES; Krylov space; nonsymmetric matrix
iterations; performance; pseudo-eigenvalues; residual
minimization; singular values",
ZMreviewer = "A.Gal{\'a}ntai (Miskolc-Egyetemvaros)",
}
@Article{Nachtigal:1992:HGA,
author = "No{\"e}l M. Nachtigal and Lothar Reichel and Lloyd N.
Trefethen",
title = "A Hybrid {GMRES} Algorithm for Nonsymmetric Linear
Systems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "3",
pages = "796--825",
month = jul,
year = "1992",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F10",
MRnumber = "MR1168080 (93a:65040)",
bibdate = "Tue Jan 21 08:54:30 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "Iterative methods in numerical linear algebra (Copper
Mountain, CO, 1990).",
ZMnumber = "0757.65035",
acknowledgement = ack-nhfb,
classmath = "*65F10 Iterative methods for linear systems",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "CGNR; CGS; convergence; generalized minimum residual
algorithm; GMRES; hybrid algorithms; iterative method;
Krylov subspace; large nonsymmetric systems; numerical
examples; pseudospectrum",
ZMreviewer = "J. P. Milaszewicz (Buenos Aires)",
}
@Article{Reddy:1992:SML,
author = "Satish C. Reddy and Lloyd N. Trefethen",
title = "Stability of the method of lines",
journal = j-NUM-MATH,
volume = "62",
number = "2",
pages = "235--267",
year = "1992",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65M20 (65F15 65M12)",
MRnumber = "MR1165912 (93d:65086)",
MRreviewer = "Dennis C. Jespersen",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Reichel:1992:EPE,
author = "Lothar Reichel and Lloyd N. Trefethen",
title = "Eigenvalues and pseudo-eigenvalues of {Toeplitz}
matrices",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "162/164",
pages = "153--185",
year = "1992",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A18 (47A75 47B35 65F15)",
MRnumber = "MR1148398 (92k:15028)",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "Directions in matrix theory (Auburn, AL, 1990)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Trefethen:1992:DNA,
author = "Lloyd N. Trefethen",
title = "The definition of numerical analysis",
journal = j-SIAM-NEWS,
volume = "25",
day = "6",
month = nov,
year = "1992",
ISSN = "0036-1437",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "Reprinted in the {\sl Bulletin\/} of the Institute for
Mathematics and its Applications, 1993.",
URL = "http://webs.um.es/eliseo/um/uploads/Main/TrefethendefNA.pdf",
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Article{Trefethen:1992:EPE,
author = "Lloyd N. Trefethen and L. Reichel",
title = "Eigenvalues and pseudo-eigenvalues of {Toeplitz}
matrices",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "162--164",
pages = "153--185",
year = "1992",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@TechReport{Trefethen:1992:NDH,
author = "L. N. Trefethen and A. E. Trefethen and S. C. Reddy
and T. A. Driscoll",
title = "A new direction in hydrodynamic stability: beyond
eigenvalues",
type = "Technical Report",
number = "CTC92TR115",
institution = "Cornell Theory Center, Cornell University",
address = "Ithaca, NY, USA",
month = "????",
year = "1992",
bibdate = "Wed Jan 07 16:28:04 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Trefethen:1992:PLN,
author = "Lloyd N. Trefethen and A. E. Trefethen and S. C.
Reddy",
title = "Pseudospectra of the linear {Navier--Stokes} evolution
operator and instability of plane {Poiseuille} and
{Couette} flows",
number = "TR 92-1291",
institution = inst-CS-CORNELL,
address = inst-cs-cornell:adr,
year = "1992",
bibdate = "Mon Jul 11 13:19:59 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
}
@InProceedings{Trefethen:1992:PM,
author = "Lloyd N. Trefethen",
title = "Pseudospectra of matrices",
crossref = "Griffiths:1991:NAP",
pages = "234--266",
year = "1992",
MRclass = "65F15 (15A18)",
MRnumber = "MR1177237 (93e:65064)",
MRreviewer = "F. Szidarovszky",
bibdate = "Mon Jul 11 13:19:59 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
}
@Article{Trefethen:1992:SML,
author = "Lloyd N. Trefethen and S. C. Reddy",
title = "Stability of the method of lines",
journal = j-NUM-MATH,
volume = "62",
number = "2",
pages = "235--267",
year = "1992",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sat Dec 9 13:03:29 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@TechReport{Greenbaum:1993:DPM,
author = "Anne Greenbaum and Lloyd N. Trefethen",
title = "Do The Pseudospectra of a Matrix Determine its
Behavior?",
type = "Technical Report",
number = "TR 93-1371",
institution = "Department of Computer Science, Cornell University",
address = "Ithaca, New York",
pages = "????",
month = aug,
year = "1993",
bibdate = "Mon Sep 26 10:24:43 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Higham:1993:SO,
author = "Desmond J. Higham and Lloyd N. Trefethen",
title = "Stiffness of {ODEs}",
journal = j-BIT,
volume = "33",
number = "2",
pages = "285--303",
year = "1993",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65L15",
MRnumber = "MR1326020 (96a:65117)",
bibdate = "Fri Nov 13 11:55:54 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit33.html",
ZMnumber = "0782.65091",
acknowledgement = ack-nhfb,
classmath = "*65L06 Multistep, Runge--Kutta, and extrapolation
methods 65L05 Initial value problems for ODE (numerical
methods) 65L20 Stability of numerical methods for ODE
34A34 Nonlinear ODE and systems, general 34E13 Multiple
scale methods",
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "numerical experiments; one-step methods; performance;
pseudospectrum; stability; stiff linear differential
equations",
ZMreviewer = "E.Hairer (Gen{\`e}ve)",
}
@TechReport{Reddy:1993:PCD,
author = "Satish C. Reddy and Lloyd N. Trefethen and D.
Pathria",
title = "Pseudospectrum of the Convection--Diffusion Operator",
type = "Technical Report",
number = "CTC 93 TR126",
institution = "Advanced Computing Research Institute, Cornell Theory
Center, Cornell University",
address = "Ithaca, New York",
pages = "????",
year = "1993",
bibdate = "Fri Sep 29 21:09:04 GMT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
mynote = "Not seen; verify.",
}
@Article{Trefethen:1993:HSE,
author = "Lloyd N. Trefethen and Anne E. Trefethen and Satish C.
Reddy and Tobin A. Driscoll",
title = "Hydrodynamic stability without eigenvalues",
journal = j-SCIENCE,
volume = "261",
number = "5121",
pages = "578--584",
day = "30",
month = jul,
year = "1993",
CODEN = "SCIEAS",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
MRclass = "76E99",
MRnumber = "MR1229495",
bibdate = "Wed Jan 07 13:20:07 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
ZMnumber = "0806.65031",
acknowledgement = ack-nhfb,
classmath = "*65F10 Iterative methods for linear systems",
fjournal = "American Association for the Advancement of Science.
Science",
journal-URL = "http://www.sciencemag.org/archive/",
keywords = "Arnoldi iterations; conjugate residual method;
convergence; GMRES algorithm; Lanczos iterations;
location of eigenvalues; weighted least squares",
ZMreviewer = "S.Zabek (Lublin)",
}
@InCollection{Trefethen:1993:NCC,
author = "Lloyd N. Trefethen",
title = "Numerical construction of conformal maps",
crossref = "Saff:1993:FCA",
pages = "??--??",
year = "1993",
bibdate = "Sat Dec 09 12:33:47 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
}
@Article{Greenbaum:1994:GCA,
author = "Anne Greenbaum and Lloyd N. Trefethen",
title = "{GMRES\slash CR} and {Arnoldi\slash L{\'a}nczos} as
Matrix Approximation Problems",
journal = j-SIAM-J-SCI-COMP,
volume = "15",
number = "2",
pages = "359--368",
month = mar,
year = "1994",
CODEN = "SJOCE3",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F10 (65F15)",
MRnumber = "MR1261459 (95e:65029)",
MRreviewer = "Zden{\v{e}}k Dost{\'a}l",
bibdate = "Tue Apr 29 18:25:50 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "Iterative methods in numerical linear algebra (Copper
Mountain Resort, CO, 1992).",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Reddy:1994:PCD,
author = "Satish C. Reddy and Lloyd N. Trefethen",
title = "Pseudospectra of the Convection-Diffusion Operator",
journal = j-SIAM-J-APPL-MATH,
volume = "54",
number = "6",
pages = "1634--1649",
month = dec,
year = "1994",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
MRclass = "47N20 (34L05 35Q99 47A10 65P05 76Rxx)",
MRnumber = "MR1301275 (95k:47108)",
MRreviewer = "D. M. Sloan",
bibdate = "Wed Dec 10 09:59:46 MST 1997",
bibsource = "Compendex database;
http://epubs.siam.org/sam-bin/dbq/toc/SIAP/54/6;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/24698",
ZMnumber = "0811.35026",
acknowledgement = ack-nhfb,
affiliation = "Oregon State Univ",
affiliationaddress = "Corvallis, OR, USA",
classification = "921.6",
classmath = "*35J25 Second order elliptic equations, boundary value
problems 35P10 Eigenfunction expansions, etc. for PD
operators 47A10 Spectrum and resolvent of linear
operators 76R99 Diffusion and convection",
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
journalabr = "SIAM J Appl Math",
keywords = "Approximation theory; Convection diffusion operator;
Function evaluation; Mathematical operators; Parabolas;
Peclet number; Peclet numbers; Pseudospectra; Spectrum
analysis",
}
@Article{Toh:1994:PPP,
author = "Kim-Chuan Toh and Lloyd N. Trefethen",
title = "Pseudozeros of Polynomials and Pseudospectra of
Companion Matrices",
journal = j-NUM-MATH,
volume = "68",
number = "3",
pages = "403--425",
year = "1994",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F35 (65H05)",
MRnumber = "MR1313152 (95m:65085)",
MRreviewer = "Guo Liang Chen",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
ZMnumber = "0808.65053",
acknowledgement = ack-nhfb,
classification = "B0290F (Interpolation and function approximation);
B0290H (Linear algebra); C4130 (Interpolation and
function approximation); C4140 (Linear algebra)",
classmath = "*65F35 Matrix norms, etc. (numerical linear algebra)
65F15 Eigenvalues (numerical linear algebra) 65H05
Single nonlinear equations (numerical methods) 65H17
Eigenvalue and bifurcation problems of nonlinear
algebraic equations",
corpsource = "Center for Appl. Math., Cornell Univ., Ithaca, NY,
USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "companion matrices; companion matrix; conditioning;
eigenvalues; eigenvalues and eigenfunctions; matrix
algebra; numerical results; poles and zeros; polynomial
zerofinding; polynomials; pseudospectra; pseudozeros;
pseudozeros of polynomials",
treatment = "T Theoretical or Mathematical",
ZMreviewer = "S.Filippi (Gie{\ss}en)",
}
@TechReport{Trefethen:1994:SPP,
author = "L. N. Trefethen",
title = "Spectra and pseudospectra for pipe {Poiseuille} flow",
type = "IPS Research Report",
number = "94-16",
institution = "Interdisciplinary Project Center for Supercomputing,
ETH-Zurich",
address = "Zurich, Switzerland",
month = "????",
year = "1994",
bibdate = "Wed Jan 07 14:40:44 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Wegert:1994:BNP,
author = "Elias Wegert and Lloyd N. Trefethen",
title = "From the {Buffon} needle problem to the {Kreiss}
matrix theorem",
journal = j-AMER-MATH-MONTHLY,
volume = "101",
number = "2",
pages = "132--139",
year = "1994",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "30C99 (15A57 60D05)",
MRnumber = "MR1259826 (95b:30036)",
MRreviewer = "A. Bultheel",
bibdate = "Wed Dec 3 17:17:33 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "The American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Baggett:1995:MLM,
author = "Jeffrey S. Baggett and Tobin A. Driscoll and Lloyd N.
Trefethen",
title = "A mostly linear model of transition to turbulence",
journal = j-PHYS-FLUIDS,
volume = "7",
number = "4",
pages = "833--838",
month = "????",
year = "1995",
CODEN = "PHFLE6",
ISSN = "1070-6631",
ISSN-L = "1070-6631",
MRclass = "76F99 (76E30)",
MRnumber = "MR1324952 (95k:76072)",
bibdate = "Wed Jan 07 13:00:42 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
ZMnumber = "1039.76509",
acknowledgement = ack-nhfb,
classmath = "*76F06 Transition to turbulence",
fjournal = "Physics of Fluids",
journal-URL = "http://scitation.aip.org/content/aip/journal/pof1",
}
@Article{Driscoll:1996:PWE,
author = "Tobin A. Driscoll and Lloyd N. Trefethen",
title = "Pseudospectra for the wave equation with an absorbing
boundary",
journal = j-J-COMPUT-APPL-MATH,
volume = "69",
number = "1",
pages = "125--142",
day = "30",
month = apr,
year = "1996",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(95)00021-6",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65J10 (35L05 47A10 65M99)",
MRnumber = "MR1391615 (97e:65056)",
bibdate = "Sat Feb 25 12:27:49 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042795000216",
ZMnumber = "0854.35060",
acknowledgement = ack-nhfb,
classmath = "*35L05 Wave equation 35P05 General spectral theory of
PDE 47A10 Spectrum and resolvent of linear operators
47D06 One-parameter semigroups and linear evolution
equations",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "absorbing boundary condition; nonnormality;
pseudospectra",
}
@Article{Toh:1996:CPA,
author = "Kim-Chuan Toh and Lloyd N. Trefethen",
title = "Calculation of pseudospectra by the {Arnoldi}
iteration",
journal = j-SIAM-J-SCI-COMP,
volume = "17",
number = "1",
pages = "1--15",
month = jan,
year = "1996",
CODEN = "SJOCE3",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15 (15A18)",
MRnumber = "MR1375262 (97i:65064)",
bibdate = "Tue Apr 29 18:25:50 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "Special issue on iterative methods in numerical linear
algebra (Breckenridge, CO, 1994).",
ZMnumber = "0842.65022",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "Arnoldi iteration; Hessenberg matrices; iterative
algorithms; pseudospectra",
ZMreviewer = "Costica Morosanu (Iasi)",
}
@TechReport{Trefethen:1996:MBU,
author = "L. N. Trefethen and D. Viswanath",
title = "Matrix behaviour, unitary reducibility, and {Hadamard}
products",
type = "Technical Report",
number = "TR96-1596",
institution = "Department of Computer Science, Cornell University",
address = "Ithaca, NY, USA",
month = jul,
year = "1996",
bibdate = "Wed Jan 07 13:26:10 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Trefethen:1996:MMM,
author = "L. N. Trefethen and A. E. Trefethen and others",
title = "{MultiMATLAB}: {MATLAB} on multiple processors",
type = "Technical Report",
number = "CTC96TR293",
institution = "Cornell Theory Center, Cornell University",
address = "Ithaca, NY, USA",
month = "????",
year = "1996",
bibdate = "Wed Jan 07 15:18:18 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Trefethen:1996:PLO,
author = "L. N. Trefethen",
title = "Pseudospectra of linear operators",
crossref = "Kirchgassner:1996:IPT",
pages = "401--434",
year = "1996",
MRclass = "65J10 (15A18 47A10 65F15)",
MRnumber = "MR1387611 (96m:65064)",
bibdate = "Wed Jan 07 13:23:39 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "Also in \cite{Trefethen:1997:PLO}.",
acknowledgement = ack-nhfb,
}
@Article{Baggett:1997:LDM,
author = "Jeffrey S. Baggett and Lloyd N. Trefethen",
title = "Low-dimensional models of subcritical transition to
turbulence",
journal = j-PHYS-FLUIDS,
volume = "9",
number = "4",
pages = "1043--1053",
year = "1997",
CODEN = "PHFLE6",
ISSN = "1070-6631",
ISSN-L = "1070-6631",
MRclass = "76E05 (76E30 76F10 76M25)",
MRnumber = "MR1437563 (98a:76030)",
MRreviewer = "Tom{\'a}s Chac{\'o}n Rebollo",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "Physics of Fluids",
journal-URL = "http://scitation.aip.org/content/aip/journal/pof1",
}
@Article{Trefethen:1997:DPM,
author = "Lloyd N. Trefethen and A. Greenbaum",
title = "Do the pseudospectra of a matrix determine its
behavior?",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "??",
pages = "??--??",
year = "1997",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "To appear. The first author reports that the paper has
been accepted, subject to minor revisions.",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@TechReport{Trefethen:1997:EMI,
author = "L. N. Trefethen and V. E. Howle",
title = "Eigenvalues and musical instruments",
type = "Technical Report",
number = "????",
institution = "????",
address = "????",
month = aug,
year = "1997",
bibdate = "Wed Jan 07 13:42:43 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Trefethen:1997:LDM,
author = "L. N. Trefethen and J. S. Baggett",
title = "Low-dimensional models of subcritical transition to
turbulence",
journal = j-PHYS-FLUIDS,
volume = "9",
number = "4",
pages = "1043--1053",
month = "????",
year = "1997",
CODEN = "PHFLE6",
ISSN = "1070-6631",
ISSN-L = "1070-6631",
bibdate = "Wed Jan 07 14:41:58 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Physics of Fluids",
journal-URL = "http://scitation.aip.org/content/aip/journal/pof1",
}
@Book{Trefethen:1997:NLA,
editor = "Lloyd N. Trefethen and David {Bau, III}",
title = "Numerical Linear Algebra",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xii + 361",
year = "1997",
ISBN = "0-89871-361-7",
ISBN-13 = "978-0-89871-361-9",
LCCN = "QA184 .T74 1997",
MRclass = "65-01 (65-02 65Fxx)",
MRnumber = "MR1444820 (98k:65002)",
MRreviewer = "Moody T. Chu",
bibdate = "Wed Jan 07 15:23:19 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Preface \\
Acknowledgments \\
Part I. Fundamentals \\
1. Matrix-vector multiplication \\
2. Orthogonal vectors and matrices \\
3. Norms \\
4. The singular value decomposition \\
5. More on the SVD \\
Part II. $Q R$ factorization and least squares \\
6. Projectors \\
7. $Q R$ factorization \\
8. Gram--Schmidt orthogonalization \\
9. MATLAB \\
10. Householder triangularization \\
11. Least squares problems \\
Part III. Conditioning and stability \\
12. Conditioning and condition numbers \\
13. Floating point arithmetic \\
14. Stability \\
15. More on stability \\
16. Stability of householder triangularization \\
17. Stability of back substitution \\
18. Conditioning of least squares problems \\
19. Stability of least squares algorithms \\
Part IV. Systems of equations \\
20. Gaussian elimination \\
21. Pivoting \\
22. Stability of Gaussian elimination \\
23. Cholesky factorization \\
Part V. Eigenvalues \\
24. Eigenvalue problems \\
25. Overview of Eigenvalue algorithms \\
26. Reduction to Hessenberg or tridiagonal form \\
27. Rayleigh quotient, inverse iteration \\
28. $Q R$ algorithm without shifts \\
29. $Q R$ algorithm with shifts \\
30. Other Eigenvalue algorithms \\
31. Computing the SVD \\
Part VI. Iterative methods \\
32. Overview of iterative methods \\
33. The Arnoldi iteration \\
34. How Arnoldi locates eigenvalues \\
35. GMRES \\
36. The Lanczos iteration \\
37. From Lanczos to Gauss quadrature \\
38. Conjugate gradients \\
39. Biorthogonalization methods \\
40. Preconditioning \\
Appendix. The definition of numerical analysis \\
Notes \\
Bibliography \\
Index",
}
@Article{Trefethen:1997:PLO,
author = "Lloyd N. Trefethen",
title = "Pseudospectra of Linear Operators",
journal = j-SIAM-REVIEW,
volume = "39",
number = "3",
pages = "383--406",
month = sep,
year = "1997",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/S0036144595295284",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "47A10 (15A18 47N40 65F15 76E05)",
MRnumber = "MR1469941 (98i:47004)",
MRreviewer = "Satish C. Reddy",
bibdate = "Sat Mar 29 09:55:51 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/39/3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/29528",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1997",
}
@Article{Driscoll:1998:PTM,
author = "Tobin A. Driscoll and Kim-Chuan C. Toh and Lloyd N.
Trefethen",
title = "From Potential Theory to Matrix Iterations in Six
Steps",
journal = j-SIAM-REVIEW,
volume = "40",
number = "3",
pages = "547--578",
month = sep,
year = "1998",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/S0036144596305582",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65F10 (31A99 65N99)",
MRnumber = "MR1642795 (99f:65049)",
MRreviewer = "Andreas Rathsfeld",
bibdate = "Sat Mar 29 09:56:00 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/40/3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/30558",
ZMnumber = "0930.65020",
acknowledgement = ack-nhfb,
classmath = "*65F10 Iterative methods for linear systems 30C20
Conformal mappings of special domains 41A10
Approximation by polynomials 30E10 Approximation in the
complex domain",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "conformal mapping; convergence; Krylov subspaces;
matrix iterations; numerical examples; polynomial
approximation; potential theory; semidefinite
programming",
onlinedate = "January 1998",
ZMreviewer = "D.Gaier (Gie{\ss}en)",
}
@InProceedings{Jonsson:1998:NAL,
author = "G. F. J{\o}nsson and L. N. Trefethen",
title = "A numerical analyst looks at the ``cutoff phenomenon''
in card shuffling and other {Markov} chains",
crossref = "Higham:1998:NAP",
pages = "150--178",
year = "1998",
MRclass = "65U05 (65F30)",
MRnumber = "MR1636951 (99i:65155)",
MRreviewer = "Sergei A. Nemnyugin",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
}
@Article{Toh:1998:CPM,
author = "Kim-Chuan Toh and Lloyd N. Trefethen",
title = "The {Chebyshev} Polynomials of a Matrix",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "20",
number = "2",
pages = "400--419",
month = apr,
year = "1998",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479896303739",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A60 (41A30)",
MRnumber = "MR1651393 (99m:15028)",
MRreviewer = "Vladimir B. Larin",
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/t/trefethen-lloyd-n.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/30373",
ZMnumber = "0922.65019",
acknowledgement = ack-nhfb,
classmath = "*65F10 Iterative methods for linear systems 15A60
Appl. of functional analysis to matrix theory 65K05
Mathematical programming (numerical methods)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "algorithm; Chebyshev polynomial of a matrix; Krylov
subspace iteration; matrix polynomial; primal-dual
interior point method; pseudospectra; semidefinite
programming",
ZMreviewer = "Alexey Alimov (Moskva)",
}
@InProceedings{Trefethen:1998:NAL,
author = "L. N. Trefethen and G. F. J{\o}nsson",
title = "A numerical analyst looks at the `cutoff phenomenon'
in card shuffling and other {Markov} chains",
crossref = "Higham:1998:NAP",
pages = "??--??",
year = "1998",
bibdate = "Wed Jan 07 13:27:45 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Trefethen:1998:SCM,
author = "Lloyd N. Trefethen and Tobin A. Driscoll",
title = "{Schwarz--Christoffel} mapping in the computer era",
crossref = "Fischer:1998:PIC",
pages = "533--542",
year = "1998",
MRclass = "30C30 (31A05 65E05)",
MRnumber = "MR1648186 (99i:30012)",
MRreviewer = "N. Papamichael",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "Extra volume III.",
}
@Article{Viswanath:1998:CNR,
author = "D. Viswanath and L. N. Trefethen",
title = "Condition Numbers of Random Triangular Matrices",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "19",
number = "2",
pages = "564--581",
month = apr,
year = "1998",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F35 (15A12 15A52 65U05)",
MRnumber = "MR1614019 (99b:65061)",
bibdate = "Fri Dec 4 12:14:09 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/19/2;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/31286",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Embree:1999:GDR,
author = "Mark Embree and Lloyd N. Trefethen",
title = "Growth and decay of random {Fibonacci} sequences",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
volume = "455",
number = "1987",
pages = "2471--2485",
day = "8",
month = jul,
year = "1999",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.1999.0412/",
ISSN = "1364-5021 (print), 1471-2946 (electronic)",
ISSN-L = "1364-5021",
MRclass = "11K31 (11B39)",
MRnumber = "MR1807827 (2001i:11098)",
MRreviewer = "Robert F. Tichy",
bibdate = "Tue Sep 27 19:08:10 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
abstract = "For $ 0 < \beta < \beta * \approx 0.70258 $, solutions
to the random recurrence $ x_{n + 1} = x_n \pm \beta
x_{n - 1} $ decay exponentially as $ n \to \infty $
with probability one, whereas for $ \beta > \beta * $,
they grow exponentially. By formulating the problem as
a Markov chain involving random matrix products and
computing its invariant measure (a fractal) the
Lyapunov constant $ \sigma (\beta) = \lim_{n \to \infty
} |x_n|^{1 / n} $ is determined numerically for a wide
range of values $ \beta $, and its dependence on $
\beta $ is observed to be non-smooth. (The limit is
defined in the almost sure sense.) This generalizes
recent work of Viswanath, who proved $ \sigma (1) =
1.131 988 24 \ldots {} $. By a simple rescaling, these
results also apply to the more general random
recurrence $ x_{n + 1} = \alpha x_n \pm \beta x_{n - 1}
$ for fixed $ \alpha $ and $ \beta $. These random
recurrence relations have links with many fields,
including ergodic theory, dynamical systems,
heavy-tailed statistics, spectral theory, continued
fractions, and condensed matter physics.",
fjournal = "The Royal Society of London. Proceedings. Series A.
Mathematical, Physical and Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
keywords = "Fibonacci sequence; Lyapunov constant; Markov chain;
random matrix products; random recurrences; Viswanath's
constant",
}
@Article{Embree:1999:GFM,
author = "Mark Embree and Lloyd N. Trefethen",
title = "{Green}'s Functions for Multiply Connected Domains via
Conformal Mapping",
journal = j-SIAM-REVIEW,
volume = "41",
number = "4",
pages = "745--761",
month = dec,
year = "1999",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/S0036144598349277",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "30E10 (30C20 31A99 65E05)",
MRnumber = "MR1722999 (2000h:30053)",
bibdate = "Sat Mar 29 09:56:11 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/41/4;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/34927",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1999",
}
@Article{Toh:1999:KMT,
author = "Kim-Chuan Toh and Lloyd N. Trefethen",
title = "The {Kreiss} matrix theorem on a general complex
domain",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "21",
number = "1",
pages = "145--165",
year = "1999",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F10 (15A60 30E10 65J10)",
MRnumber = "MR1709731 (2000h:65054)",
MRreviewer = "Guo Liang Chen",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
ZMnumber = "0946.65029",
classmath = "*65F35 Matrix norms, etc. (numerical linear algebra)
65F10 Iterative methods for linear systems 15A60 Appl.
of functional analysis to matrix theory 30E10
Approximation in the complex domain",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "conformal mapping; Faber polynomials; Hilbert space;
Kreiss matrix theorem; Krylov subspaces; polynomials of
a matrix",
ZMreviewer = "Michael Sever (Jerusalem)",
}
@Article{Trefethen:1999:CP,
author = "Lloyd N. Trefethen",
title = "Computation of pseudospectra",
journal = j-ACTA-NUMERICA,
volume = "8",
pages = "247--295",
year = "1999",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S0962492900002932",
ISBN = "0-521-77088-2",
ISBN-13 = "978-0-521-77088-0",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
MRclass = "65F15 (65F35 65Y05)",
MRnumber = "MR1819647 (2002b:65062)",
MRreviewer = "Rafikul Alam",
bibdate = "Sat Sep 24 10:23:38 MDT 2011",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.1.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
crindex = "Manquant",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
onlinedate = "07 November 2008",
}
@TechReport{Trefethen:1999:MMM,
author = "Anne E. Trefethen and Vijay S. Menon and Chi-Chao
Chang and Grzegorz J. Czajkowski and Chris Myers and
Lloyd N. Trefethen",
title = "{MultiMATLAB}: {MATLAB} on Multiple Processors",
institution = "Cornell Theory Center and Computer Science
Department",
address = "Cornell University, Ithaca, NY",
day = "19",
month = aug,
year = "1999",
bibdate = "Thu Oct 24 08:03:25 2002",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://www.cs.cornell.edu/Info/People/lnt/multimatlab.html",
acknowledgement = ack-nhfb,
}
@InProceedings{Trefethen:1999:SP,
author = "Lloyd N. Trefethen",
editor = "Mark Ainsworth and Jeremy Levesley and Marco
Marletta",
booktitle = "The Graduate Student's Guide to Numerical Analysis
'98",
title = "Spectra and Pseudospectra",
publisher = pub-SV,
address = pub-SV:adr,
pages = "217--250",
year = "1999",
bibdate = "Wed Aug 24 16:03:45 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Trefethen:1999:SPB,
author = "Lloyd N. Trefethen",
title = "Spectra and pseudospectra. {The} behaviour of
non-normal matrices and operators",
crossref = "Ainsworth:1999:GSG",
pages = "217--250",
year = "1999",
MRclass = "65F15 (15A18)",
MRnumber = "MR1715035",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
}
@Article{Trefethen:1999:SPP,
author = "Anne E. Trefethen and Lloyd N. Trefethen and Peter J.
Schmid",
title = "Spectra and pseudospectra for pipe {Poiseuille} flow",
journal = j-COMPUT-METH-APPL-MECH-ENG,
volume = "175",
number = "3--4",
pages = "413--420",
year = "1999",
CODEN = "CMMECC",
ISSN = "0045-7825, 0374-2830",
ISSN-L = "0045-7825",
MRclass = "76M25",
MRnumber = "MR1702189 (2000c:76069)",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "Computer Methods in Applied Mechanics and
Engineering",
journal-URL = "http://www.sciencedirect.com/science/journal/00457825",
}
@Article{Trefethen:1999:SRa,
author = "Nick Trefethen",
title = "Survey and Review",
journal = j-SIAM-REVIEW,
volume = "41",
number = "1",
pages = "1--2",
month = mar,
year = "1999",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Oct 27 14:32:49 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/41/1;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97019",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Trefethen:1999:SRb,
author = "Nick Trefethen",
title = "Survey and Review",
journal = j-SIAM-REVIEW,
volume = "41",
number = "2",
pages = "197--197",
month = jun,
year = "1999",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000041000002000197000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:56:07 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/41/2;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97024",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1999",
}
@Article{Trefethen:1999:SRc,
author = "Nick Trefethen",
title = "Survey and Review",
journal = j-SIAM-REVIEW,
volume = "41",
number = "3",
pages = "415--415",
month = sep,
year = "1999",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000041000003000415000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:56:09 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/41/3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97029",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1999",
}
@Article{Trefethen:1999:SRd,
author = "Nick Trefethen",
title = "Survey and Review",
journal = j-SIAM-REVIEW,
volume = "41",
number = "4",
pages = "635--635",
month = dec,
year = "1999",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000041000004000635000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:56:11 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/41/4;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97035",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1999",
}
@Article{Trefethen:19xx:PTM,
author = "L. N. Trefethen and T. A. Driscoll and K.-C. Toh",
title = "From potential theory to matrix iterations in six
steps",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "??",
number = "??",
pages = "??--??",
month = "????",
year = "19xx",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Wed Jan 07 16:22:20 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "To appear.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Toh:2000:KMT,
author = "Kim-Chuan Toh and Lloyd N. Trefethen",
title = "The {Kreiss} Matrix Theorem on a General Complex
Domain",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "21",
number = "1",
pages = "145--165",
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/t/trefethen-lloyd-n.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/32402",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Trefethen:2000:HMS,
author = "L. N. Trefethen and L. M. Trefethen",
title = "How many shuffles to randomize a deck of cards?",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
volume = "456",
number = "2002",
pages = "2561--2568",
day = "8",
month = oct,
year = "2000",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.2000.0625",
ISSN = "1364-5021 (print), 1471-2946 (electronic)",
ISSN-L = "1364-5021",
MRclass = "60C05 (05A05 60B10 60J10 94A17)",
MRnumber = "MR1796496 (2001k:60009)",
MRreviewer = "David J. Grabiner",
bibdate = "Tue Sep 27 19:07:32 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
abstract = "A celebrated theorem of Aldous, Bayer and Diaconis
asserts that it takes $ \asymp 3 / 2 l o g_2 n $ riffle
shuffles to randomize a deck of $n$ cards,
asymptotically as $ n \to \infty $, and that the
randomization occurs abruptly according to a `cut-off
phenomenon'. These results depend upon measuring
randomness by a quantity known as the total variation
distance. If randomness is measured by uncertainty or
entropy in the sense of information theory, the
behaviour is different. It takes only $ \asymp \log_2 n
$ shuffles to reduce the information to a proportion
arbitrarily close to zero, and $ \asymp 3 / 2 \log_2 n
$ to reduce it to an arbitrarily small number of bits.
At $ 3 / 2 > \log_2 n $ shuffles, ca. $ 0.0601 $ bits
remain, independently of $n$.",
fjournal = "The Royal Society of London. Proceedings. Series A.
Mathematical, Physical and Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
}
@Book{Trefethen:2000:SMM,
author = "Lloyd N. Trefethen",
title = "Spectral Methods in {MATLAB}",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xvi + 165",
year = "2000",
ISBN = "0-89871-465-6 (paperback), 0-89871-959-3 (e-book)",
ISBN-13 = "978-0-89871-465-4 (paperback), 978-0-89871-959-8
(e-book)",
LCCN = "QA377 .T65 2000",
MRclass = "65-01 (65-04)",
MRnumber = "MR1776072 (2001c:65001)",
bibdate = "Tue Jan 23 09:04:41 2001",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2000.bib",
series = "Software, environments, tools",
abstract = "This is the only book on spectral methods built around
MATLAB programs. Along with finite differences and
finite elements, spectral methods are one of the three
main technologies for solving partial differential
equations on computers. Since spectral methods involve
significant linear algebra and graphics they are very
suitable for the high level programming of MATLAB. This
hands-on introduction is built around forty short and
powerful MATLAB programs, which the reader can download
from the World Wide Web. This book presents the key
ideas along with many figures, examples, and short,
elegant MATLAB programs for readers to adapt to their
own needs. It covers ODE and PDE boundary value
problems, eigenvalues and pseudospectra, linear and
nonlinear waves, and numerical quadrature.",
acknowledgement = ack-njh,
keywords = "differential equations, partial --- numerical
solutions --- data processing; Matlab; spectral theory
(mathematics)",
tableofcontents = "Preface \\
Acknowledgments \\
A note on the MATLAB programs \\
1. Differentiation matrices \\
2. Unbounded grids: The semidiscrete Fourier transform
\\
3. Periodic grids --- The DFT and FFT \\
4. Smoothness and spectral accuracy \\
5. Polynomial interpolation and clustered grids \\
6. Chebyshev differentiation matrices \\
7. Boundary value problems \\
8. Chebyshev series and the FFT \\
9. Eigenvalues and pseudospectra \\
10. Time-stepping and stability regions \\
11. Polar coordinates \\
12. Integrals and quadrature formulas \\
13. More about boundary conditions \\
14. Fourth-order problems \\
Afterword \\
Bibliography \\
Index",
}
@Article{Trefethen:2000:SRa,
author = "Nick Trefethen",
title = "Survey and Review",
journal = j-SIAM-REVIEW,
volume = "42",
number = "1",
pages = "1--1",
month = mar,
year = "2000",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000042000001000001000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:56:13 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/42/1;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97041",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 2000",
}
@Article{Trefethen:2000:SRb,
author = "Nick Trefethen",
title = "Survey and Review",
journal = j-SIAM-REVIEW,
volume = "42",
number = "2",
pages = "159--159",
month = jun,
year = "2000",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000042000002000159000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:56:15 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/42/2;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97050",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 2000",
}
@Article{Trefethen:2000:SRIa,
author = "Nick Trefethen",
title = "Survey and review --- Introduction",
journal = j-SIAM-REVIEW,
volume = "42",
number = "3",
pages = "367--367",
month = sep,
year = "2000",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000042000003000367000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:56:18 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/42/3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97051",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 2000",
xxonlinedate = "Sep-2000",
xxtitle = "Survey and Review",
}
@Article{Trefethen:2000:SRIb,
author = "Nick Trefethen",
title = "Survey and review --- Introduction",
journal = j-SIAM-REVIEW,
volume = "42",
number = "4",
pages = "553--553",
month = dec,
year = "2000",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000042000004000553000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:56:20 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/42/4;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97056",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "December 2000",
}
@Article{Banjai:2001:NSO,
author = "Lehel Banjai and Lloyd N. Trefethen",
title = "Numerical solution of the omitted area problem of
univalent function theory",
journal = j-COMPUT-METH-FUNCT-THEORY,
volume = "1",
number = "1",
pages = "259--273",
year = "2001",
CODEN = "????",
ISSN = "1617-9447",
MRclass = "30C30 (30C75)",
MRnumber = "MR1931615 (2003k:30014)",
MRreviewer = "N. Papamichael",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
ZMnumber = "1007.30009",
classmath = "*30C30 Numerical methods in conformal mapping theory
30C75 Extremal problems for (quasi-)conformal mappings,
other methods 65E05 Numerical methods in complex
analysis",
fjournal = "Computational Methods and Function Theory",
keywords = "numerical conformal mapping; omitted area problem;
univalent function theory",
}
@Article{Embree:2001:GET,
author = "Mark Embree and Lloyd N. Trefethen",
title = "Generalizing Eigenvalue Theorems to Pseudospectra
Theorems",
journal = j-SIAM-J-SCI-COMP,
volume = "23",
number = "2",
pages = "583--590",
month = mar,
year = "2001",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827500373012",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed Jul 25 09:55:57 MDT 2001",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/23/2;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/37301",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Misc{Embree:2001:PG,
author = "Mark Embree and Lloyd N. Trefethen",
title = "Pseudospectra Gateway",
howpublished = "Web site",
year = "2001",
bibdate = "Sun Jun 19 16:38:45 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://www.comlab.ox.ac.uk/pseudospectra",
abstract = "Eigenvalue analysis of non-hermitian matrices and
operators can be misleading: Predictions often fail to
match observations. Specifically, trouble may arise
when the associated sets of eigenvectors are
ill-conditioned with respect to the norm of applied
interest. In the case of the familiar Euclidean or
2-norm, this means that the matrix or operator is
non-normal, and the eigenvectors are not orthogonal.
Pseudospectra provide an analytical and graphical
alternative for investigating non-normal matrices and
operators.",
acknowledgement = ack-nhfb,
}
@Article{Howle:2001:EMI,
author = "V. E. Howle and Lloyd N. Trefethen",
title = "Eigenvalues and musical instruments",
journal = j-J-COMPUT-APPL-MATH,
volume = "135",
number = "1",
pages = "23--40",
day = "1",
month = oct,
year = "2001",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(00)00560-4",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "74H45 (00A69 34B05 70J10)",
MRnumber = "MR1854442 (2002i:74024)",
bibdate = "Sat Feb 25 12:45:20 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700005604",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Trefethen:2001:SPL,
author = "Lloyd N. Trefethen and Marco Contedini and Mark
Embree",
title = "Spectra, pseudospectra, and localization for random
bidiagonal matrices",
journal = j-COMM-PURE-APPL-MATH,
volume = "54",
number = "5",
pages = "595--623",
year = "2001",
CODEN = "CPAMAT",
ISSN = "0010-3640 (print), 1097-0312 (electronic)",
ISSN-L = "0010-3640",
MRclass = "15A52 (15A18 60F99)",
MRnumber = "MR1811128 (2002c:15047)",
MRreviewer = "Nicholas S. Witte",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "Communications on Pure and Applied Mathematics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
}
@Article{Trefethen:2001:SRa,
author = "Nick Trefethen",
title = "Survey and Review",
journal = j-SIAM-REVIEW,
volume = "43",
number = "1",
pages = "1--1",
month = mar,
year = "2001",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000043000001000001000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:56:22 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/43/1;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97061",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 2001",
}
@Article{Trefethen:2001:SRb,
author = "Nick Trefethen",
title = "Survey and Review",
journal = j-SIAM-REVIEW,
volume = "43",
number = "2",
pages = "233--233",
month = jun,
year = "2001",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000043000002000233000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:56:24 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/43/2;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97066",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 2001",
}
@Article{Trefethen:2001:SRc,
author = "Nick Trefethen",
title = "Survey and Review",
journal = j-SIAM-REVIEW,
volume = "43",
number = "3",
pages = "411--411",
month = sep,
year = "2001",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000043000003000411000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:56:26 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/43/3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97071",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 2001",
}
@Article{Trefethen:2001:SRd,
author = "Nick Trefethen",
title = "Survey and Review",
journal = j-SIAM-REVIEW,
volume = "43",
number = "4",
pages = "583--583",
month = dec,
year = "2001",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000043000004000583000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:56:28 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/43/4;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97076",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 2001",
}
@Article{Wright:2001:CLC,
author = "Thomas G. Wright and Lloyd N. Trefethen",
title = "Computing {Lyapunov} constants for random recurrences
with smooth coefficients",
journal = j-J-COMPUT-APPL-MATH,
volume = "132",
number = "2",
pages = "331--340",
day = "15",
month = jul,
year = "2001",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65C40",
MRnumber = "MR1840632 (2002d:65010)",
bibdate = "Sat Feb 25 12:45:19 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700004374",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Wright:2001:LSC,
author = "Thomas G. Wright and Lloyd N. Trefethen",
title = "Large-Scale Computation of Pseudospectra Using
{ARPACK} and {\tt eigs}",
journal = j-SIAM-J-SCI-COMP,
volume = "23",
number = "2",
pages = "591--605",
month = mar,
year = "2001",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S106482750037322X",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15 (65F50)",
MRnumber = "MR1861267 (2002h:65061)",
bibdate = "Wed Jul 25 09:55:57 MDT 2001",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/23/2;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "Copper Mountain Conference (2000).",
URL = "http://epubs.siam.org/sam-bin/dbq/article/37322",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "Matlab",
}
@Article{Bottcher:2002:PCT,
author = "Albrecht B{\"o}ttcher and Mark Embree and Lloyd N.
Trefethen",
title = "Piecewise continuous {Toeplitz} matrices and
operators: slow approach to infinity",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "24",
number = "2",
pages = "484--489",
year = "2002",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479800376971",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "47B35 (15A18 15A60 47A10)",
MRnumber = "MR1951133 (2004b:47049)",
MRreviewer = "Paolo Tilli",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Book{Driscoll:2002:SCM,
author = "Tobin A. Driscoll and Lloyd N. Trefethen",
title = "{Schwarz--Christoffel} mapping",
volume = "8",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xvi + 132",
year = "2002",
ISBN = "0-521-80726-3",
ISBN-13 = "978-0-521-80726-5",
LCCN = "QA360 .D75 2002",
MRclass = "30C30 (30-02 30-04 65E05)",
MRnumber = "MR1908657 (2003e:30012)",
MRreviewer = "N. Papamichael",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
series = "Cambridge Monographs on Applied and Computational
Mathematics",
tableofcontents = "Preface xv \\
1 Introduction / 1 \\
1.1 The Schwarz--Christoffel idea / 1 \\
1.2 History / 5 \\
2 Essentials of Schwarz--Christoffel mapping / 11 \\
2.1 Polygons / 11 \\
2.2 The Schwarz--Christoffel formula / 12 \\
2.3 Polygons with one or two vertices / 14 \\
2.4 Triangles / 19 \\
2.5 Rectangles and elliptic functions / 21 \\
2.6 Crowding / 23 \\
3 Numerical methods / 27 \\
3.1 Side-length parameter problem / 27 \\
3.2 Quadrature / 32 \\
3.3 Inverting the map / 34 \\
3.4 Cross-ratio parameter problem / 35 \\
3.5 Mapping using cross-ratios / 41 \\
3.6 Software / 45 \\
4 Variations / 47 \\
4.1 Mapping from the disk / 48 \\
4.2 Mapping from a strip / 49 \\
4.3 Mapping from a rectangle / 54 \\
4.4 Exterior maps / 60 \\
4.5 Periodic regions and fractals / 61 \\
4.6 Reflections and other transformations / 66 \\
4.7 Riemann surfaces / 67 \\
4.8 Gearlike regions / 69 \\
4.9 Doubly connected regions / 73 \\
4.10 Circular-arc polygons / 79 \\
4.11 Curved boundaries / 84 \\
5 Applications / 87 \\
5.1 Why use Schwarz--Christoffel maps? / 88 \\
5.2 Piecewise-constant boundary conditions / 89 \\
5.3 Alternating Dirichlet and Neumann conditions / 93
\\
5.4 Oblique derivative boundary conditions / 100 \\
5.5 Generalized parameter problems / 113 \\
5.6 Free-streamline flows / 115 \\
5.7 Mesh generation / 120 \\
5.8 Polynomial approximation and matrix iterations /
123 \\
5.9 Symmetric multiply connected domains / 127 \\
Using the SC Toolbox / 131 \\
Bibilography / 137 \\
Index / 151",
}
@TechReport{Dussaud:2002:HDC,
author = "Eric Dussaud and Chris Husband and Hoang Nguyen and
Dan Reynolds and Christiaan Stolk",
title = "Hundred Digit Challenge Solutions",
institution = "Department of Computational and Applied Mathematics,
Rice University",
address = "Houston, TX, USA",
pages = "21",
day = "16",
month = may,
year = "2002",
bibdate = "Tue Jan 03 16:43:13 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "See
\cite{Trefethen:2002:HDH,Trefethen:2002:DCC,Trefethen:2002:SDD}.",
URL = "http://www.caam.rice.edu/caam/trs/2002/TR02-06.pdf;
http://www.caam.rice.edu/caam/trs/2002/TR02-06.ps;
http://www.caam.rice.edu/caam/trs/2002_abstracts.html#TR02-06",
acknowledgement = ack-nhfb,
remark = "CAAM Technical Report",
}
@Misc{Gonnet:2002:SSD,
author = "Gaston Gonnet and Robert Israel",
title = "Solutions to the {SIAM 100-Dollar, 100-Digit
Challenge}",
howpublished = "World-Wide Web document.",
year = "2002",
bibdate = "Tue Jan 03 16:53:24 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "See
\cite{Trefethen:2002:HDH,Trefethen:2002:DCC,Trefethen:2002:SDD}.",
URL = "http://www.math.ubc.ca/~israel/challenge/challenge.html",
acknowledgement = ack-nhfb,
}
@Misc{Kaplan:2002:BSS,
author = "Danny Kaplan and Stan Wagon",
title = "Brief Solutions to the {SIAM Hundred-Dollar,
Hundred-Digit Challenge}",
howpublished = "World-Wide Web document.",
day = "27",
month = jun,
year = "2002",
bibdate = "Tue Jan 03 16:49:32 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "See
\cite{Trefethen:2002:HDH,Trefethen:2002:DCC,Trefethen:2002:SDD}.",
URL = "http://stanwagon.com/wagon/Misc/HTMLLinks/SIAMchallenge_2.html",
acknowledgement = ack-nhfb,
}
@Article{Keller:2002:LEH,
author = "Joseph B. Keller",
title = "Letter to the {Editor}: The Hundred-dollar,
Hundred-digit Challenge",
journal = j-SIAM-NEWS,
volume = "35",
number = "10",
pages = "??--??",
month = dec,
year = "2002",
ISSN = "0036-1437",
bibdate = "Tue Jan 03 16:40:28 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://www.siam.org/siamnews/12-02/letter.htm",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Misc{Kern:2002:SHD,
author = "Michel Kern",
title = "Solution to the {``Hundred-dollar, Hundred-digit
Challenge''}",
howpublished = "World-Wide Web document.",
pages = "14",
day = "17",
month = may,
year = "2002",
bibdate = "Tue Jan 03 16:33:02 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "See
\cite{Trefethen:2002:HDH,Trefethen:2002:DCC,Trefethen:2002:SDD}.",
URL = "http://www-rocq.inria.fr/~kern/Challenge/challenge.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Kern:2002:SSH,
author = "Michel Kern",
title = "Solution to the {SIAM ``Hundred-dollar, Hundred-digit
Challenge''}",
type = "Report",
number = "4472",
institution = "INRIA",
address = "Unit{\'e} de recherche INRIA Rocquencourt, Domaine de
Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex,
France",
pages = "21",
month = may,
year = "2002",
ISSN = "0249-6399",
bibdate = "Tue Jan 03 16:34:51 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "See
\cite{Trefethen:2002:HDH,Trefethen:2002:DCC,Trefethen:2002:SDD}.",
URL = "http://www-rocq.inria.fr/who/Michel.Kern/Challenge/RR-challenge.pdf;
http://www-rocq.inria.fr/~kern/Challenge/challenge.html;
http://www.lacim.uqam.ca/~plouffe/OEIS/citations/RR-4472.pdf",
acknowledgement = ack-nhfb,
}
@Misc{Laurie:2002:STH,
author = "Dirk Laurie",
title = "Solutions to {Trefethen}'s Hundred-dollar,
Hundred-digit challenge problems",
howpublished = "World-Wide Web document.",
pages = "2",
day = "23",
month = may,
year = "2002",
bibdate = "Tue Jan 03 16:29:42 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "See
\cite{Trefethen:2002:HDH,Trefethen:2002:DCC,Trefethen:2002:SDD}.",
URL = "http://dip.sun.ac.za/~laurie/trefethen-challenge/;
http://dip.sun.ac.za/~laurie/trefethen-challenge/howsolved.pdf",
acknowledgement = ack-nhfb,
}
@Misc{McInturff:2002:SHD,
author = "Kim McInturff and Peter S. Simon",
title = "Solutions for the Hundred-Dollar, Hundred-Digit
Challenge",
howpublished = "World-Wide Web document.",
pages = "46",
day = "29",
month = apr,
year = "2002",
bibdate = "Tue Jan 03 16:25:21 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "See
\cite{Trefethen:2002:HDH,Trefethen:2002:DCC,Trefethen:2002:SDD}.",
URL = "http://www.vcnet.com/~simonp/;
http://www.vcnet.com/~simonp/solutions.pdf",
acknowledgement = ack-nhfb,
}
@Misc{Medley:2002:SC,
author = "Brian Medley and Bernard B. Beard and Marijke van
Gans",
title = "The 2002 {SIAM} Challenge",
howpublished = "World-Wide Web document.",
year = "2002",
bibdate = "Tue Jan 03 16:58:20 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "See
\cite{Trefethen:2002:HDH,Trefethen:2002:DCC,Trefethen:2002:SDD}.",
URL = "http://www.maxwellian.demon.co.uk/~marijke/SIAM2002/;
http://www.maxwellian.demon.co.uk/~marijke/SIAM2002/siamscim.pdf",
acknowledgement = ack-nhfb,
}
@Misc{Specht:2002:HSH,
author = "Eckard Specht and Martin Wohlgemuth and Clemens Raab
and Lutz Gehlen",
title = "How to solve the {``A Hundred-Dollar, Hundred-Digit
Challenge''}",
howpublished = "World-Wide Web document.",
pages = "15",
year = "2002",
bibdate = "Tue Jan 03 16:27:38 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "See
\cite{Trefethen:2002:HDH,Trefethen:2002:DCC,Trefethen:2002:SDD}.",
URL = "http://matheplanet.com/matheplanet/nuke/html/matroid/siam/siam_results.pdf",
acknowledgement = ack-nhfb,
}
@Article{Trefethen:2002:DCC,
author = "Lloyd N. Trefethen",
title = "The \$100, 100-digit Challenge: Chastened Challenge
Sponsor: ``{I} Misjudged''",
journal = j-SIAM-NEWS,
volume = "35",
number = "6",
pages = "4",
month = jul # "\slash " # aug,
year = "2002",
ISSN = "0036-1437",
bibdate = "Tue Jan 03 17:04:04 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://www.siam.org/siamnews/07-02/challengeupdate.pdf",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
remark = "From the text: ``In the January announcement I wrote,
If anyone gets 50 digits in total, I will be impressed.
Well, I misjudged. In the end, along with plenty of
scores in the twenties, forties, and sixties, at the
top we had twenty perfect scores. After them came five
teams who scored 99 out of 100. Six further teams
scored between 90 and 98.''",
}
@Article{Trefethen:2002:HDH,
author = "Lloyd N. Trefethen",
title = "A Hundred-Dollar, Hundred-Digit Challenge",
journal = j-SIAM-NEWS,
volume = "35",
number = "1",
pages = "??--??",
month = jan,
year = "2002",
ISSN = "0036-1437",
bibdate = "Tue Jan 03 15:43:17 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "See solutions
\cite{Bornemann:2004:SDC,Dussaud:2002:HDC,Gonnet:2002:SSD,Kaplan:2002:BSS,Kern:2002:SHD,Kern:2002:SSH,Laurie:2002:STH,McInturff:2002:SHD,Medley:2002:SC,Specht:2002:HSH,Trefethen:2002:DCC,Trefethen:2002:SDD}.
From the solutions Web site: ``Ninety-four teams from
twenty-five countries entered the competition. Of
these, twenty teams scored 100 points and thus are
counted as FIRST PRIZE WINNERS''.",
URL = "http://dip.sun.ac.za/~laurie/trefethen-challenge/challenge.ps;
http://mathworld.wolfram.com/Hundred-DollarHundred-DigitChallengeProblems.html;
http://spiff.rit.edu/classes/phys317/lectures/intro/hundred_dollar.pdf;
http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/hundred.html;
http://www.siam.org/siamnews/01-02/challenge.pdf",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Article{Trefethen:2002:SDD,
author = "Lloyd N. Trefethen",
title = "The {SIAM} 100-Dollar, 100-Digit Challenge",
journal = j-SIAM-NEWS,
volume = "35",
number = "6",
pages = "2",
month = jul # "\slash " # aug,
year = "2002",
ISSN = "0036-1437",
bibdate = "Tue Jan 03 17:12:22 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://www.siam.org/siamnews/06-02/challengedigits.pdf",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Article{Trefethen:2002:SRa,
author = "Nick Trefethen",
title = "Survey and Review",
journal = j-SIAM-REVIEW,
volume = "44",
number = "1",
pages = "1--1",
month = mar,
year = "2002",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000044000001000001000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:56:31 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/44/1;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97081",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 2002",
}
@Article{Trefethen:2002:SRb,
author = "Nick Trefethen",
title = "Survey and Review",
journal = j-SIAM-REVIEW,
volume = "44",
number = "2",
pages = "167--167",
month = jun,
year = "2002",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000044000002000167000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:56:33 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/44/2;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97086",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 2002",
}
@Article{Trefethen:2002:SRc,
author = "Nick Trefethen",
title = "Survey and Review",
journal = j-SIAM-REVIEW,
volume = "44",
number = "3",
pages = "309--309",
month = sep,
year = "2002",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000044000003000309000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:56:35 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/44/3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97091",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 2002",
}
@Article{Trefethen:2002:SRd,
author = "Nick Trefethen",
title = "Survey and Review",
journal = j-SIAM-REVIEW,
volume = "44",
number = "4",
pages = "523--523",
month = dec,
year = "2002",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000044000004000523000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:56:37 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/44/4;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97096",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 2002",
}
@Article{Trefethen:2002:SRI,
author = "N. Trefethen",
title = "Survey and review --- Introduction",
journal = j-SIAM-REVIEW,
volume = "44",
number = "4",
pages = "523--523",
month = "????",
year = "2002",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.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 = "December 2002",
}
@Article{vanderVorst:2002:CMC,
author = "Henk van der Vorst and Iain Duff and Howard Elman and
Ronal Freund and Tim Kelley and Seymour Parter and
Gerhard Starke and Nick Trefethen and Panayot
Vassilevski and Homer Walker and Olof Widlund",
title = "{2000 Copper Mountain Conference}",
journal = j-SIAM-J-SCI-COMP,
volume = "23",
number = "2",
pages = "vii--vii",
month = mar,
year = "2002",
CODEN = "SJOCE3",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed Jul 25 09:55:57 MDT 2001",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/23/2;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97414",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Wright:2002:PRM,
author = "Thomas G. Wright and Lloyd N. Trefethen",
title = "Pseudospectra of rectangular matrices",
journal = j-IMA-J-NUMER-ANAL,
volume = "22",
number = "4",
pages = "501--519",
month = oct,
year = "2002",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/22.4.501",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65F15",
MRnumber = "MR1936516 (2003m:65056)",
MRreviewer = "Jesse L. Barlow",
bibdate = "Fri Oct 18 09:49:23 MDT 2002",
bibsource = "http://www3.oup.co.uk/imanum/hdb/Volume_22/Issue_04/;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://www3.oup.co.uk/imanum/hdb/Volume_22/Issue_04/220501.sgm.abs.html;
http://www3.oup.co.uk/imanum/hdb/Volume_22/Issue_04/pdf/220501.pdf",
abstract = "Pseudospectra of rectangular matrices vary
continuously with the matrix entries, a feature that
eigenvalues of these matrices do not have. Some
properties of eigenvalues and pseudospectra of
rectangular matrices are explored, and an efficient
algorithm for the computation of pseudospectra is
proposed. Applications are given in (square) eigenvalue
computation (Lanczos iteration), square pseudospectra
approximation (Arnoldi iteration), control theory
(nearest uncontrollable system) and game theory.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Banjai:2003:MMS,
author = "Lehel Banjai and L. N. Trefethen",
title = "A Multipole Method for {Schwarz--Christoffel} Mapping
of Polygons with Thousands of Sides",
journal = j-SIAM-J-SCI-COMP,
volume = "25",
number = "3",
pages = "1042--1065",
month = may,
year = "2003",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827502411675",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "30C30 (65E05)",
MRnumber = "MR2046124 (2004m:30011)",
MRreviewer = "N. Papamichael",
bibdate = "Mon Jan 12 19:00:43 MST 2004",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/25/3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/41167",
ZMnumber = "1060.30012",
acknowledgement = ack-nhfb,
classmath = "*30C30 Numerical methods in conformal mapping theory
65E05 Numerical methods in complex analysis 70F10
n-body problem",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "conformal mapping; fast multipole method; Koch
snowflake; Schwarz--Christoffel mapping",
}
@Article{Bottcher:2003:PCT,
author = "Albrecht B{\"o}ttcher and Mark Embree and Lloyd N.
Trefethen",
title = "Piecewise Continuous {Toeplitz} Matrices and
Operators: {Slow} Approach to Infinity",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "24",
number = "2",
pages = "484--489",
month = apr,
year = "2003",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Aug 15 05:45:45 MDT 2003",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/24/2;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/37697",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Meseguer:2003:LPF,
author = "{\'A}. Meseguer and L. N. Trefethen",
title = "Linearized pipe flow to {Reynolds} number $ 10^7 $",
journal = j-J-COMPUT-PHYS,
volume = "186",
number = "1",
pages = "178--197",
day = "20",
month = mar,
year = "2003",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/S0021-9991(03)00029-9",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
MRclass = "76M22",
MRnumber = "MR1967366",
bibdate = "Mon Jan 2 22:12:28 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999103000299",
ZMnumber = "1047.76565",
acknowledgement = ack-nhfb,
classmath = "*76M22 Spectral methods 76D05 Navier--Stokes equations
(fluid dynamics)",
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Book{Saff:2003:FCA,
author = "Edward B. Saff and Arthur David Snider",
title = "Fundamentals of Complex Analysis: with Applications to
Engineering and Science",
publisher = pub-PH,
address = pub-PH:adr,
edition = "Third",
pages = "xi + 511",
year = "2003",
ISBN = "0-13-907874-6, 0-13-017968-X (International ed.)",
ISBN-13 = "978-0-13-907874-3, 978-0-13-017968-5 (International
ed.)",
LCCN = "QA300 .S18 2003",
bibdate = "Thu Nov 17 07:04:29 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
library.ox.ac.uk:210/ADVANCE;
melvyl.cdlib.org:210/CDL90;
z3950.loc.gov:7090/Voyager",
note = "With an appendix by Lloyd N. Trefethen and Tobin A.
Driscoll.",
acknowledgement = ack-nhfb,
keywords = "MATLAB toolbox",
remark = "Rev. ed. of: Fundamentals of complex analysis for
mathematics, science, and engineering. 2nd ed. c1993.",
subject = "Mathematical analysis; Functions of complex
variables",
tableofcontents = "1: Complex numbers \\
2: Analytic functions \\
3: Elementary functions \\
4: Complex integration \\
5: Series representations for analytic functions \\
6: Residue Theory \\
7: Conformal mapping \\
8: The transforms of applied mathematics \\
A: Numerical construction of conformal maps \\
B: Table of conformal mappings",
}
@Article{Battles:2004:EMC,
author = "Zachary Battles and Lloyd N. Trefethen",
title = "An Extension of {MATLAB} to Continuous Functions and
Operators",
journal = j-SIAM-J-SCI-COMP,
volume = "25",
number = "5",
pages = "1743--1770",
month = sep,
year = "2004",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827503430126",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "41-04 (65-04)",
MRnumber = "MR2087334 (2005e:41001)",
bibdate = "Sat Apr 16 12:07:14 MDT 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/25/5;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/43012",
ZMnumber = "1057.65003",
acknowledgement = ack-nhfb,
classmath = "*65D05 Interpolation (numerical methods) 41-04 Machine
computation, programs (approximations and expansions)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "barycentric formula; Chebyshev points; FFT;
interpolation; MATLAB; spectral methods",
}
@Article{Berrut:2004:BLI,
author = "Jean-Paul Berrut and Lloyd N. Trefethen",
title = "Barycentric {Lagrange} Interpolation",
journal = j-SIAM-REVIEW,
volume = "46",
number = "3",
pages = "501--517",
month = sep,
year = "2004",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/S0036144502417715",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65D05",
MRnumber = "MR2115059 (2005k:65018)",
MRreviewer = "Mao Dong Ye",
bibdate = "Sat Apr 16 12:47:32 MDT 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/46/3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/41771",
ZMnumber = "1061.65006",
acknowledgement = ack-nhfb,
classmath = "*65D05 Interpolation (numerical methods) 65L10
Boundary value problems for ODE (numerical methods)
41A05 Interpolation 65L60 Finite numerical methods for
ODE 34B15 Nonlinear boundary value problems of ODE",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "barycentric formula; Chebyshev interpolation;
collocation method; Lagrange polynomial interpolation;
Laurent interpolation; Newton interpolation; Sinc
interpolation; stability; trigonometric interpolation",
}
@Book{Bornemann:2004:SDC,
author = "Folkmar Bornemann and Dirk Laurie and Stan Wagon and
J{\"o}rg Waldvogel",
title = "The {SIAM} 100-digit challenge",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xii + 306",
year = "2004",
ISBN = "0-89871-561-X (paperback)",
ISBN-13 = "978-0-89871-561-3 (paperback)",
LCCN = "QA297 .S4782 2004",
MRclass = "65-02",
MRnumber = "MR2076374 (2005c:65002)",
MRreviewer = "Brian Bradie",
bibdate = "Tue Nov 25 07:34:14 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "A study in high-accuracy numerical computing, with a
foreword by David H. Bailey. See
\cite{Trefethen:2002:HDH}.",
price = "US\$57.00",
URL = "http://www-m8.mathematik.tu-muenchen.de/m3/ftp/Bornemann/pdf/story.pdf",
ZMnumber = "1060.65002",
abstract = "This book takes readers on a thrilling tour of some of
the most important and powerful areas of contemporary
numerical mathematics. The tour is organized along the
10 problems of the SIAM 100-Digit Challenge, a contest
posed by Nick Trefethen of Oxford University in the
January/February 2002 issue of SIAM News. The complete
story of the contest as well as a lively interview with
Nick Trefethen are also included. The authors, members
of teams that solved all 10 problems, show in detail
multiple approaches for solving each problem, ranging
from elementary to sophisticated, from brute-force to
schemes that can be scaled to provide thousands of
digits of accuracy and that can solve even larger
related problems. The authors touch on virtually every
major technique of modern numerical analysis: matrix
computation, iterative linear methods, limit
extrapolation and convergence acceleration, numerical
quadrature, contour integration, discretization of
PDEs, global optimization, Monte Carlo and evolutionary
algorithms, error control, interval and high-precision
arithmetic, and many more.",
tableofcontents = "Foreword \\
Preface \\
The Story \\
1: A Twisted Tail \\
2: Reliability amid Chaos \\
3: How Far Away Is Infinity? \\
4: Think Globally, Act Locally \\
5: A Complex Optimization \\
6: Biasing for a Fair Return \\
7: Too Large to Be Easy, Too Small to Be Hard \\
8: In the Moment of Heat \\
9: Gradus ad Parnassum \\
10: Hitting the Ends \\
Appendix A: Convergence Acceleration \\
Appendix B: Extreme Digit-Hunting \\
Appendix C: Code \\
Appendix D: More Problems \\
References \\
Index",
}
@Article{Trefethen:2004:WPP,
author = "Lloyd N. Trefethen and S. J. Chapman",
title = "Wave packet pseudomodes of twisted {Toeplitz}
matrices",
journal = j-COMM-PURE-APPL-MATH,
volume = "57",
number = "9",
pages = "1233--1264",
year = "2004",
CODEN = "CPAMAT",
DOI = "https://doi.org/10.1002/cpa.20034",
ISSN = "0010-3640 (print), 1097-0312 (electronic)",
ISSN-L = "0010-3640",
MRclass = "47B35 (15A57 47A75)",
MRnumber = "MR2059680 (2005c:47035)",
MRreviewer = "Stefano Serra Capizzano",
bibdate = "Tue Nov 25 07:34:14 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "Communications on Pure and Applied Mathematics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
}
@Article{Betcke:2005:RMP,
author = "Timo Betcke and Lloyd N. Trefethen",
title = "Reviving the Method of Particular Solutions",
journal = j-SIAM-REVIEW,
volume = "47",
number = "3",
pages = "469--491",
month = sep,
year = "2005",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/S0036144503437336",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Dec 30 07:13:11 MST 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/47/3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/43733",
ZMnumber = "02205852",
acknowledgement = ack-nhfb,
classmath = "*65N35 Collocation methods (BVP of PDE) 65F22
Ill-posedness, regularization 65N25 Numerical methods
for eigenvalue problems (BVP of PDE)",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "eigenvalues; method of particular solutions; subspace
angles",
}
@Article{Kassam:2005:FOT,
author = "Aly-Khan Kassam and Lloyd N. Trefethen",
title = "Fourth-Order Time-Stepping for Stiff {PDEs}",
journal = j-SIAM-J-SCI-COMP,
volume = "26",
number = "4",
pages = "1214--1233",
month = jul,
year = "2005",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827502410633",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65M70 (65L05 65M20)",
MRnumber = "MR2143482",
bibdate = "Sat Apr 16 12:07:25 MDT 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/26/4;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/41063",
ZMnumber = "02207102",
acknowledgement = ack-nhfb,
classmath = "*65M70 Spectral, collocation and related methods (IVP
of PDE) 65L05 Initial value problems for ODE (numerical
methods) 65M20 Method of lines (IVP of PDE)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "Allen--Cahn; Burgers; ETD; exponential
time-differencing; implicit-explicit; integrating
factor; KdV; Kuramoto--Sivashinsky; split step",
}
@Book{Trefethen:2005:SPB,
author = "Lloyd N. Trefethen and Mark Embree",
title = "Spectra and Pseudospectra: the Behavior of Nonnormal
Matrices and Operators",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xviii + 606",
year = "2005",
ISBN = "0-691-11946-5",
ISBN-13 = "978-0-691-11946-5",
LCCN = "QA320 .T67 2005",
MRclass = "15-02 (15A18 47A10 47A50)",
MRnumber = "MR2155029",
bibdate = "Tue Nov 25 07:34:14 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "The behavior of nonnormal matrices and operators",
URL = "http://www.loc.gov/catdir/enhancements/fy0654/2005046573-b.html;
http://www.loc.gov/catdir/enhancements/fy0654/2005046573-d.html;
http://www.loc.gov/catdir/enhancements/fy0654/2005046573-t.html",
tableofcontents = "Preface / xiii \\
Acknowledgments / xv \\
I. Introduction / 1 \\
1. Eigenvalues / 3 \\
2. Pseudospectra of matrices / 12 \\
3. A matrix example / 22 \\
4. Pseudospectra of linear operators / 27 \\
5. An operator example / 34 \\
6. History of pseudospectra / 41 \\
II. Toeplitz Matrices / 47 \\
7. Toeplitz matrices and boundary pseudomodes / 49 \\
8. Twisted Toeplitz matrices and wave packet
pseudomodes / 62 \\
9. Variations on twisted Toeplitz matrices / 74 \\
III. Differential Operators / 85 \\
10. Differential operators and boundary pseudomodes /
87 \\
11. Variable coefficients and wave packet pseudomodes /
98 \\
12. Advection-diffusion operators / 115 \\
13. Lewy--Hormander nonexistence of solutions / 126 \\
IV. Transient Effects and Nonnormal Dynamics / 133 \\
14. Overview of transients and pseudospectra / 135 \\
15. Exponentials of matrices and operators / 148 \\
16. Powers of matrices and operators / 158 \\
17. Numerical range, abscissa, and radius / 166 \\
18. The Kreiss Matrix Theorem / 176 \\
19. Growth bound theorem for semigroups / 185 \\
V. Fluid Mechanics / 193 \\
20. Stability of fluid flows / 195 \\
21. A model of transition to turbulence / 207 \\
22. Orr--Sommerfeld and Airy operators / 215 \\
23. Further problems in fluid mechanics / 224 \\
VI. Matrix Iterations / 229 \\
24. Gauss--Seidel and SOR iterations / 231 \\
25. Upwind effects and SOR convergence / 237 \\
26. Krylov subspace iterations / 244 \\
27. Hybrid iterations / 254 \\
28. Arnoldi and related eigenvalue iterations / 263 \\
29. The Chebyshev polynomials of a matrix / 278 \\
VII. Numerical Solution of Differential Equations / 287
\\
30. Spectral differentiation matrices / 289 \\
31. Nonmodal instability of PDE discretizations / 295
\\
32. Stability of the method of lines / 302 \\
33. Stiffness of OD Es / 314 \\
34. GKS-stability of boundary conditions / 322 \\
VIII. Random Matrices / 331 \\
35. Random dense matrices / 333 \\
36. Hatano--Nelson matrices and localization / 339 \\
37. Random Fibonacci matrices / 351 \\
38. Random triangular matrices / 359 \\
IX. Computation of Pseudospectra / 369 \\
39. Computation of matrix pseudospectra / 371 \\
40. Projection for large-scale matrices / 381 \\
41. Other computational techniques / 391 \\
42. Pseudospectral abscissae and radii / 397 \\
43. Discretization of continuous operators / 405 \\
44. A flow chart of pseudospectra algorithms / 416 \\
X. Further Mathematical Issues / 421 \\
45. Generalized eigenvalue problems / 423 \\
46. Pseudospectra of rectangular matrices / 430 \\
47. Do pseudospectra determine behavior? / 437 \\
48. Scalar measures of nonnormality / 442 \\
49. Distance to singularity and instability / 447 \\
50. Structured pseudospectra / 458 \\
51. Similarity transformations and canonical forms /
466 \\
52. Eigenvalue perturbation theory / 473 \\
53. Backward error analysis / 485 \\
54. Group velocity and pseudospectra / 492 \\
XI. Further Examples and Applications / 499 \\
55. Companion matrices and zeros of polynomials / 501
\\
56. Markov chains and the cutoff phenomenon / 508 \\
57. Card shuffling / 519 \\
58. Population ecology / 526 \\
59. The Papkovich--Fadle operator / 534 \\
60. Lasers / 542 \\
References / 555 \\
Index / 597",
}
@Article{Trefethen:2005:WPP,
author = "Lloyd N. Trefethen",
title = "Wave packet pseudomodes of variable coefficient
differential operators",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
volume = "461",
number = "2062",
pages = "3099--3122",
day = "13",
month = jul,
year = "2005",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.2005.1500",
ISSN = "1364-5021 (print), 1471-2946 (electronic)",
ISSN-L = "1364-5021",
MRclass = "34L99 (34D09 47E05 47G30 81Q20)",
MRnumber = "MR2172219",
bibdate = "Tue Nov 25 07:34:14 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
abstract = "The pseudospectra of non-selfadjoint linear ordinary
differential operators with variable coefficients are
considered. It is shown that when a certain winding
number or twist condition is satisfied, closely related
to H{\"o}rmander's commutator condition for partial
differential equations, $ \epsilon
$-pseudoeigenfunctions of such operators for
exponentially small values of $ \epsilon $ exist in the
form of localized wave packets. In contrast to related
results of Davies and of Dencker, Sj{\"o}strand \&
Zworski, the symbol need not be smooth. Applications in
fluid mechanics, non-hermitian quantum mechanics and
other areas are presented with the aid of high-accuracy
numerical computations.",
fjournal = "Proceedings of The Royal Society of London. Series A.
Mathematical, Physical and Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
}
@Article{Tee:2006:RSC,
author = "T. W. Tee and Lloyd N. Trefethen",
title = "A rational spectral collocation method with adaptively
transformed {Chebyshev} grid points",
journal = j-SIAM-J-SCI-COMP,
volume = "28",
number = "5",
pages = "1798--1811 (electronic)",
year = "2006",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/050641296",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65M70",
MRnumber = "MR2272189 (2008k:65213)",
MRreviewer = "Becca Thomases",
bibdate = "Tue Nov 25 07:34:14 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@InCollection{Trefethen:2006:CEP,
author = "Lloyd N. Trefethen and Timo Betcke",
booktitle = "Recent advances in differential equations and
mathematical physics",
title = "Computed eigenmodes of planar regions",
volume = "412",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "297--314",
year = "2006",
MRclass = "35J05 (35P05 65N25)",
MRnumber = "MR2259116 (2008a:35042)",
MRreviewer = "Francesco Zirilli",
bibdate = "Tue Nov 25 07:34:14 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
series = "Contemp. Math.",
}
@Unpublished{Trefethen:2006:FTR,
author = "L. N. Trefethen and J. A. C. Weideman",
title = "The Fast Trapezoid Rule in Scientific Computing",
year = "2006",
bibdate = "Mon Nov 24 20:49:48 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "Unpublished manuscript.",
acknowledgement = ack-nhfb,
}
@InCollection{Trefethen:2006:NSP,
author = "Nike Trefethen",
booktitle = "Seminaire: {{\'E}quations aux D{\'e}riv{\'e}es
Partielles}. 2005--2006",
title = "Nonhermitian systems and pseudospectra",
publisher = "{\'E}cole Polytechnique",
address = "Palaiseau, France",
pages = "x + 13",
year = "2006",
MRclass = "47A10 (15A18 47A50)",
MRnumber = "MR2276076 (2007h:47010)",
bibdate = "Tue Nov 25 07:34:14 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
series = "S\'emin. \'Equ. D\'eriv. Partielles",
URL = "http://www.numdam.org/item?id=SEDP_2005-2006____A10_0",
}
@Article{Trefethen:2006:TQR,
author = "L. N. Trefethen and J. A. C. Weideman and T.
Schmelzer",
title = "{Talbot} quadratures and rational approximations",
journal = j-BIT-NUM-MATH,
volume = "46",
number = "3",
pages = "653--670",
month = sep,
year = "2006",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-006-0077-9",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65D30; 41A20",
bibdate = "Mon Nov 24 22:25:27 MST 2008",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=46&issue=3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
note = "In memory of Germund Dahlquist (1925--2005).",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=46&issue=3&spage=653",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "Carath{\'e}odory--Fej{\'e}r approximation; Hankel
contour; inverse Laplace transform; quadrature;
rational approximation; special functions; Talbot
contour; trapezoid rule",
}
@Article{Weideman:2006:OTC,
author = "J. A. C. Weideman and L. N. Trefethen",
title = "Optimizing {Talbot}'s Contours for the Inversion of
the {Laplace} Transform",
journal = j-SIAM-J-NUMER-ANAL,
volume = "44",
number = "6",
pages = "2342--2362",
month = jan,
year = "2006",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/050625837",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Fri May 28 08:26:12 2010",
bibsource = "http://siamdl.aip.org/dbt/dbt.jsp?KEY=SJNAAM&Volume=44&Issue=6;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
abstract = "Talbot's method for the numerical inversion of the
Laplace transform consists of numerically integrating
the Bromwich integral on a special contour by means of
the trapezoidal or midpoint rules. In this paper we
address the issue of parameter selection in the method,
for the particular situation when parabolic PDEs are
solved. In the process the well-known subgeometric
convergence rate $ O(\exp ( - c \sqrt {N})) $ of this
method is improved to the geometric rate $ O(\exp ( - c
N)) $, with $N$ the number of nodes in the integration
rule. The value of the maximum decay rate $c$ is
explicitly determined. Numerical results for two
versions of the heat equation are presented. With the
choice of parameters derived here, the rule of thumb is
that to achieve an accuracy of $ 10^{- \ell } $ at any
given time, the associated elliptic problem has to be
solved no more than $ \ell $ times.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Gutknecht:2007:PSV,
author = "Martin Gutknecht and Michael Overton and Lothar
Reichel and Daniel B. Szyld and Nick Trefethen and Paul
{Van Dooren} and Andy Wathen",
title = "Preface: {Special} volume dedicated to {Gene Golub} on
the occasion of his 75th birthday",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "28",
pages = "vii",
year = "2007\slash 2008",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
MRclass = "65-06 (01A70)",
MRnumber = "MR2455655",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "Special volume for Gene Golub.",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{Schmelzer:2007:CGF,
author = "Thomas Schmelzer and Lloyd N. Trefethen",
title = "Computing the Gamma Function Using Contour Integrals
and Rational Approximations",
journal = j-SIAM-J-NUMER-ANAL,
volume = "45",
number = "2",
pages = "558--571",
month = "????",
year = "2007",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/050646342",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Mon Nov 24 18:03:07 MST 2008",
bibsource = "http://siamdl.aip.org/dbt/dbt.jsp?KEY=SJNAAM&Volume=45&Issue=2;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Schmelzer:2007:EMF,
author = "Thomas Schmelzer and Lloyd N. Trefethen",
title = "Evaluating matrix functions for exponential
integrators via {Carath{\'e}odory--Fej{\'e}r}
approximation and contour integrals",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "29",
pages = "1--18",
year = "2007\slash 2008",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
MRclass = "65M20 (30E10 41A20 65L05)",
MRnumber = "MR2494943 (2010b:65190)",
MRreviewer = "Othmar Koch",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://etna.mcs.kent.edu/vol.29.2007-2008/pp1-18.dir/pp1-18.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{Trefethen:2007:CNF,
author = "Lloyd N. Trefethen",
title = "Computing numerically with functions instead of
numbers",
journal = j-MATH-COMPUT-SCI,
volume = "1",
number = "1",
pages = "9--19",
month = dec,
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1007/s11786-007-0001-y",
ISSN = "1661-8270 (print), 1661-8289 (electronic)",
ISSN-L = "1661-8270",
MRclass = "41Axx (68W30)",
MRnumber = "MR2384813",
bibdate = "Thu Jul 9 15:43:39 MDT 2009",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1661-8270&volume=1&issue=1;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1661-8270&volume=1&issue=1&spage=9",
acknowledgement = ack-nhfb,
fjournal = "Mathematics in Computer Science",
journal-URL = "http://www.springerlink.com/content/1661-8270/",
keywords = "Mathematics Subject Classification (2000); Primary
41A10; Secondary 68W30",
}
@Article{Weideman:2007:KPF,
author = "J. A. C. Weideman and L. N. Trefethen",
title = "The kink phenomenon in {Fej{\'e}r} and
{Clenshaw--Curtis} quadrature",
journal = j-NUM-MATH,
volume = "107",
number = "4",
pages = "707--727",
month = oct,
year = "2007",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-007-0101-2",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65D30 (41A55)",
MRnumber = "MR2342649 (2008i:65048)",
MRreviewer = "Komali S. Sastri",
bibdate = "Tue Nov 25 07:34:14 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Weideman:2007:PHC,
author = "J. A. C. Weideman and L. N. Trefethen",
title = "Parabolic and hyperbolic contours for computing the
{Bromwich} integral",
journal = j-MATH-COMPUT,
volume = "76",
number = "259",
pages = "1341--1356",
month = jul,
year = "2007",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D30 (44A10 65R10)",
MRnumber = "MR2299777 (2008c:65072)",
MRreviewer = "S. Hitotumatu",
bibdate = "Tue Nov 25 07:34:14 2008",
bibsource = "http://www.ams.org/mcom/2007-76-259;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://www.ams.org/mcom/2007-76-259/S0025-5718-07-01945-X/home.html;
http://www.ams.org/mcom/2007-76-259/S0025-5718-07-01945-X/S0025-5718-07-01945-X.dvi;
http://www.ams.org/mcom/2007-76-259/S0025-5718-07-01945-X/S0025-5718-07-01945-X.pdf;
http://www.ams.org/mcom/2007-76-259/S0025-5718-07-01945-X/S0025-5718-07-01945-X.ps",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Driscoll:2008:CSA,
author = "Tobin A. Driscoll and Folkmar Bornemann and Lloyd N.
Trefethen",
title = "The {\tt chebop} system for automatic solution of
differential equations",
journal = j-BIT,
volume = "48",
number = "4",
pages = "701--723",
year = "2008",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-008-0198-4",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65Y15 (65L10 65M70 65N35)",
MRnumber = "MR2465699 (2009j:65381)",
MRreviewer = "Kenneth Wright",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@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",
bibdate = "Tue Nov 25 07:34:14 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Hale:2008:NQF,
author = "Nicholas Hale and Lloyd N. Trefethen",
title = "New quadrature formulas from conformal maps",
journal = j-SIAM-J-NUMER-ANAL,
volume = "46",
number = "2",
pages = "930--948",
year = "2008",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/07068607X",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65D32 (30C20 30E10 30E20 41A10 65D30)",
MRnumber = "MR2383217 (2008m:65074)",
MRreviewer = "F. W. Stallmann",
bibdate = "Tue Nov 25 07:34:14 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Trefethen:2008:GQB,
author = "Lloyd N. Trefethen",
title = "Is {Gauss} quadrature better than
{Clenshaw--Curtis}?",
journal = j-SIAM-REVIEW,
volume = "50",
number = "1",
pages = "67--87",
year = "2008",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/060659831",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65D32 (41A20 41A55 41A58)",
MRnumber = "MR2403058",
bibdate = "Tue Nov 25 07:34:14 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://link.aip.org/link/?SIR/50/67/1",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Pachon:2009:BRA,
author = "Ricardo Pach{\'o}n and Lloyd N. Trefethen",
title = "{Barycentric--Remez} algorithms for best polynomial
approximation in the {{\tt chebfun}} system",
journal = j-BIT-NUM-MATH,
volume = "49",
number = "4",
pages = "721--741",
month = dec,
year = "2009",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-009-0240-1",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon May 24 15:36:47 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=49&issue=4;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=49&issue=4&spage=721",
acknowledgement = ack-nhfb,
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Pachon:2010:PSC,
author = "Ricardo Pach{\'o}n and Rodrigo B. Platte and Lloyd N.
Trefethen",
title = "Piecewise-smooth chebfuns",
journal = j-IMA-J-NUMER-ANAL,
volume = "30",
number = "4",
pages = "898--916",
month = oct,
year = "2010",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/drp008",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
bibdate = "Wed Oct 13 18:32:48 MDT 2010",
bibsource = "http://imanum.oxfordjournals.org/content/30/4.toc;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://imajna.oxfordjournals.org/content/30/4/898.full.pdf+html",
abstract = "Algorithms are described that make it possible to
manipulate piecewise-smooth functions on real intervals
numerically with close to machine precision. Break
points are introduced in some such calculations at
points determined by numerical root finding and in
others by recursive subdivision or automatic edge
detection. Functions are represented on each smooth
subinterval by Chebyshev series or interpolants. The
algorithms are implemented in object-oriented Matlab in
an extension of the chebfun system, which was
previously limited to smooth functions on $ [ - 1, 1]
$.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "barycentric interpolation; chebfun system; chebfuns;
Chebyshev series; edge detection; Matlab",
onlinedate = "July 28, 2009",
}
@InCollection{Platte:2010:CNK,
author = "R. B. Platte and L. N. Trefethen",
editor = "Alistair D. Fitt and John Norbury and Eddie Wilson and
Hilary Ockendon",
booktitle = "Progress in industrial mathematics at {ECMI 2008}",
title = "{Chebfun}: a new kind of numerical computing",
volume = "15",
publisher = pub-SV,
address = pub-SV:adr,
pages = "69--87",
year = "2010",
DOI = "https://doi.org/10.1007/978-3-642-12110-4_5",
ISBN = "3-642-12110-1",
ISBN-13 = "978-3-642-12110-4",
MRclass = "65D99 (65Y15)",
MRnumber = "2767023",
bibdate = "Fri Nov 9 17:28:33 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
series = "Mathematics in Industry",
acknowledgement = ack-nhfb,
}
@Article{Suli:2010:BMB,
author = "Endre S{\"u}li and Nick Trefethen and Andy Wathen",
title = "{Bill Morton}'s 80th birthday conference",
journal = j-MATH-TODAY,
volume = "46",
number = "4",
pages = "174--175",
year = "2010",
ISSN = "1361-2042",
MRclass = "65-03",
MRnumber = "2676141",
bibdate = "Thu Mar 31 10:01:47 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Today",
journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
}
@Article{Trefethen:2010:HTQ,
author = "Lloyd N. Trefethen",
title = "{Householder} triangularization of a quasimatrix",
journal = j-IMA-J-NUMER-ANAL,
volume = "30",
number = "4",
pages = "887--897",
month = oct,
year = "2010",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/drp018",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65F25 (15A03 65D05 65F20 65T50)",
MRnumber = "2727808 (2012c:65070)",
MRreviewer = "Pablo Guerrero-Garc{\'{\i}}a",
bibdate = "Wed Oct 13 18:32:48 MDT 2010",
bibsource = "http://imanum.oxfordjournals.org/content/30/4.toc;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://imajna.oxfordjournals.org/content/30/4/887.full.pdf+html",
abstract = "A standard algorithm for computing the $ Q R $
factorization of a matrix $A$ is Householder
triangularization. Here this idea is generalized to the
situation in which $A$ is a quasimatrix, that is, a
`matrix' whose `columns' are functions defined on an
interval $ [a, b] $. Applications are mentioned to
quasimatrix least squares fitting, singular value
decomposition and determination of ranks, norms and
condition numbers, and numerical illustrations are
presented using the chebfun system.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "$Q R$ factorization; chebfun; Householder
triangularization; Matlab; quasimatrix; singular value
decomposition",
onlinedate = "August 21, 2009",
}
@Article{Chapman:2011:FBR,
author = "S. J. Chapman and James Lottes and Lloyd N.
Trefethen",
title = "Four bugs on a rectangle",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
volume = "467",
number = "2127",
pages = "881--896",
day = "8",
month = mar,
year = "2011",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.2010.0506",
ISSN = "1364-5021 (print), 1471-2946 (electronic)",
ISSN-L = "1364-5021",
MRclass = "91A24 (68T99)",
MRnumber = "2765232 (2012a:91032)",
bibdate = "Tue Sep 27 19:02:07 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
abstract = "The idealized mathematical problem of four bugs in
cyclic pursuit starting from a 2-by-1 rectangle is
considered, and asymptotic formulas are derived to
describe the motion. In contrast to the famous case of
four bugs on a square, here the trajectories quickly
freeze to essentially one dimension. After the first
rotation about the centre point, the scale of the
configuration has shrunk by a factor of $
10^{427907250} $, and this number is then exponentiated
four more times with each successive cycle. Relations
to Knuth's double-arrow notation and level-index
arithmetic are discussed.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society A: Mathematical,
Physical, \& Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
keywords = "cyclic pursuit; Knuth arrow notation; level-index
arithmetic",
onlinedate = "November 10, 2010",
}
@Article{Gonnet:2011:RRI,
author = "Pedro Gonnet and Ricardo Pach{\'o}n and Lloyd N.
Trefethen",
title = "Robust rational interpolation and least-squares",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "38",
pages = "146--167",
year = "2011",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
MRclass = "65D05 (41A20 41A21)",
MRnumber = "2871863",
MRreviewer = "Ana Cristina Matos",
bibdate = "Thu Jun 9 12:14:22 MDT 2011",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{Platte:2011:IFS,
author = "Rodrigo B. Platte and Lloyd N. Trefethen and Arno B.
J. Kuijlaars",
title = "Impossibility of Fast Stable Approximation of Analytic
Functions from Equispaced Samples",
journal = j-SIAM-REVIEW,
volume = "53",
number = "2",
pages = "308--318",
month = "????",
year = "2011",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/090774707",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "41A25 (30E10 41A05 65D05)",
MRnumber = "2806639 (2012e:41018)",
MRreviewer = "Alexey L. Lukashov",
bibdate = "Thu Jun 9 09:27:06 MDT 2011",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/53/2;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sirev/resource/1/siread/v53/i2/p308_s1",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "May 05, 2011",
}
@Article{Richardson:2011:SFA,
author = "Mark Richardson and Lloyd N. Trefethen",
title = "A Sinc Function Analogue of {Chebfun}",
journal = j-SIAM-J-SCI-COMP,
volume = "33",
number = "5",
pages = "2519--2535",
month = "????",
year = "2011",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/110825947",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "41A30 (41-04 65D99 65Y15)",
MRnumber = "2861635 (2012i:41016)",
MRreviewer = "Masaru Kamada",
bibdate = "Sat Oct 15 12:30:32 MDT 2011",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/33/5;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
URL = "http://epubs.siam.org/sisc/resource/1/sjoce3/v33/i5/p2519_s1",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "October 13, 2011",
}
@Article{Trefethen:2011:SMP,
author = "Lloyd N. Trefethen",
title = "Six myths of polynomial interpolation and quadrature",
journal = j-MATH-TODAY,
volume = "47",
number = "4",
pages = "184--188",
year = "2011",
CODEN = "????",
ISSN = "1361-2042",
MRclass = "65D05 (41A10)",
MRnumber = "2952622",
bibdate = "Fri Nov 9 17:28:33 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Today",
journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
}
@InCollection{Trefethen:2011:TDP,
author = "Lloyd N. Trefethen",
title = "Ten digit problems",
crossref = "Schleicher:2011:IMC",
pages = "119--136",
year = "2011",
DOI = "https://doi.org/10.1007/978-3-642-19533-4_9",
bibdate = "Sat Mar 23 16:35:46 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-642-19533-4_9",
acknowledgement = ack-nhfb,
}
@Book{Trefethen:2011:TIC,
author = "Lloyd N. Trefethen",
title = "{Trefethen}'s index cards: forty years of notes about
people, words and mathematics",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xv + 368",
year = "2011",
DOI = "https://doi.org/10.1142/8207",
ISBN = "981-4360-69-4 (paperback), 981-4458-41-4 (e-book)",
ISBN-13 = "978-981-4360-69-2 (paperback), 978-981-4458-41-2
(e-book)",
LCCN = "????",
bibdate = "Fri Sep 20 08:18:13 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.worldscientific.com/worldscibooks/10.1142/8207",
acknowledgement = ack-nhfb,
subject = "Trefethen, Lloyd N; Mathematicians; Quotations;
Mathematics; Quotations, maxims, etc",
tableofcontents = "Ego \\
Kids \\
Aging and Death \\
Sex \\
Living with Others \\
The Meaning of Life \\
Politics and Society \\
Cold War Nukes \\
Education \\
Britain \\
Famous People \\
Optimizing Your Life \\
The Life of the Professor \\
Music \\
Words \\
Writing and Literature \\
Memory \\
Misperceptions \\
Knowledge and Truth \\
Analogies \\
Bad Logic \\
God and Religion \\
Good and Evil \\
Science \\
Stars and Planets \\
Mathematics \\
Big Numbers \\
Mathematics and Science in Everyday Life \\
Inventions \\
Computers \\
Life and DNA \\
Hearts, Minds and Bodies",
}
@Article{VanDeun:2011:RIC,
author = "Joris {Van Deun} and Lloyd N. Trefethen",
title = "A robust implementation of the
{Carath{\'e}odory--Fej{\'e}r} method for rational
approximation",
journal = j-BIT-NUM-MATH,
volume = "51",
number = "4",
pages = "1039--1050",
month = dec,
year = "2011",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-011-0331-7",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Tue Dec 13 11:50:53 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=51&issue=4;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
URL = "http://www.springerlink.com/content/ag2514840142707r/;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=51&issue=4&spage=1039",
abstract = "Best rational approximations are notoriously difficult
to compute. However, the difference between the best
rational approximation to a function and its
Carath{\'e}odory--Fej{\'e}r (CF) approximation is often
so small as to be negligible in practice, while CF
approximations are far easier to compute. We present a
robust and fast implementation of this method in the
Chebfun software system and illustrate its use with
several examples. Our implementation handles both
polynomial and rational approximation and substantially
improves upon earlier published software.",
acknowledgement = ack-nhfb,
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "Carath{\'e}odory--Fej{\'e}r approximation; Chebfun;
Near-best rational approximation",
onlinedate = "04 May 2011",
}
@Article{Hale:2012:CNQ,
author = "Nicholas Hale and Lloyd N. Trefethen",
title = "{Chebfun} and numerical quadrature",
journal = j-SCI-CHINA-MATH,
volume = "55",
number = "9",
pages = "1749--1760",
year = "2012",
DOI = "https://doi.org/10.1007/s11425-012-4474-z",
ISSN = "1674-7283 (print), 1869-1862 (electronic)",
ISSN-L = "1869-1862",
MRclass = "????",
MRnumber = "2960859",
bibdate = "Fri Nov 9 17:28:33 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
ajournal = "Sci. China Math.",
fjournal = "Science China. Mathematics",
journal-URL = "http://link.springer.com/journal/11425",
}
@Article{Webb:2012:SBI,
author = "Marcus Webb and Lloyd N. Trefethen and Pedro Gonnet",
title = "Stability of barycentric interpolation formulas for
extrapolation",
journal = j-SIAM-J-SCI-COMP,
volume = "34",
number = "6",
pages = "A3009--A3015",
year = "2012",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/110848797",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65D05 (41A20)",
MRnumber = "3029839",
bibdate = "Mon Jul 15 10:52:44 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Gonnet:2013:RPA,
author = "Pedro Gonnet and Stefan G{\"u}ttel and Lloyd N.
Trefethen",
title = "Robust {Pad{\'e}} Approximation via {SVD}",
journal = j-SIAM-REVIEW,
volume = "55",
number = "1",
pages = "101--117",
month = "????",
year = "2013",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/110853236",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65F15 (41A21)",
MRnumber = "3089442",
bibdate = "Thu Mar 7 09:46:22 MST 2013",
bibsource = "http://epubs.siam.org/toc/siread/55/1;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.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 2013",
}
@Article{Townsend:2013:ECT,
author = "Alex Townsend and Lloyd N. Trefethen",
title = "An Extension of {Chebfun} to Two Dimensions",
journal = j-SIAM-J-SCI-COMP,
volume = "35",
number = "6",
pages = "C495--C518",
month = "????",
year = "2013",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/130908002",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65Y15 (41-04 41A63 65D05)",
MRnumber = "3138114",
MRreviewer = "Luis Verde-Star",
bibdate = "Tue Feb 11 14:37:53 MST 2014",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/35/6;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.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 2013",
}
@Book{Trefethen:2013:ATA,
author = "Lloyd N. Trefethen",
title = "Approximation Theory and Approximation Practice",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "viii + 305",
year = "2013",
ISBN = "1-61197-239-6 (paperback)",
ISBN-13 = "978-1-61197-239-9 (paperback)",
LCCN = "QA221 .T73 2013",
MRclass = "41-01 (41-04 65-06)",
MRnumber = "3012510",
MRreviewer = "Ana Cristina Matos",
bibdate = "Fri Jun 21 15:10:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
acknowledgement = ack-nhfb,
tableofcontents = "1. Introduction \\
2. Chebyshev Points and Interpolants \\
3. Chebyshev Polynomials and Series \\
4. Interpolants, Projections, and Aliasing \\
5. Barycentric Interpolation Formula \\
6. Weierstrass Approximation Theorem \\
7. Convergence for Differentiable Functions \\
8. Convergence for Analytic Functions \\
9. Gibbs Phenomenon \\
10. Best Approximation \\
11. Hermite Integral Formula \\
12. Potential Theory and Approximation \\
13. Equispaced Points, Runge Phenomenon \\
14. Discussion of High-Order Interpolation \\
15. Lebesgue Constants \\
16. Best and Near-Best \\
17. Orthogonal Polynomials \\
18. Polynomial Roots and Colleague Matrices \\
19. Clenshaw--Curtis and Gauss Quadrature \\
20. Carath{\'e}odory--Fej{\'e}r Approximation \\
21. Spectral Methods \\
22. Linear Approximation: Beyond Polynomials \\
23. Nonlinear Approximation: Why Rational Functions \\
24. Rational Best Approximation \\
25. Two Famous Problems \\
26. Rational Interpolation and Linearized Least-Squares
\\
27. Pad{\'e} Approximation \\
28. Analytic Continuation and Convergence Acceleration
\\
Appendix: Six Myths of Polynomial Interpolation and
Quadrature \\
References \\
Index",
}
@Article{Trefethen:2013:BRV,
author = "Lloyd N. Trefethen",
title = "Book Review: {{\booktitle{Visual complex functions: an
introduction with phase portraits}}, by Elias Wegert.
Birkh{\"a}user\slash Springer Basel AG, Basel, 2012.
\$59.95. xiv + 360 pp., softcover. ISBN
978-3-0348-0179-9}",
journal = j-SIAM-REVIEW,
volume = "55",
number = "4",
pages = "791--797",
year = "2013",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/130973533",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "00A17",
MRnumber = "3136803",
bibdate = "Mon Sep 15 06:37:56 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
remark = "Book review of MR3024399.",
}
@InCollection{Trefethen:2013:ZPG,
author = "Lloyd N. Trefethen",
title = "{Zehnstellige Probleme}. ({German}) [{Ten}-digit
problems]",
crossref = "Schleicher:2013:EME",
pages = "121--140",
year = "2013",
bibdate = "Thu Mar 23 07:27:57 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Austin:2014:NAB,
author = "Anthony P. Austin and Peter Kravanja and Lloyd N.
Trefethen",
title = "Numerical Algorithms Based on Analytic Function Values
at Roots of Unity",
journal = j-SIAM-J-NUMER-ANAL,
volume = "52",
number = "4",
pages = "1795--1821",
month = "????",
year = "2014",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/130931035",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65E05 (41A10 41A20 65D05)",
MRnumber = "3240851",
MRreviewer = "Ana Cristina Matos",
bibdate = "Sat Sep 13 09:22:34 MDT 2014",
bibsource = "http://epubs.siam.org/http://epubs.siam.org/toc/sjnaam/52/4;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal2010.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
onlinedate = "January 2014",
}
@Book{Driscoll:2014:CG,
editor = "Tobin A. Driscoll and Nicholas Hale and Lloyd N.
Trefethen",
booktitle = "{Chebfun} Guide",
title = "{Chebfun} Guide",
publisher = "Pafnuty Publications",
address = "Oxford, UK",
pages = "x + 202 (various paging)",
year = "2014",
bibdate = "Sun Feb 14 08:48:22 2021",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://www.chebfun.org/docs/guide/",
acknowledgement = ack-nhfb,
remark = "First edition for Chebfun 5. No ISBN or LCCN data are
assigned. The book PDF file is freely available for
download, and printed copies are for sale.",
tableofcontents = "1: Getting Started with Chebfun / Lloyd N.
Trefethen \\
2: Integration and Differentiation / Lloyd N. Trefethen
\\
3: Rootfinding and Minima and Maxima / Lloyd N.
Trefethen \\
4: Chebfun and Approximation Theory / Lloyd N.
Trefethen \\
5: Complex Chebfuns / Lloyd N. Trefethen \\
6: Quasimatrices and Least-Squares / Lloyd N. Trefethen
\\
7: Linear Differential Operators and Equations / Tobin
A. Driscoll \\
8: Chebfun Preferences / Lloyd N. Trefethen \\
9: Infinite Intervals, Infinite Function Values, and
Singularities / Lloyd N. Trefethen \\
10: Nonlinear ODEs, IVPs, and Chebgui / Lloyd N.
Trefethen \\
11: Periodic Chebfuns / Grady B. Wright and Lloyd N.
Trefethen \\
12: Chebfun2: Getting Started / Alex Townsend \\
13: Chebfun2: Integration and Differentiation / Alex
Townsend \\
14: Chebfun2: Rootfinding and Optimisation / Alex
Townsend \\
15: Chebfun2: Vector Calculus and 2D Surfaces / Alex
Townsend \\
16: Diskfun / Heather Wilber \\
17: Spherefun / Alex Townsend, Heather Wilber, and
Grady B. Wright \\
18: Chebfun3 / Behnam Hashemi and Nick Trefethen \\
19: SPIN, SPIN2, SPIN3 and SPINSPHERE for stiff PDEs /
H. Montanelli and L. N. Trefethen \\
20: Ballfun / Nicolas Boulle and Alex Townsend",
}
@Article{Javed:2014:TRE,
author = "Mohsin Javed and Lloyd N. Trefethen",
title = "A trapezoidal rule error bound unifying the
{Euler--Maclaurin} formula and geometric convergence
for periodic functions",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
volume = "470",
number = "2161",
pages = "20130571",
year = "2014",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.2013.0571",
ISSN = "1364-5021 (print), 1471-2946 (electronic)",
ISSN-L = "1364-5021",
MRclass = "65D30",
MRnumber = "3145072",
MRreviewer = "G. A. Evans",
bibdate = "Mon Sep 15 06:42:59 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of The Royal Society of London. Series A.
Mathematical, Physical and Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
pagecount = "9",
}
@Article{Trefethen:2014:ECT,
author = "Lloyd N. Trefethen and J. A. C. Weideman",
title = "The Exponentially Convergent Trapezoidal Rule",
journal = j-SIAM-REVIEW,
volume = "56",
number = "3",
pages = "385--458",
month = "????",
year = "2014",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/130932132",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65D30",
MRnumber = "3245858",
MRreviewer = "G. A. Evans",
bibdate = "Sat Sep 13 08:20:41 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/56/3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.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 2014",
}
@Article{Austin:2015:CER,
author = "Anthony P. Austin and Lloyd N. Trefethen",
title = "Computing Eigenvalues of Real Symmetric Matrices with
Rational Filters in Real Arithmetic",
journal = j-SIAM-J-SCI-COMP,
volume = "37",
number = "3",
pages = "A1365--A1387",
month = "????",
year = "2015",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/140984129",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15 (15B48 41A20)",
MRnumber = "3352612",
MRreviewer = "Hanif Mirzaei",
bibdate = "Sat Aug 8 06:48:44 MDT 2015",
bibsource = "http://epubs.siam.org/toc/sjoce3/37/3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
ZMnumber = "1328.15016",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2015",
}
@Article{Chapman:2015:MFC,
author = "S. Jonathan Chapman and David P. Hewett and Lloyd N.
Trefethen",
title = "Mathematics of the {Faraday} Cage",
journal = j-SIAM-REVIEW,
volume = "57",
number = "3",
pages = "398--417",
month = "????",
year = "2015",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/140984452",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "31A35 (78A30)",
MRnumber = "3376763",
bibdate = "Sat Aug 8 06:17:25 MDT 2015",
bibsource = "http://epubs.siam.org/toc/siread/57/3;
https://www.math.utah.edu/pub/bibnet/authors/f/feynman-richard-p.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
ZMnumber = "1339.31001",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "Faraday cage; harmonic function; homogenization;
Matlab; screening; shielding",
onlinedate = "January 2015",
remark = "From page 299: ``One of the few mathematical
treatments [of the Faraday cage] we have found is in
section 7-5 of Vol. 2 of \booktitle{The Feynman
Lectures on Physics} [11], where so far as we can tell,
the analysis is incorrect. Feynman considers equal
charges rather than equal potentials, his wires are of
infinitesimal radius, there is no wavelength or indeed
external field in his discussion, and the strength of
the effect is predicted to be exponential.''",
}
@Article{Townsend:2015:CAM,
author = "A. Townsend and L. N. Trefethen",
title = "Continuous analogues of matrix factorizations",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "471",
number = "2173",
pages = "20140585",
day = "8",
month = jan,
year = "2015",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.2014.0585",
ISSN = "0080-4630 (print), 2053-9169 (electronic)",
ISSN-L = "0080-4630",
MRclass = "65F05 (15A23 65F20)",
MRnumber = "3285359",
MRreviewer = "Jos{\'e}-Javier Mart{\'\i}nez",
bibdate = "Thu Oct 01 11:09:18 2015",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://rspa.royalsocietypublishing.org/content/471/2173/20140585",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society of London. Series A,
Mathematical and physical sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/content/current",
pagecount = "21",
}
@Article{Trefethen:2015:CNF,
author = "Lloyd N. Trefethen",
title = "Computing numerically with functions instead of
numbers",
journal = j-CACM,
volume = "58",
number = "10",
pages = "91--97",
month = oct,
year = "2015",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/2814847",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Sep 30 07:29:42 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/cacm2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
URL = "http://cacm.acm.org/magazines/2015/10/192390/fulltext",
abstract = "Science and engineering depend upon computation of
functions such as flow fields, charge distributions,
and quantum states. Ultimately, such computations
require some kind of discretization, but in recent
years, it has become possible in many cases to hide the
discretizations from the user. We present the Chebfun
system for numerical computation with functions, which
is based on a key idea: an analogy of floating-point
arithmetic for functions rather than numbers.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "Chebfun; Chebyshev approximation; floating-point
arithmetic; Matlab; rational arithmetic; symbolic
algebra",
}
@Article{Trefethen:2015:PCA,
author = "Lloyd N. Trefethen",
title = "The {Princeton} companion to applied mathematics [book
review of {MR3380576}]",
journal = j-SIAM-REVIEW,
volume = "57",
number = "3",
pages = "469--473",
year = "2015",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/15N973927",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "00A17 00-01 00A05 00A06 00A69 00A71 00A79 65-00 70-00
74-00 76-00 80-00 90-00 91-00 92-00 93-00 94-00",
MRnumber = "3408007",
bibdate = "Wed Mar 22 19:22:59 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
ZMnumber = "1336.00088",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Wright:2015:ECP,
author = "Grady B. Wright and Mohsin Javed and Hadrien
Montanelli and Lloyd N. Trefethen",
title = "Extension of {Chebfun} to Periodic Functions",
journal = j-SIAM-J-SCI-COMP,
volume = "37",
number = "5",
pages = "C554--C573",
month = "????",
year = "2015",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/141001007",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "42A10 (42A15 65T40 65Y15)",
MRnumber = "3414471",
MRreviewer = "Alexandru Ioan Mitrea",
bibdate = "Sat Oct 31 07:53:41 MDT 2015",
bibsource = "http://epubs.siam.org/toc/sjoce3/37/5;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
ZMnumber = "1348.42003",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2015",
remark = "Special Section: 2014 Copper Mountain Conference",
}
@Article{Javed:2016:EMG,
author = "Mohsin Javed and Lloyd N. Trefethen",
title = "{Euler--Maclaurin} and {Gregory} interpolants",
journal = j-NUM-MATH,
volume = "132",
number = "1",
pages = "201--216",
month = jan,
year = "2016",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-015-0713-x",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65D05 (41A05 42A15 65D32 65T40)",
MRnumber = "3439220",
MRreviewer = "Mircea Ivan",
bibdate = "Mon Jan 25 07:56:51 MST 2016",
bibsource = "http://link.springer.com/journal/211/132/1;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/nummath2010.bib",
URL = "http://link.springer.com/article/10.1007/s00211-015-0713-x",
ZMnumber = "1334.41002",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Trefethen:2016:IY,
author = "Lloyd N. Trefethen",
title = "Inverse {Yogiisms}",
journal = j-NAMS,
volume = "63",
number = "11",
pages = "1281--1285",
month = dec,
year = "2016",
CODEN = "AMNOAN",
DOI = "https://doi.org/10.1090/noti1446",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "00A35 01A80",
MRnumber = "3585636",
MRreviewer = "John H. Mason",
bibdate = "Wed Mar 22 19:24:14 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib; https://www.math.utah.edu/pub/tex/bib/nams2010.bib",
ZMnumber = "1352.01065",
acknowledgement = ack-nhfb,
ajournal = "Notices Amer. Math. Soc.",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
}
@Article{Trefethen:2016:SFC,
author = "Lloyd N. Trefethen",
title = "Surprises of the {Faraday} Cage",
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 12:14:33 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/feynman-richard-p.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "https://sinews.siam.org/DetailsPage/TabId/900/ArtMID/2243/ArticleID/757/Surprises-of-the-Faraday-Cage.aspx",
acknowledgement = ack-nhfb,
keywords = "Michael Faraday; Richard P. Feynman",
}
@Article{Aurentz:2017:BOS,
author = "Jared L. Aurentz and Lloyd N. Trefethen",
title = "Block Operators and Spectral Discretizations",
journal = j-SIAM-REVIEW,
volume = "59",
number = "2",
pages = "423--446",
month = "????",
year = "2017",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/16M1065975",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65Fxx",
MRnumber = "3646500",
MRreviewer = "Ralf Zimmermann",
bibdate = "Fri Aug 25 10:08:13 MDT 2017",
bibsource = "http://epubs.siam.org/toc/siread/59/2;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.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 2017",
}
@Article{Aurentz:2017:CCS,
author = "Jared L. Aurentz and Lloyd N. Trefethen",
title = "Chopping a {Chebyshev} Series",
journal = j-TOMS,
volume = "43",
number = "4",
pages = "33:1--33:21",
month = mar,
year = "2017",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2998442",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65G50 (65Y04)",
MRnumber = "3638570",
bibdate = "Fri Mar 24 08:51:05 MDT 2017",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Chebfun and related software projects for numerical
computing with functions are based on the idea that at
each step of a computation, a function $ f(x) $ defined
on an interval $ [a, b] $ is ``rounded'' to a
prescribed precision by constructing a Chebyshev series
and chopping it at an appropriate point. Designing a
chopping algorithm with the right properties proves to
be a surprisingly complex and interesting problem. We
describe the chopping algorithm introduced in Chebfun
Version 5.3 in 2015 after many years of discussion and
the considerations that led to this design.",
acknowledgement = ack-nhfb,
articleno = "33",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Austin:2017:TIQ,
author = "Anthony P. Austin and Lloyd N. Trefethen",
title = "Trigonometric Interpolation and Quadrature in
Perturbed Points",
journal = j-SIAM-J-NUMER-ANAL,
volume = "55",
number = "5",
pages = "2113--2122",
month = "????",
year = "2017",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/16M1107760",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "42A15 (65D30 65T40 94A20)",
MRnumber = "3693604",
MRreviewer = "Kai Bittner",
bibdate = "Fri Jan 12 06:50:43 MST 2018",
bibsource = "http://epubs.siam.org/http://epubs.siam.org/toc/sjnaam/55/5;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal2010.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
onlinedate = "January 2017",
}
@Article{Hashemi:2017:CTD,
author = "Behnam Hashemi and Lloyd N. Trefethen",
title = "{Chebfun} in Three Dimensions",
journal = j-SIAM-J-SCI-COMP,
volume = "39",
number = "5",
pages = "C341--C363",
month = "????",
year = "2017",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/16M1083803",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "41A10 (15A69 41-04 65Y15)",
MRnumber = "3704268",
bibdate = "Fri Jan 12 07:30:22 MST 2018",
bibsource = "http://epubs.siam.org/toc/sjoce3/39/5;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.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{Trefethen:2017:CAI,
author = "Lloyd N. Trefethen",
title = "Cubature, Approximation, and Isotropy in the
Hypercube",
journal = j-SIAM-REVIEW,
volume = "59",
number = "3",
pages = "469--491",
month = "????",
year = "2017",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/16M1066312",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "41A63 (65C05 65D30 65Y20)",
MRnumber = "3683677",
MRreviewer = "Dietrich Braess",
bibdate = "Fri Aug 25 10:08:16 MDT 2017",
bibsource = "http://epubs.siam.org/toc/siread/59/3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.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 2017",
}
@Article{Trefethen:2017:MPA,
author = "Lloyd N. Trefethen",
title = "Multivariate polynomial approximation in the
hypercube",
journal = j-PROC-AM-MATH-SOC,
volume = "145",
number = "11",
pages = "4837--4844",
year = "2017",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/proc/13623",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "41A63 (41A10)",
MRnumber = "3691999",
MRreviewer = "Jean-Paul Calvi",
bibdate = "Fri Apr 26 06:30:25 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
}
@Article{Filip:2018:RMA,
author = "Silviu-Ioan Filip and Yuji Nakatsukasa and Lloyd N.
Trefethen and Bernhard Beckermann",
title = "Rational Minimax Approximation via Adaptive
Barycentric Representations",
journal = j-SIAM-J-SCI-COMP,
volume = "40",
number = "4",
pages = "A2427--A2455",
month = "????",
year = "2018",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/17M1132409",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "41A20 (65D15)",
MRnumber = "3840899",
MRreviewer = "J. Szabados",
bibdate = "Wed Nov 7 09:01:35 MST 2018",
bibsource = "http://epubs.siam.org/toc/sjoce3/40/4;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.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{Nakatsukasa:2018:AAR,
author = "Yuji Nakatsukasa and Olivier S{\`e}te and Lloyd N.
Trefethen",
title = "The {AAA} Algorithm for Rational Approximation",
journal = j-SIAM-J-SCI-COMP,
volume = "40",
number = "3",
pages = "A1494--A1522",
month = "????",
year = "2018",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/16M1106122",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "41A20 (41A05 65D05)",
MRnumber = "3805855",
MRreviewer = "Andr{\'e} Pierro de Camargo",
bibdate = "Wed Nov 7 09:01:32 MST 2018",
bibsource = "http://epubs.siam.org/toc/sjoce3/40/3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.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 = "Adaptive Antoulas--Anderson (AAA) algorithm",
onlinedate = "January 2018",
}
@Article{Nakatsukasa:2018:RA,
author = "Yuji Nakatsukasa and Lloyd N. Trefethen",
title = "Rational approximation of $ x^n $",
journal = j-PROC-AM-MATH-SOC,
volume = "146",
number = "12",
pages = "5219--5224",
year = "2018",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/proc/14187",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "41A20 (41A25)",
MRnumber = "3866860",
MRreviewer = "Vasiliy A. Prokhorov",
bibdate = "Tue Dec 29 06:43:55 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
}
@Book{Trefethen:2018:EO,
author = "Lloyd N. Trefethen and {\'A}sgeir Birkisson and Tobin
A. Driscoll",
title = "Exploring {ODEs}",
volume = "157",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "vii + 335",
year = "2018",
ISBN = "1-61197-515-8 (hardcover)",
ISBN-13 = "978-1-61197-515-4 (hardcover)",
LCCN = "QA371 .T67 2018",
MRclass = "34-01 (34-04) 34A05 34A12 34A30 34A34 34C23 34C25",
MRnumber = "3743065",
bibdate = "Fri Apr 26 06:34:05 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Introduction \\
First-order scalar linear ODEs \\
First-order scalar nonlinear ODEs \\
Second-order equations and damped oscillations \\
Boundary-value problems \\
Eigenvalues of linear BVPs \\
Variable coefficients and adjoints \\
Resonance \\
Second-order equations in the phase plane \\
Systems of equations \\
The fundamental existence theorem \\
Random functions and random odes \\
Chaos \\
Linear systems and linearization \\
Stable and unstable fixed points \\
Multiple solutions of nonlinear BVPs \\
Bifurcation \\
Continuation and path-following \\
Periodic ODEs \\
Boundary and interior layers \\
Into the complex plane \\
Time-dependent PDEs",
}
@Article{Trefethen:2018:SSL,
author = "Lloyd N. Trefethen",
title = "Series solution of {Laplace} problems",
journal = j-ANZIAM-J,
volume = "60",
number = "1",
pages = "1--26",
year = "2018",
CODEN = "AJNOA2",
DOI = "https://doi.org/10.1017/S1446181118000093",
ISSN = "1446-1811 (print), 1446-8735 (electronic)",
ISSN-L = "1446-1811",
MRclass = "31A35 (35C10 35J05 35J08)",
MRnumber = "3853349",
MRreviewer = "Alain Brillard",
bibdate = "Fri Apr 26 06:34:50 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "The ANZIAM Journal. The Australian \& New Zealand
Industrial and Applied Mathematics Journal",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
}
@Article{Filip:2019:SRF,
author = "Silviu Filip and Aurya Javeed and Lloyd N. Trefethen",
title = "Smooth Random Functions, Random {ODEs}, and {Gaussian}
Processes",
journal = j-SIAM-REVIEW,
volume = "61",
number = "1",
pages = "185--205",
month = "????",
year = "2019",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/17M1161853",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "42A16 (60G15 62M40)",
MRnumber = "3908322",
bibdate = "Thu Apr 25 17:17:51 MDT 2019",
bibsource = "http://epubs.siam.org/toc/siread/61/1;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.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 2019",
}
@Article{Gopal:2019:NLH,
author = "Abinand Gopal and Lloyd N. Trefethen",
title = "New {Laplace} and {Helmholtz} solvers",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "116",
number = "21",
pages = "10223--10225",
year = "2019",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.1904139116",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
MRclass = "65N35",
MRnumber = "3956366",
MRreviewer = "Behzad Nemati Saray",
bibdate = "Tue Dec 29 06:43:55 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/content/by/year",
}
@Article{Gopal:2019:RCM,
author = "Abinand Gopal and Lloyd N. Trefethen",
title = "Representation of conformal maps by rational
functions",
journal = j-NUM-MATH,
volume = "142",
number = "2",
pages = "359--382",
year = "2019",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-019-01023-z",
ISSN = "0029-599x (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "30C30 (41A20 65E05)",
MRnumber = "3941934",
bibdate = "Fri Apr 26 06:35:30 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Gopal:2019:SLP,
author = "Abinand Gopal and Lloyd N. Trefethen",
title = "Solving {Laplace} Problems with Corner Singularities
via Rational Functions",
journal = j-SIAM-J-NUMER-ANAL,
volume = "57",
number = "5",
pages = "2074--2094",
month = "????",
year = "2019",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/19M125947X",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Fri Apr 24 15:19:01 MDT 2020",
bibsource = "http://epubs.siam.org/http://epubs.siam.org/toc/sjnaam/57/5;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal2010.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
onlinedate = "January 2019",
}
@Article{Nakatsukasa:2020:ARC,
author = "Yuji Nakatsukasa and Lloyd N. Trefethen",
title = "An algorithm for real and complex rational minimax
approximation",
journal = j-SIAM-J-SCI-COMP,
volume = "42",
number = "5",
pages = "A3157--A3179",
month = "????",
year = "2020",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/19M1281897",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65D15 (41A20)",
MRnumber = "4161312",
bibdate = "Fri Mar 12 11:40:01 MST 2021",
bibsource = "http://epubs.siam.org/toc/sjoce3/42/5;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.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 2020",
}
@Book{Trefethen:2020:ATA,
author = "Lloyd N. Trefethen",
title = "Approximation theory and approximation practice",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Extended",
pages = "xi + 363",
year = "2020",
ISBN = "1-61197-593-X",
ISBN-13 = "978-1-61197-593-2",
MRclass = "41-01 (41-04 65-01)",
MRnumber = "4050406",
MRreviewer = "Ralitza Kovacheva",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Trefethen:2020:EPE,
author = "Lloyd N. Trefethen",
title = "Eight Perspectives on the Exponentially
Ill-Conditioned Equation $ \varepsilon y'' - x y' + y =
0 $",
journal = j-SIAM-REVIEW,
volume = "62",
number = "2",
pages = "439--462",
month = "????",
year = "2020",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/18M121232X",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "34E20",
MRnumber = "4094477",
MRreviewer = "Yoshitsugu Takei",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "http://epubs.siam.org/toc/siread/62/2;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.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 2020",
}
@Article{Trefethen:2020:NCM,
author = "Lloyd N. Trefethen",
title = "Numerical Conformal Mapping with Rational Functions",
journal = j-COMPUT-METH-FUNCT-THEORY,
volume = "20",
number = "3-4",
pages = "369--387",
year = "2020",
DOI = "https://doi.org/10.1007/s40315-020-00325-w",
ISSN = "1617-9447 (print), 2195-3724 (electronic)",
ISSN-L = "1617-9447",
MRclass = "30C30 (41A20 65E10)",
MRnumber = "4175490",
MRreviewer = "Chenglie Hu",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Computational Methods and Function Theory",
journal-URL = "https://www.springer.com/journal/40315",
}
@Article{Trefethen:2020:QIC,
author = "Lloyd N. Trefethen",
title = "Quantifying the ill-conditioning of analytic
continuation",
journal = j-BIT-NUM-MATH,
volume = "60",
number = "4",
pages = "901--915",
month = dec,
year = "2020",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-020-00802-7",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "30B40 (30-04 65E05)",
MRnumber = "4179710",
MRreviewer = "Chenglie Hu",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
URL = "https://link.springer.com/article/10.1007/s10543-020-00802-7",
acknowledgement = ack-nhfb,
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
online-date = "Published: 28 January 2020 Pages: 901 - 915",
}
@Article{Trefethen:2020:RFB,
author = "Lloyd N. Trefethen",
title = "Rational functions and beyond",
journal = j-SIAM-NEWS,
volume = "53",
number = "10",
pages = "1, 3",
year = "2020",
ISSN = "1557-9573",
MRclass = "65D15",
MRnumber = "4636567",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "https://sinews.siam.org/",
}
@Article{Brubeck:2021:VA,
author = "Pablo D. Brubeck and Yuji Nakatsukasa and Lloyd N.
Trefethen",
title = "{Vandermonde} with {Arnoldi}",
journal = j-SIAM-REVIEW,
volume = "63",
number = "2",
pages = "405--415",
month = "????",
year = "2021",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/19M130100X",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65D05 (30C20 33C45 41A05 97H60)",
MRnumber = "4253796",
MRreviewer = "Arnak Poghosyan",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "http://epubs.siam.org/toc/siread/63/2;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.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 2021",
}
@Article{Nakatsukasa:2021:RLA,
author = "Yuji Nakatsukasa and Lloyd N. Trefethen",
title = "Reciprocal-Log Approximation and Planar {PDE}
Solvers",
journal = j-SIAM-J-NUMER-ANAL,
volume = "59",
number = "6",
pages = "2801--2822",
month = "????",
year = "2021",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/20M1369555",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65N35 (41A30 65E05)",
MRnumber = "4332971",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "http://epubs.siam.org/http://epubs.siam.org/toc/sjnaam/59/6;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal2020.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
onlinedate = "January 2021",
}
@Article{Trefethen:2021:ENC,
author = "Lloyd N. Trefethen and Yuji Nakatsukasa and J. A. C.
Weideman",
title = "Exponential node clustering at singularities for
rational approximation, quadrature, and {PDEs}",
journal = j-NUM-MATH,
volume = "147",
number = "1",
pages = "227--254",
month = jan,
year = "2021",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-020-01168-2",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "41A20 (65D32 65N35)",
MRnumber = "4207522",
MRreviewer = "Kanstantin Smatrytski",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/nummath2020.bib",
URL = "http://link.springer.com/article/10.1007/s00211-020-01168-2;
https://link.springer.com/content/pdf/10.1007/s00211-020-01168-2.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Brubeck:2022:LSS,
author = "Pablo D. Brubeck and Lloyd N. Trefethen",
title = "Lightning {Stokes} Solver",
journal = j-SIAM-J-SCI-COMP,
volume = "44",
number = "3",
pages = "A1205--A1226",
month = "????",
year = "2022",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/21M1408579",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65N35 (65N22 76D07)",
MRnumber = "4418039",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "http://epubs.siam.org/toc/sjoce3/44/3;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
URL = "https://epubs.siam.org/doi//doi/10.1137/21M1408579",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Hashemi:2022:REP,
author = "Behnam Hashemi and Yuji Nakatsukasa and Lloyd N.
Trefethen",
title = "Rectangular eigenvalue problems",
journal = j-ADV-COMPUT-MATH,
volume = "48",
number = "6",
pages = "1--16",
year = "2022",
CODEN = "ACMHEX",
DOI = "https://doi.org/10.1007/s10444-022-09994-8",
ISSN = "1019-7168 (print), 1572-9044 (electronic)",
ISSN-L = "1019-7168",
MRclass = "65N25 (47A75 65N35)",
MRnumber = "4510504",
MRreviewer = "Zhifeng Weng",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
articleno = "80",
fjournal = "Advances in Computational Mathematics",
journal-URL = "http://link.springer.com/journal/10444",
}
@Book{Trefethen:2022:AMA,
author = "Lloyd N. Trefethen",
title = "An Applied Mathematician's Apology",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "ix + 79",
year = "2022",
ISBN = "1-61197-718-5",
ISBN-13 = "978-1-61197-718-9",
MRclass = "01A70 (00A69 65-03)",
MRnumber = "4477363",
MRreviewer = "James Stephan Walker",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Trefethen:2022:EQF,
author = "Lloyd N. Trefethen",
title = "Exactness of Quadrature Formulas",
journal = j-SIAM-REVIEW,
volume = "64",
number = "1",
pages = "132--150",
month = "????",
year = "2022",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/20M1389522",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65D32",
MRnumber = "4373871",
MRreviewer = "Michael J. Carley",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "http://epubs.siam.org/toc/siread/64/1;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "https://epubs.siam.org/doi/10.1137/20M1389522",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Book{Trefethen:2022:NLA,
author = "Lloyd N. Trefethen and David {Bau, III}",
title = "Numerical Linear Algebra",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Anniversary",
pages = "xvi + 370",
year = "2022",
ISBN = "1-61197-715-0; 1-61197-716-9",
ISBN-13 = "978-1-61197-715-8; 978-1-61197-716-5",
MRclass = "65-01 (65-02)",
MRnumber = "4713493",
bibdate = "Tue May 28 15:23:11 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "With a foreword by James G. Nagy.",
acknowledgement = ack-nhfb,
}
@Article{Trefethen:2022:SRT,
author = "Lloyd N. Trefethen",
title = "Some recollections of {Trefethen} and {Bau} on the
occasion of its 25th anniversary",
journal = j-SIAM-NEWS,
volume = "55",
number = "5",
pages = "6--6",
year = "2022",
ISSN = "1557-9573",
MRclass = "65-03",
MRnumber = "4667147",
fjournal = "SIAM News",
journal-URL = "https://sinews.siam.org/",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
bibdate = "Tue May 28 15:23:11 2024",
acknowledgement = ack-nhfb,
}
@InCollection{Costa:2023:ALS,
author = "Stefano Costa and Lloyd N. Trefethen",
booktitle = "{European Congress of Mathematics}",
title = "{AAA}-least squares rational approximation and
solution of {Laplace} problems",
publisher = "EMS Press",
address = "Berlin, Germany",
pages = "511--534",
year = "2023",
ISBN = "3-9854705-1-0; 3-9854755-1-2",
ISBN-13 = "978-3-9854705-1-8; 978-3-9854755-1-3",
MRclass = "41A20 (30E10 44A15 65N35)",
MRnumber = "4615756",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Herremans:2023:RSR,
author = "Astrid Herremans and Daan Huybrechs and Lloyd N.
Trefethen",
title = "Resolution of Singularities by Rational Functions",
journal = j-SIAM-J-NUMER-ANAL,
volume = "61",
number = "6",
pages = "2580--2600",
month = nov,
year = "2023",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/23m1551821",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Mon May 27 16:15:47 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal2020.bib",
acknowledgement = ack-nhfb,
ajournal = "SIAM J. Numer. Anal.",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Huybrechs:2023:AIE,
author = "Daan Huybrechs and Lloyd N. Trefethen",
title = "{AAA} interpolation of equispaced data",
journal = j-BIT-NUM-MATH,
volume = "63",
number = "2",
pages = "1--19",
month = jun,
year = "2023",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-023-00959-x",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65D05 (41A20 65D15)",
MRnumber = "4561136",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
URL = "https://link.springer.com/article/10.1007/s10543-023-00959-x",
acknowledgement = ack-nhfb,
ajournal = "Bit Num. Math.",
articleno = "21",
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "Adaptive Antoulas--Anderson (AAA) algorithm",
}
@Article{Trefethen:2023:BML,
author = "Nick Trefethen",
title = "A bifurcation in {Moore}'s law?",
journal = j-SIAM-NEWS,
volume = "56",
number = "7",
pages = "2",
year = "2023",
ISSN = "0036-1437",
MRclass = "68M07",
MRnumber = "4683762",
bibdate = "Tue May 28 15:23:11 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "https://sinews.siam.org/",
}
@Article{Trefethen:2023:NAC,
author = "Lloyd N. Trefethen",
title = "Numerical analytic continuation",
journal = j-JAPAN-J-INDUST-APPL-MATH,
volume = "40",
number = "3",
pages = "1587--1636",
year = "2023",
CODEN = "JAPJI7",
DOI = "https://doi.org/10.1007/s13160-023-00599-2",
ISSN = "0916-7005 (print), 1868-937X (electronic)",
ISSN-L = "0916-7005",
MRclass = "30B40 (32D15 35B60 41A20)",
MRnumber = "4644441",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
ajournal = "Jpn. J. Ind. Appl. Math.",
fjournal = "Japan Journal of Industrial and Applied Mathematics",
}
@Article{Trefethen:2023:SLE,
author = "Lloyd N. Trefethen",
title = "Spectacularly large expansion coefficients in
{M{\"u}ntz}'s theorem",
journal = "La Matematica",
volume = "2",
number = "1",
pages = "31--36",
year = "2023",
DOI = "https://doi.org/10.1007/s44007-022-00039-6",
ISSN = "2730-9657",
MRclass = "41A10 (42C30)",
MRnumber = "4565921",
MRreviewer = "R. A. Zalik",
bibdate = "Wed Nov 29 15:03:53 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
ajournal = "Matematica",
fjournal = "La Matematica",
}
@Article{Driscoll:2024:ARA,
author = "Tobin A. Driscoll and Yuji Nakatsukasa and Lloyd N.
Trefethen",
title = "{AAA} rational approximation on a continuum",
journal = j-SIAM-J-SCI-COMP,
volume = "46",
number = "2",
pages = "A929--A952",
year = "2024",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/23M1570508",
ISSN = "1064-8275,1095-7197",
ISSN-L = "1064-8275",
MRclass = "65D15 (41A20)",
MRnumber = "4715289",
bibdate = "Tue May 28 15:23:11 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "https://doi.org/10.1137/23M1570508",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Xue:2024:CTD,
author = "Yidan Xue and Sarah L. Waters and Lloyd N. Trefethen",
title = "Computation of two-dimensional {Stokes} flows via
lightning and {AAA} rational approximation",
journal = j-SIAM-J-SCI-COMP,
volume = "46",
number = "2",
pages = "A1214--A1234",
year = "2024",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/23M1576876",
ISSN = "1064-8275,1095-7197",
ISSN-L = "1064-8275",
MRclass = "65N35 (76D07)",
MRnumber = "4727132",
bibdate = "Tue May 28 15:23:11 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "https://doi.org/10.1137/23M1576876",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Area:2016:ACS,
author = "Iv{\'a}n Area and Dimitar K. Dimitrov and Eduardo
Godoy and Vanessa G. Paschoa",
title = "Approximate Calculation of Sums {II}: {Gaussian} Type
Quadrature",
journal = j-SIAM-J-NUMER-ANAL,
volume = "54",
number = "4",
pages = "2210--2227",
month = "????",
year = "2016",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/140993752",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Fri Sep 23 11:00:53 MDT 2016",
bibsource = "http://epubs.siam.org/http://epubs.siam.org/toc/sjnaam/54/4;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal2010.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "Chebfun",
onlinedate = "January 2016",
}
@Article{Corless:2016:BRT,
author = "Robert M. Corless",
title = "Book review of: {L. N. Trefethen,
\booktitle{Approximation theory and approximation
practice}}",
journal = j-SIAM-REVIEW,
volume = "58",
number = "1",
pages = "159--163",
year = "2016",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/16N974048",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRnumber = "00A17 41-01 41-04 41Axx 65Dxx",
bibdate = "Thu Mar 23 06:41:59 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
ZMnumber = "1336.00019",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Proceedings{Anonymous:1980:PAN,
editor = "Anonymous",
booktitle = "{Proceedings of the 1980 Army Numerical Analysis and
Computers Conference, Moffett Field, California,
February 20--21, 1980}",
title = "{Proceedings of the 1980 Army Numerical Analysis and
Computers Conference, Moffett Field, California,
February 20--21, 1980}",
publisher = pub-US-ARO,
address = pub-US-ARO:adr,
pages = "????",
year = "1980",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Tue Jan 03 14:03:41 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "Six microfiches.",
series = "ARO Rep. 80",
acknowledgement = ack-nhfb,
}
@Proceedings{Butzer:1981:BCI,
editor = "Paul Leo Butzer and F. (Franziska) Feh{\'e}r",
booktitle = "{E. B. Christoffel}, the influence of his work on
mathematics and the physical sciences",
title = "{E. B. Christoffel}, the influence of his work on
mathematics and the physical sciences",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xxiv + 761",
year = "1981",
DOI = "https://doi.org/10.1007/978-3-0348-5452-8",
ISBN = "3-7643-1162-2",
ISBN-13 = "978-3-7643-1162-9",
LCCN = "QA7 I57 1981; QA 7 .I57 1981; QA76 .I556 1981",
bibdate = "Tue Jan 3 12:47:30 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
sirsi.library.utoronto.ca:2200/UNICORN",
URL = "https://link.springer.com/book/10.1007/978-3-0348-5452-8",
acknowledgement = ack-nhfb,
meetingname = "International Christoffel Symposium in Honour of
Christoffel on the 150th Anniversary of His Birth
(1979: Aachen, Germany, and Monschau, Germany)",
remark = "In English, French, German, and Italian. Contains
expanded versions of the twelve invited lectures given
at the International Christoffel Symposium, held on
November 8--11, 1979 at Achen and Monschau.",
subject = "Christoffel, Edwin Bruno; Mathematics; Science",
subject-dates = "1829--1900",
tableofcontents = "Front Matter / i--xxv \\
Portrait of E. B. Christoffel / ii \\
Preface / v \\
Publications of E. B. Christoffel / ix \\
Contents / xi \\
List of Sponsors / xvii \\
Addresses by G. Urban, F.-W. Janssen, and W. Kruse /
xvii \\
\\
I: Christoffel and His Time \\
\\
Front Matter / 1--1 \\
An Outline of the Life and Work of E. B. Christoffel
(1829--1900) / Paul L. Butzer / 2--29 \\
Zur Genealogie E. B. Christoffels / Manfred Jansen /
30--32 \\
Christoffel und die Mathematik an der polytechnischen
Schule Z{\"u}rich / Max-Albert Knus / 33--41 \\
Die Berliner Gewerbeakademie und ihre Mathematiker /
Eberhard Knobloch / 42--51 \\
Das Mathematische Seminar der Universit{\"a}t
Strassburg 1872--1900 / Friedrich R. Wollmersh{\"a}user
/ 52--70 \\
\\
II: Gauss--Christoffel Quadrature Formulae \\
\\
Front Matter / 71--71 \\
A Survey of Gauss--Christoffel Quadrature Formulae /
Walter Gautschi / 72--147 \\
Numeri di Christoffel e polinomi s-ortogonali /
Alessandro Ossicini, Francesco Rosati / 148--157 \\
\\
III: Orthogonal Polynomials, Continued Fractions and
Pad{\'e} Approximation \\
\\
Front Matter / 159--159 \\
Die Bedeutung der Christoffelschen Summenformel f{\"u}r
die Entwicklung nach Orthogonalpolynomen / J. Meixner /
160--172 \\
Orthogonal Polynomials which Satisfy Second Order
Differential Equations / F. V. Atkinson, W. N. Everitt
/ 173--181 \\
{\"U}ber Orthogonalpolynome mit besonderen
Eigenschaften / Wolfgang Hahn / 182--189 \\
The Work of E. B. Christoffel on the Theory of
Continued Fractions / Peter Wynn / 190--202 \\
A Priori Truncation Error Estimates for Stieltjes
Fractions / Wolfgang J. Thron / 203--211 \\
Generalisations of Pad{\'e} Approximation for Chebyshev
and Fourier Series / J. S. R. Chisholm, A. K. Common /
212--231 \\
An Asymptotic, Pad{\'e} Approximant Method for Legendre
Series / George A. Baker Jr., J. E. Gubernatis /
232--242 \\
\\
IV: Christoffel--Schwarz Transformation and Conformal
Representation \\
\\
Front Matter / 243--243 \\
Die Bedeutung der Arbeiten Christoffels f{\"u}r die
Funktionentheorie / Albert Pfluger / 244--252 \\
Remarks on the Schwarz--Christoffel Transformation / A.
W. Goodman / 253--262 \\
Computer Application of the Schwarz--Christoffel
Transformation / Lloyd N. Trefethen / 263--274 \\
Regularity Properties of Solutions of Elliptic
Equations Near Corners / A. Azzam, E. Kreyszig /
275--289 \\
Das logarithmische Potential und die konforme Abbildung
mehrfach zusammenh{\"a}ngender Gebiete / Dieter Gaier /
290--303 \\
\\
V: Theta Functions, Automorphic Functions and Riemann
Surfaces \\
\\
Front Matter / 305--305 \\
On Automorphic Functions / Christian Pommerenke /
306--313 \\
Semigroups of Holomorphic Maps of a Riemann Surface
into itself which are Homomorphs of the Set of Positive
Reals Considered Additively / Maurice Heins / 314--331
\\
Bemerkungen zur isometrischen Verheftung ebener Gebiete
/ Alfred Huber / 332--335 \\
Eine Bemerkung zu Andrianovs expliziten Formeln f{\"u}r
die Wirkung der Heckeoperatoren auf Thetareihen /
Eberhard Freitag / 336--351 \\
Schottky's Invariant and Quadratic Forms \\
Jun-ichi Igusa / 352--362 \\
\\
VI: Differential Equations, Potential Theory \\
\\
Front Matter / 363--363 \\
A propos d un travail de Christoffel sur les
{\'e}quations diff{\'e}rentielles / J. Martinet /
364--366 \\
{\"U}ber die Beitr{\"a}ge Christoffels zur
Potentialtheorie / Marcel Brelot / 367--377 \\
Application d un Th{\'e}or{\`e}me de H{\"o}rmander
{\`a} l Etude des Singularit{\'e}s des Probl{\`e}mes
aux Limites Hyperboliques / H. G. Garnir, E.
Lejeune-Rifaut / 378--390 \\
On Fundamental Systems of Differential Semi-Invariants
in Several Variables / Hisasi Morikawa / 391--396 \\
Parabolicity and the Riemann Theorem / Mitsuru Nakai,
Leo Sario / 397--400 \\
On the Structure of the Set of Eigenfunctions of
Certain Irregular Boundary Problems / Agnes I. Benedek,
Rafael Panzone / 401--410 \\
\\
VII: Shock Waves, Continuum Mechanics \\
\\
Front Matter / 411--411 \\
Historischer {\"U}berblick zur mathematischen Theorie
von Unstetigkeitswellen seit Riemann und Christoffel /
Ernst H{\"o}lder / 412--434 \\
G. Herglotz Behandlung von Beschleunigungswellen in
seiner Vorlesung \ogMechanik der Kontinua\fg angewandt
auf die Stosswellen von Christoffel / Ernst H{\"o}lder
/ 435--448 \\
Unstetigkeitsfl{\"a}chen in der Kontinuumsmechanik / W.
Arrenbrecht, J. Ballmann / 449--460 \\
\\
VIII: Riemannian Geometry, Submanifolds \\
\\
Front Matter / 461--461 \\
Die Bedeutung von Christoffel f{\"u}r die Geometrie /
W. Klingenberg / 462--473 \\
E. B. Christoffels Weg zum absoluten
Differentialkalk{\"u}l und sein Beitrag zur Theorie des
Kr{\"u}mmungstensors / M. Pinl / 474--479 \\
Une caract{\'e}risation purement m{\'e}trique des
vari{\'e}t{\'e}s Riemanniennes {\`a} courbure constante
/ Marcel Berger / 480--492 \\
Immersions et rep{\`e}res mobiles / Daniel Bernard /
493--507 \\
The Euclidean Laplacian / Thomas James Willmore /
508--516 \\
\\
IX: Invariant Theory, Differential Operators and Field
Physics \\
\\
Front Matter / 517--517 \\
Christoffel und die Invariantentheorie / W. Burau /
518--525 \\
Christoffel's Work on the Equivalence Problem for
Riemannian Spaces and Its Importance for Modem Field
Theories of Physics / J{\"u}rgen Ehlers / 526--542 \\
Some Characterizations of Differential Operators on
Vector Bundles / M. De Wilde, P. Lecomte / 543--549 \\
Connections in Generalized Gauge Fields / Hanno Rund /
550--560 \\
Remarks on the Cauchy Problem for the Maxwell Equations
in a Curved Space-Time / Hans Triebel / 561--566 \\
\\
X: Affine and Projective Structures, Nonlinear
Differential Geometry \\
\\
Front Matter / 567--567 \\
Die Bedeutung Christoffelscher Zusammenh{\"a}nge in der
affinen Differentialgeometrie / Woldemar Barthel,
Reinhard Volkmer / 568--583 \\
On Projective Covariant Differentiation / Robert C.
Gunning / 584--591 \\
Generic Minimal Submanifolds with Flat Normal
Connection / Kentaro Yano, Masahiro Kon / 592--599 \\
{\"U}ber die Verallgemeinerung der Christoffelschen
{\"U}bertragungstheorie in Linienelementenr{\"a}umen /
Arthur Mo{\'o}r / 600--610 \\
Die Verallgemeinerung Christoffelscher
Zusammenh{\"a}nge in der nichtlinearen
Differentialgeometrie / Woldemar Barthel, Helmut Pabel
/ 611--623 \\
\\
XI: G-Spaces, Convex Bodies and Foundations \\
\\
Front Matter / 625--625 \\
Symmetric Spaces and Ellipses / H. Busemann, B. B.
Phadke / 626--635 \\
Zum Beweis eines Eindeutigkeitssatzes von A. D.
Aleksandrow / Kurt Leichtweiss / 636--652 \\
Der Liouvillesche Satz {\"u}ber winkeltreue
(orthogonaltreue) Abbildungen f{\"u}r singul{\"a}re
Metriken / Walter Benz / 653--656 \\
Affine Einbettung absoluter R{\"a}ume beliebiger
Dimension / Helmut Karzel, Monika K{\"o}nig / 657--670
\\
\\
XII: Dispersion of Light, Dynamical Systems \\
\\
Front Matter / 671--671 \\
A Cohomological Invariant of Discrete Dynamical Systems
/ Victor Guillemin, Richard Melrose / 672--679 \\
Dispersion und mechanische {\"A}thertheorien im
19.Jahrhundert / Karl von Meyenn / 680--703 \\
Generalized Riemann Integrals and the Divergence
Theorem for Differentiable Vector Fields / Jean Mawhin
/ 704--714 \\
\\
XIII: Short Communications \\
\\
Front Matter / 715--717 \\
Index to the ``Short Communications'' / 716 \\
\\
Short Articles on Christoffel's Work \\
\\
Christoffel's Work on Shock Waves / F. V. Atkinson /
718--720 \\
Subsequent Work on Christoffel's Problem about
Determining a Surface from Local Measurements / Wm. J.
Firey / 721--723 \\
Recognition of Christoffel's Work on Quadrature during
and after His Lifetime / Walter Gautschi / 724--727 \\
Remarks on E. B. Christoffel's Paper: {\"U}ber die
kleinen Schwingungen eines periodisch eingerichteten
Systems materieller Punkte / Jean Mawhin / 728--730 \\
Remark upon Developments in the Theories of the Moment
Problem and of Quadrature, Subsequent to the Work of
Christoffel / P. Wynn / 731--734 \\
Kommentar eines Geod{\"a}ten zu einer Arbeit E. B.
Christoffels / Erik W. Grafarend / 735--742 \\
\\
Short Commentaries \\
\\
Das Werk Christoffels f{\"u}r die Differentialgeometrie
/ W. Barthel / 743--743 \\
Der Ricci-Kalk{\"u}l im Vergleich zur Methode der
Pfaffschen Formen / W. Haack / 743--744 \\
Christoffel's Work in Complex Analysis / M. Heins /
744--744 \\
Christoffel's Paper of 1866 on Implicit Differential
Equations / J. Mawhin / 744--745 \\
Der Einflu{\ss} Christoffels auf die Potentialtheorie /
M. Brelot / 745--745 \\
Zum Vortrag von Herrn Brelot {\"u}ber Christoffels
Beitr{\"a}ge zur Potentialtheorie / Cl. M{\"u}ller /
745--746 \\
Zur Christoffel--Darboux-Formel / H. Kalf / 746--747 \\
Christoffels Bedeutung vom Standpunkt des Physikers /
K. Bleuler / 747--747 \\
On the Concept of Connections (Gauge Theories) in
Modern Physics / H. A. Kastrup / 747--748 \\
Christoffel und die Feldphysik / J. Ehlers / 748--748
\\
\\
Comments on the Ranking of Christoffel \\
\\
Christoffel und die Differentialgeometrie / W.
Klingenberg / 749--749 \\
Christoffel und die Geometrie / K. Leichtweiss /
749--749 \\
Christoffel und die Funktionentheorie / A. Pfluger /
749--749 \\
Christoffel and Numerical Analysis / W. Gautschi /
749--749 \\
Christoffel und die Kontinuumsmechanik / E. H{\"o}lder
/ 750--750 \\
A General Evaluation of Christoffel / P. L. Butzer, F.
Feh{\'e}r / 750--750 \\
Back Matter / 751--761 \\
\\
Alphabetical List of Paper / 751 \\
Index of AMS Subject Classification Numbers / 754 \\
Index of Key Words and Phrases / 757",
}
@Proceedings{Collatz:1982:WNM,
editor = "L. (Lothar) Collatz and G{\"u}nther Meinardus and H.
(Helmut) Werner",
booktitle = "{Workshop on Numerical Methods of Approximation
Theory, Oberwolfach, January 18--24, 1981 = Tagung
{\"u}ber Numerische Methoden der Approximationstheorie,
Oberwolfach, 18.--24. Januar 1981}",
title = "{Workshop on Numerical Methods of Approximation
Theory, Oberwolfach, January 18--24, 1981 = Tagung
{\"u}ber Numerische Methoden der Approximationstheorie,
Oberwolfach, 18.--24. Januar 1981}",
volume = "59",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "265",
year = "1982",
ISBN = "3-7643-1304-8",
ISBN-13 = "978-3-7643-1304-3",
LCCN = "QA221 .T129n 1981; QA297.5 .N85",
bibdate = "Tue Jan 3 14:12:53 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
melvyl.cdlib.org:210/CDL90",
series = "Numerical methods of approximation theory;
International series of numerical mathematics",
acknowledgement = ack-nhfb,
meetingname = "Tagung {\"u}ber Numerische Methoden der
Approximationstheorie (1981: Oberwolfach, Germany)",
remark = "English and German.",
subject = "Approximation theory; Congresses",
}
@Proceedings{Chui:1983:ATI,
editor = "C. K. Chui and Larry L. Schumaker and J. D. Ward",
booktitle = "{Approximation theory IV: proceedings of the
International Symposium on Approximation Theory held at
Texas A and M University, College Station, Texas, on
January 10--14, 1983}",
title = "{Approximation theory IV: proceedings of the
International Symposium on Approximation Theory held at
Texas A and M University, College Station, Texas, on
January 10--14, 1983}",
publisher = pub-AP,
address = pub-AP:adr,
pages = "xvii + 785",
year = "1983",
ISBN = "0-12-174580-5",
ISBN-13 = "978-0-12-174580-6",
LCCN = "QA297.5 .I54 1983",
bibdate = "Tue Jan 3 14:06:42 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "International Symposium on Approximation Theory (1983:
Texas A and M University)",
subject = "Approximation theory; Congresses",
}
@Proceedings{Werner:1983:CAC,
editor = "H. (Helmut) Werner and others",
booktitle = "{Computational aspects of complex analysis:
proceedings of the NATO Advanced Study Institute held
at Braunlage, Harz, Germany, July 26--August 6, 1982}",
title = "{Computational aspects of complex analysis:
proceedings of the NATO Advanced Study Institute held
at Braunlage, Harz, Germany, July 26--August 6, 1982}",
volume = "102",
publisher = pub-REIDEL,
address = pub-REIDEL:adr,
pages = "viii + 426",
year = "1983",
ISBN = "90-277-1571-8",
ISBN-13 = "978-90-277-1571-5",
LCCN = "QA300 .N29 1982",
bibdate = "Tue Jan 3 12:47:45 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
z3950.loc.gov:7090/Voyager",
series = "NATO advanced study institutes series. Series C,
Mathematical and physical sciences",
acknowledgement = ack-nhfb,
meetingname = "NATO Advanced Study Institute (1982: Braunlage,
Germany)",
subject = "Mathematical analysis; Data processing; Congresses;
Functions of complex variables",
}
@Proceedings{Collatz:1984:WNM,
editor = "L. (Lothar) Collatz and G{\"u}nther Meinardus and H.
(Helmut) Werner",
booktitle = "{Workshop on Numerical Methods of Approximation
Theory, Oberwolfach, March 20--26, 1983 = Tagung
{\"u}ber Numerische Methoden der Approximationstheorie,
Oberwolfach, 20.-26. M{\"a}rz 1983}",
title = "{Workshop on Numerical Methods of Approximation
Theory, Oberwolfach, March 20--26, 1983 = Tagung
{\"u}ber Numerische Methoden der Approximationstheorie,
Oberwolfach, 20.-26. M{\"a}rz 1983}",
volume = "67",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "148",
year = "1984",
ISBN = "3-7643-1580-6",
ISBN-13 = "978-3-7643-1580-1",
LCCN = "QA221 .T129n 1983",
bibdate = "Tue Jan 3 14:00:06 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
melvyl.cdlib.org:210/CDL90",
series = "Numerical methods of approximation theory;
International series of numerical mathematics",
acknowledgement = ack-nhfb,
meetingname = "Tagung {\"u}ber Numerische Methoden der
Approximationstheorie (1983: Oberwolfach, Germany)",
remark = "English and German.",
subject = "Approximation theory; Congresses",
}
@Proceedings{Graves-Morris:1984:RAI,
editor = "P. R. Graves-Morris and E. B. Saff and Richard S.
Varga",
booktitle = "{Rational approximation and interpolation: proceedings
of the United Kingdom--United States conference held at
Tampa, Florida, December 12--16, 1983}",
title = "{Rational approximation and interpolation: proceedings
of the United Kingdom--United States conference held at
Tampa, Florida, December 12--16, 1983}",
volume = "1105",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xii + 528",
year = "1984",
ISBN = "0-387-13899-4 (U.S.)",
ISBN-13 = "978-0-387-13899-2 (U.S.)",
LCCN = "QA3 .L28 no. 1105; QA297",
bibdate = "Tue Jan 3 14:15:32 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
z3950.loc.gov:7090/Voyager",
price = "DM72.00",
series = ser-LNM,
acknowledgement = ack-nhfb,
remark = "Conference on Rational Approximation and
Interpolation, held 12/12--16/83 in Tampa, Fla., and
sponsored by the U.S. National Science Foundation and
the U.K. Science and Engineering Research Council.",
subject = "Approximation theory; Congresses; Interpolation",
}
@Proceedings{Vichnevetsky:1984:ACM,
editor = "R. Vichnevetsky and R. S. Stepleman",
booktitle = "{Advances in computer methods for partial differential
equations V: proceedings of the Fifth IMACS
International Symposium on Computer Methods for Partial
Differential Equations held at Lehigh University ---
Bethlehem, Pennsylvania, USA., June 19--21, 1984}",
title = "{Advances in computer methods for partial differential
equations V: proceedings of the Fifth IMACS
International Symposium on Computer Methods for Partial
Differential Equations held at Lehigh University ---
Bethlehem, Pennsylvania, USA., June 19--21, 1984}",
publisher = pub-IMACS,
address = pub-IMACS:adr,
pages = "558",
year = "1984",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Tue Jan 03 14:09:58 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Vichnevetsky:1984:IFD,
editor = "R. Vichnevetsky and R. Stepleman",
booktitle = "Advances in computer methods for partial differential
equations-V: proceedings of the fifth IMACS
International Symposium on Computer Methods for Partial
Differential Equations, held at Lehigh University,
Bethlehem, Pennsylvania, USA, June 19--June 21, 1984",
title = "Advances in computer methods for partial differential
equations-{V}: proceedings of the fifth {IMACS}
International Symposium on Computer Methods for Partial
Differential Equations, held at Lehigh University,
Bethlehem, Pennsylvania, {USA}, June 19--June 21,
1984",
publisher = pub-IMACS,
address = pub-IMACS:adr,
pages = "558",
year = "1984",
ISBN = "",
ISBN-13 = "",
LCCN = "QA377.I2 1984",
bibdate = "Wed Jan 07 16:40:54 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Duffy:1985:PSS,
author = "L. Richard Duffy and Detlef Laugwitz",
title = "Problems and Solutions: Solutions of Advanced
Problems: 6460",
journal = j-AMER-MATH-MONTHLY,
volume = "92",
number = "9",
pages = "671--671",
month = nov,
year = "1985",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:07 MDT 1999",
bibsource = "http://www.jstor.org/journals/00029890.htm;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "See also \cite{Duffy:1984:PSA}.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Proceedings{Engquist:1985:LSC,
editor = "Bj{\"o}rn Engquist and Stanley Osher and Richard
Somerville",
title = "Large-scale computations in fluid mechanics",
volume = "22",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "xv + 370",
year = "1985",
ISBN = "0-8218-1122-3",
ISBN-13 = "978-0-8218-1122-1",
LCCN = "QA901 .L37 1985",
bibdate = "Tue Jan 3 14:18:30 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
z3950.loc.gov:7090/Voyager",
series = "Lectures in applied mathematics",
acknowledgement = ack-nhfb,
remark = "Papers presented at the Fifteenth AMS--SIAM Summer
Seminar on Applied Mathematics, held at Scripps
Institution of Oceanography, June 27--July 8, 1983.",
subject = "Fluid mechanics; Congresses; Numerical analysis",
}
@Article{LeVeque:1985:PSS,
author = "J. LeVeque and Lloyd N. Trefethen and James C. Smith",
title = "Problems and Solutions: Solutions of Advanced
Problems: 6462",
journal = j-AMER-MATH-MONTHLY,
volume = "92",
number = "10",
pages = "740--741",
month = dec,
year = "1985",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:09 MDT 1999",
bibsource = "http://www.jstor.org/journals/00029890.htm;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "See also \cite{Duffy:1984:PSA}.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Mattics:1985:APS,
author = "L. E. Mattics and Harald Niederreiter",
title = "Advanced Problems and Solutions: Solutions: 6461",
journal = j-AMER-MATH-MONTHLY,
volume = "92",
number = "9",
pages = "672--672",
month = nov,
year = "1985",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:07 MDT 1999",
bibsource = "http://www.jstor.org/journals/00029890.htm;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "See also \cite{Duffy:1984:PSA}.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Proceedings{Chui:1986:ATV,
editor = "C. K. Chui and Larry L. Schumaker and J. D. Ward",
booktitle = "{Approximation theory V}",
title = "{Approximation theory V}",
publisher = pub-AP,
address = pub-AP:adr,
pages = "xviii + 654",
year = "1986",
ISBN = "0-12-174581-3",
ISBN-13 = "978-0-12-174581-3",
LCCN = "QA221 .S92 1986; QA221.S92",
bibdate = "Tue Jan 3 14:22:17 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
library.mit.edu:9909/mit01",
note = "Proceedings of the Fifth International Symposium on
Approximation Theory, held at Texas A and M University
on January 13--17, 1986.",
acknowledgement = ack-nhfb,
meetingname = "International Symposium on Approximation Theory (5th:
1986: Texas A and M University)",
subject = "Approximation theory; Congresses",
}
@Proceedings{Griffiths:1986:NA,
editor = "D. F. (David Francis) Griffiths and G. A. (G.
Alistair) Watson",
booktitle = "Numerical analysis",
title = "Numerical analysis",
volume = "140",
publisher = pub-LONGMAN,
address = pub-LONGMAN:adr,
pages = "262",
year = "1986",
ISBN = "0-470-20669-1, 0-582-98897-7",
ISBN-13 = "978-0-470-20669-0, 978-0-582-98897-2",
LCCN = "QA297 .N8251 1986",
bibdate = "Tue Jan 3 14:22:04 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
library.ox.ac.uk:210/ADVANCE",
note = "The 11th Dundee Biennial Conference on Numerical
Analysis, held at the University of Dundee on 25--28
June 1985.",
series = "Pitman Research Notes in Mathematics",
acknowledgement = ack-nhfb,
meetingname = "Dundee Conference on Numerical Analysis (11th: 1985)",
subject = "Numerical analysis; Congresses",
}
@Proceedings{Mason:1987:AAB,
editor = "J. C. Mason and M. G. Cox",
booktitle = "{Algorithms for approximation: based on the
proceedings of the IMA Conference on Algorithms for the
Approximation of Functions and Data, held at the Royal
Military College of Science, Shrivenham, July 1985}",
title = "{Algorithms for approximation: based on the
proceedings of the IMA Conference on Algorithms for the
Approximation of Functions and Data, held at the Royal
Military College of Science, Shrivenham, July 1985}",
volume = "10",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xvi + 694 + 8",
year = "1987",
ISBN = "0-19-853612-7",
ISBN-13 = "978-0-19-853612-3",
LCCN = "QA221 .A5361 1987; QA221 .I47 1985",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/ruhe-axel.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$90",
series = "The Institute of Mathematics and Its Applications
conference series, new series",
acknowledgement = ack-nhfb,
bibno = "39820",
catcode = "G.1.2; G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Approximation; G.1.2
Elementary function approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation",
genterm = "theory; algorithms",
guideno = "1987-16080",
meetingname = "IMA Conference on Algorithms for the Approximation of
Functions and Data (1985: Royal Military College of
Science, Shrivenham)",
procdate = "The Institute of mathematics and its applications
conference series; 10 July 1985",
procloc = "Shrivenham, UK",
sub = "Proceedings of the IMA Conference on Algorithms for
the approximation of functions",
subject = "Approximation theory; Data processing; Congresses; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
tableofcontents = "Preface / v \\
Contributors / xiii \\
\\
I Development of Algorithms \\
\\
1. Spline Approximation and Smoothing \\
\\
G. T. Anthony and M. G. Cox / The fitting of extremely
large data sets by bivariate splines / 5 \\
W. Dahmen / Subdivision algorithms --- recent results,
some extensions and further developments / 21 \\
P. Dierckx / Fast algorithms for smoothing data over a
disc or a sphere using tensor product splines / 51 \\
T. Lyche and K. M{\o}rken / A discrete approach to knot
removal and degree reduction algorithms for splines /
67 \\
R. H. J. Gmelig Meyling / On algorithms and
applications for bivariate B-splines / 83 \\
\\
2. Spline Interpolation and Shape Preservation \\
\\
R. E. Carlson / Shape preserving interpolation / 97 \\
M. G. Cox and H. M. Jones / Shape preserving spline
approximation in the $\ell_1$-norm / 115 \\
J. A. Gregory / A review of curve interpolation with
shape control / 131 \\
\\
3. Multivariate Interpolation \\
\\
M. J. D. Powell / Radial basis functions for
multivariable interpolation: a review / 143 \\
R. A. Lorentz / On the determinant of a bivariate
Birkhoff interpolation problem / 169 \\
A. Le Mehaute / Interpolation with piecewise
polynomials in more than one variable / 181 \\
\\
4. Least Square Methods \\
\\
R. Farwig / Multivariate interpolation of scattered
data by moving least squares methods / 193 \\
F. Yoshimoto / Least squares approximation by one-pass
methods with piecewise polynomials / 213 \\
\\
5. Rational Approximation \\
\\
L. N. Trefethen and M. H. Gutknecht / Pad{\'e}, stable
Pad{\'e}, and Chebyshev--Pad{\'e} approximation / 227
\\
P. T. Breuer / A new method for real rational uniform
approximation / 265 \\
C. B. Dunham / Rationals with repeated poles / 285 \\
A. Iserles and S. P. N{\o}rsett / Error control of
rational approximation with a matrix argument / 293 \\
\\
6. Complex and Nonlinear Approximation \\
\\
K. Madsen / General algorithms for discrete non-linear
parameter estimation / 309 \\
G. Opfer / Complex rational approximation with
numerical experiments / 327 \\
G. A. Watson / Data fitting by positive sums of
exponentials / 337 \\
J. C. Mason and P. Owen / Some simple algorithms for
constrained complex and rational approximation / 357
\\
\\
7. Computer-Aided Design and Blending \\
\\
L. L. Schumaker / Numerical aspects of spaces of
piecewise polynomials on triangulations / 373 \\
M. V. Golitschek / The $H$-sets of the blending
functions / 407 \\
D. Levin / Multidimensional reconstruction by
set-valued approximations/ 421 \\
\\
II Applications \\
\\
8. Applications in Numerical Analysis \\
\\
H. P. Blatt, A, Iserles and E. B. Saff / Remarks on the
behaviour of zeros of best approximating polynomials
and rational functions / 437 \\
J. Gilbert and W. A. Light / Multigrid methods and the
alternating algorithm / 447 \\
K. Jetter and J. St{\"o}ckler / On the computation of
Gauss--Birkhoff quadrature formulas / 459 \\
E. Schock / Error bounds for the solution of integral
equations by Galerkin-like methods / 471 \\
N. M. Temme / On the computation of the incomplete
gamma functions for large values of the parameters /
479 \\
\\
9. Applications in Partial Differential Equations \\
\\
J. R. Rice / Adaptive tensor product grids for singular
problems / 493 \\
W. Freeden / Harmonic splines for solving boundary
value problems of potential theory / 507 \\
D. C. Hanscomb / Recovery of fluid flow fields / 531
\\
L. Reichel / The selection of subspace and collocation
points in the boundary collocation method for some
plane elliptic boundary problems / 541 \\
\\
10. Applications in Other Disciplines \\
\\
L. Andersson, K. Holmstr{\"o}m and A. Ruhe / Complex
formation constants --- a problem from solution
chemistry / 557 \\
D. E. Roberts and P. R. Graves-Morris / The application
of generalised inverse rational interpolants in the
model analysis of vibrating structures I / 573 \\
A. Daman and J. C. Mason / A generalised
cross-validation method for meteorological data with
gaps / 595 \\
K. P. Jackson and J. C. Mason / The approximation by
complex functions of stresses in cracked domains / 6ll
\\
J. H. McDonnell / Equally spaced cubic splines for
representing time histories / 623 \\
B. L. Rahimi and S. W. Ellacott / Dynamic phase
analysis of heart anomalies / 641 \\
\\
III Software \\
\\
J. G. Hayes / NAG algorithms for the approximation of
functions and data / 653 \\
G. T. Anthony and M. G. Cox / The National Physical
Laboratory's Data Approximation Subroutine Library /
669 \\
\\
M. G. Cox (editor) / Panel Discussion / 689",
}
@Proceedings{Morton:1988:NMF,
editor = "K. W. Morton and M. J. (Michael John) Baines",
booktitle = "{Numerical methods for fluid dynamics III: based on
the proceedings of a conference organized by the
Institute for Computational Fluid Dynamics of the
Universities of Oxford and Reading in association with
the Institute of Mathematics and [its] Applications on
numerical methods for fluid dynamics, held in Oxford in
March 1988}",
title = "{Numerical methods for fluid dynamics III: based on
the proceedings of a conference organized by the
Institute for Computational Fluid Dynamics of the
Universities of Oxford and Reading in association with
the Institute of Mathematics and [its] Applications on
numerical methods for fluid dynamics, held in Oxford in
March 1988}",
volume = "17",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xvii + 529",
year = "1988",
ISBN = "0-19-853632-1",
ISBN-13 = "978-0-19-853632-1",
LCCN = "TA357 .N8726 1988",
bibdate = "Tue Jan 3 12:30:04 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$75.00",
series = "The Institute of Mathematics and Its Applications
conference, new series",
acknowledgement = ack-nhfb,
subject = "Fluid dynamics; Mathematics; Congresses; Numerical
calculations",
}
@Proceedings{Mason:1990:AAI,
editor = "J. C. Mason and M. G. Cox",
booktitle = "{Algorithms for approximation II: based on the
proceedings of the Second International Conference on
Algorithms for Approximation, held at Royal Military
College of Science, Shrivenham, July 1988}",
title = "{Algorithms for approximation II: based on the
proceedings of the Second International Conference on
Algorithms for Approximation, held at Royal Military
College of Science, Shrivenham, July 1988}",
publisher = pub-CHAPMAN-HALL,
address = pub-CHAPMAN-HALL:adr,
pages = "514",
year = "1990",
ISBN = "0-412-34580-3",
ISBN-13 = "978-0-412-34580-7",
LCCN = "QA221 .I54 1988",
bibdate = "Thu Sep 01 23:55:44 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Algorithms for
Approximation (2nd: 1988: Royal Military College of
Science, Shrivenham, England)",
subject = "Approximation theory; Data processing; Congresses",
tableofcontents = "Part One: Development of Algorithms / 1 \\
1. Spline Approximation / 3 \\
E. Arge, M. Dcehlen, T. Lyche and K. Morken /
Constrained spline approximation of functions and data
based on constrained knot removal / 4 \\
G. T. Anthony and M. G. Cox / Near real-time spline
fitting of long sequences of uniformly-spaced data / 21
\\
M. Bozzini and F. de Tisi / An algorithm for knot
location in bivariate least squares spline
approximation / 30 \\
M. G. Cox, P. M. Harris and H. M. Jones / A knot
placement strategy for least squares spline fitting
based on the use of local polynomial approximations /
37 \\
G. Opfer / An algorithm for nonlinear splines with
non-negativity constraints / 46 \\
C. Potier and C. Vercken / Spline curve fitting of
digitized contours / 54 \\
C. Rabut / A B-spline approximation algorithm for
quasi-interpolation or filtering / 62 \\
P. W. Smith / On knots and nodes for spline
interpolation / 72 \\
2. Polynomial and Piecewise Polynomial Approximation /
79 \\
W. Dahmen / A basis for certain spaces of multivariate
polynomials and exponentials / 80 \\
F. N. Fritschi / Monotone piecewise cubic data fitting
/ 99 \\
M. Heilmann and M. W. M{\"u}ller / Direct and converse
results on simultaneous approximation by the method of
Bernstein--Durrmeyer operators / 107 \\
A. Iserles, P. E. Koch, S. P. N{\o}rsett and J. M.
Sanz-Serna / Orthogonality and approximation in a
Sobolev space / 117 \\
M. A. Lachance / Piecewise polynomial approximation of
polynomial curves / 125 \\
E. Quak and L. L. Schumaker / Calculation of the energy
of a piecewise polynomial surface / 134 \\
3. Interpolation / 145 \\
M. D. Buhmann and M. J. D. Powell / Radial basis
function interpolation on an infinite regular grid /
146 \\
L. Brutman / The Fourier operator of even order and its
application to an extremum problem in interpolation /
170 \\
N. Dyn and A. Ron / On multivariate polynomial
interpolation / 177 \\
N. Dyn, D. Levin and S. Rippen / Algorithms for the
construction of data dependent triangulations / 185 \\
C. Rademacher and K. Scherer / Algorithms for computing
best parametric cubic interpolation / 193 \\
4. Smoothing and Constraint Methods / 209 \\
M. Von Golitschek and L. L. Schumaker / Data fitting by
penalized least squares / 210 \\
K. W. Bosworth / A semiinfinite programming algorithm
for constrained best approximation / 228 \\
M. Bozzini and L. Lenarduzzi / Inference region for a
method of local approximation by using the residuals /
236 \\
5. Complex Approximation / 245 \\
G. A. Watson / Numerical methods for Chebyshev
approximation of complex-valued functions / 246 \\
P. T. P. Tang / A fast algorithm for linear complex
Chebyshev approximation / 265 \\
Part Two: Applications / 275 \\
6. Computer Aided Design and Geometric Modelling / 277
\\
N. Dyn, J. A. Gregory and D. Levin / Uniform
subdivision algorithms for curves and surfaces / 278
\\
T. B. Boffey, M. G. Cox, L. M. Delves and C. J.
Pursglove / Approximation by spheres / 296 \\
T. A. Foley / Interpolation of scattered data on a
spherical domain / 303 \\
A. B. Forbes / Least squares best fit geometric
elements / 311 \\
W. Freeden and J. C. Mason / Uniform piecewise
approximation on the sphere / 320 \\
7. Applications in Numerical Analysis / 335 \\
L. N. Trefethen / Approximation theory and numerical
linear algebra / 336 \\
M. Frontini, G. Rodriguez and S. Seatzu / An algorithm
for computing minimum norm solutions of the finite
moment problem / 361 \\
R. H. J. Gmelig Meyling / Numerical solution of the
biharmonic equation using different types of bivariate
spline functions / 369 \\
G. O. Olaofe / Quadrature solution of integral
equations: a uniform treatment of Fredholm and Volterra
equations / 377 \\
G. Walz / Increasing the convergence modulus of an
asymptotic expansion: an algorithm for numerical
differentiation / 387 \\
J. Williams / Approximation and parameter estimation in
ordinary differential equations / 395 \\
8. Applications in Other Disciplines / 405 \\
C. Zala and I. Barrodale / Applications of discrete
$L_1$ methods in science and engineering / 406 \\
J. C. Mason, A. E. Trefethen and S. J. Wilde /
Constrained complex approximation algorithms in
communication engineering / 424 \\
R. W. Allen and J. G. Metcalfe / Integration of
absolute amplitude from a decibel B-spline fit / 449
\\
M. G. Cox and H. M. Jones / A nonlinear least squares
data fitting problem arising in microwave measurement /
458 \\
J. C. Mason and S. J. Wilde / A complex minimax
algorithm for phase-only adaptation in antenna arrays /
466 \\
Part Three: Catalogue of Algorithms / 477 \\
E. Grosse / A catalogue of algorithms for approximation
/ 479",
}
@Proceedings{Griffiths:1991:NAP,
editor = "D. F. Griffiths and G. A. Watson",
booktitle = "Numerical analysis, 1991: proceedings of the 14th
Dundee Conference, June 1991",
title = "Numerical analysis, 1991: proceedings of the 14th
Dundee Conference, June 1991",
volume = "260",
publisher = pub-LONGMAN,
address = pub-LONGMAN:adr,
pages = "292",
year = "1991",
ISBN = "0-582-08908-5",
ISBN-13 = "978-0-582-08908-2",
LCCN = "QA297 .D85 1991",
bibdate = "Mon Jan 15 11:05:56 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
series = "Pitman Research Notes in Mathematics",
acknowledgement = ack-nhfb,
}
@Book{Saff:1993:FCA,
author = "E. B. Saff and Arthur David Snider",
booktitle = "Fundamentals of complex analysis for mathematics,
science, and engineering",
title = "Fundamentals of complex analysis for mathematics,
science, and engineering",
publisher = pub-PH,
address = pub-PH:adr,
edition = "Second",
pages = "xi + 468",
year = "1993",
ISBN = "0-13-327461-6",
ISBN-13 = "978-0-13-327461-5",
LCCN = "QA300 .S18 1993",
bibdate = "Tue Jan 3 14:22:20 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
library.mit.edu:9909/mit01",
price = "US\$48.75",
acknowledgement = ack-nhfb,
subject = "Mathematical analysis; Functions of complex
variables",
}
@Proceedings{Kirchgassner:1996:IPT,
editor = "Klaus Kirchgassner and Oskar Mahrenholtz and Reinhard
Mennicken",
booktitle = "{ICIAM 95: proceedings of the Third International
Congress on Industrial and Applied Mathematics held in
Hamburg, Germany, July 3--7, 1995}",
title = "{ICIAM 95: proceedings of the Third International
Congress on Industrial and Applied Mathematics held in
Hamburg, Germany, July 3--7, 1995}",
volume = "87",
publisher = "Akademie Verlag",
address = "Berlin, Germany",
pages = "487",
year = "1996",
ISBN = "3-05-501682-3",
ISBN-13 = "978-3-05-501682-0",
LCCN = "QA1 .I73 1995",
bibdate = "Sat Oct 24 15:57:08 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
series = "Mathematical research",
acknowledgement = ack-nhfb,
}
@Proceedings{Fischer:1998:PIC,
editor = "Gerd Fischer and Hannes Stoppel and Ulf Rehmann",
booktitle = "{Proceedings of the International Congress of
Mathematicians, Berlin 1998, August 18--27}",
title = "{Proceedings of the International Congress of
Mathematicians, Berlin 1998, August 18--27}",
publisher = "Deutscher Mathematiker-Vereinigung",
address = "Bielefeld, Germany",
pages = "????",
year = "1998",
ISSN = "1431-0635",
LCCN = "QA1 .I61 1998",
bibdate = "Tue Jan 3 14:20:09 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
melvyl.cdlib.org:210/CDL90",
series = j-DOC-MATH,
acknowledgement = ack-nhfb,
fjournal = "Documenta Mathematica",
meetingname = "International Congress of Mathematicians (1998:
Berlin, Germany)",
remark = "At head of title: Documenta mathematica, Journal der
Deutschen Mathematiker-Vereinigung, extra volume ICM
1998. Volume 1: Plenary lectures and ceremonies. Volume
2--3: Invited lectures.",
subject = "Mathematics; Congresses",
}
@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,
address = pub-LONGMAN: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/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{Ainsworth:1999:GSG,
editor = "M. 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-SV,
address = pub-SV:adr,
pages = "x + 250",
year = "1999",
ISBN = "3-540-65752-5",
ISBN-13 = "978-3-540-65752-1",
ISSN = "0179-3632",
LCCN = "QA297 .E57 1998",
bibdate = "Tue Jan 3 15:24:14 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
z3950.loc.gov:7090/Voyager",
series = "Springer series in computational mathematics",
acknowledgement = ack-nhfb,
meetingname = "EPSRC Numerical Analysis Summer School (8th: 1998:
University of Leicester)",
remark = "The Eighth EPSRC Numerical Analysis Summer School was
held at the University of Leicester from the 5th to the
17th of July, 1998.",
subject = "Numerical analysis",
}
@Book{Iserles:1999:AN,
author = "Arieh Iserles",
booktitle = "Acta numerica 1999",
title = "Acta numerica 1999",
volume = "8",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "295",
year = "1999",
ISBN = "0-521-77088-2 (hardcover)",
ISBN-13 = "978-0-521-77088-0 (hardcover)",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
LCCN = "QA279 1999",
bibdate = "Tue Jan 3 15:29:09 MST 2006",
bibsource = "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
series = "Acta Numerica",
acknowledgement = ack-nhfb,
}
@Article{Bottcher:2006:SPB,
author = "Albrecht B{\"o}ttcher",
title = "Book Review: {{\em Spectra and Pseudospectra: The
Behavior of Nonnormal Matrices and Operators by Lloyd
N. Trefethen and Mark Embree, Princeton University
Press, Princeton and Oxford, 2005, xvii + 606 pages,
ISBN 0-691-11946-5}}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "416",
number = "2--3",
pages = "1098--1101",
day = "15",
month = jul,
year = "2006",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Tue Jun 6 18:36:11 MDT 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
http://www.sciencedirect.com/science/journal/00243795",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Book{Schleicher:2011:IMC,
editor = "Dierk Schleicher and Malte Lackmann",
booktitle = "An Invitation to Mathematics: From Competitions to
Research",
title = "An Invitation to Mathematics: From Competitions to
Research",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiv + 220",
year = "2011",
ISBN = "3-642-19532-6 (soft cover), 3-642-19533-4 (e-book)",
ISBN-13 = "978-3-642-19532-7 (soft cover), 978-3-642-19533-4
(e-book)",
LCCN = "????",
bibdate = "Sat Mar 23 16:04:27 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
tableofcontents = "Preface: what is mathematics? \\
Welcome! \\
Structure and randomness in the prime numbers / Terence
Tao \\
How to solve a Diophantine equation / Michael Stoll \\
From sex to quadratic forms / Simon Norton \\
Small divisors: number theory in dynamical systems /
Jean-Christophe Yoccoz \\
How do IMO problems compare with research problems?
Ramsey theory as a case study / W. Timothy Gowers \\
How do research problems compare with IMO problems? A
walk around games / Stanislav Smirnov \\
Graph theory over 45 years / L{\'a}szl{\'o} Lov{\'a}sz
\\
Communication complexity / Alexander A. Razborov \\
Ten digit problems / Lloyd N. Trefethen \\
The ever-elusive blowup in the mathematical description
of fluids / Robert M. Kerr and Marcel Oliver \\
About the Hardy inequality / Nader Masmoudi \\
The lion and the Christian, and other pursuit and
evasion games / B{\'e}la Bollob{\'a}s \\
Three mathematics competitions / G{\"u}nter M. Ziegler
\\
Complex dynamics, the Mandelbrot set, and Newton's
method: or, On useless and useful mathematics / Dierk
Schleicher",
}
@Book{Schleicher:2013:EME,
author = "Dierk Schleicher and Malte Lackmann",
booktitle = "{Eine Einladung in die Mathematik: Einblicke in
aktuelle Forschung}. ({German}) [{An} invitation to
mathematics: insights into current research]",
title = "{Eine Einladung in die Mathematik: Einblicke in
aktuelle Forschung}. ({German}) [{An} invitation to
mathematics: insights into current research]",
publisher = "Springer Spektrum",
address = "Heidelberg, Germany",
pages = "xv + 228",
year = "2013",
DOI = "https://doi.org/10.1007/978-3-642-25798-8",
ISBN = "3-642-25797-6, 3-642-25798-4 (e-book)",
ISBN-13 = "978-3-642-25797-1, 978-3-642-25798-8 (e-book)",
LCCN = "QA37.3 .E3615 2013eb",
bibdate = "Thu Mar 23 07:12:45 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
URL = "http://public.eblib.com/choice/publicfullrecord.aspx?p=1082421;
http://site.ebrary.com/id/10640332",
abstract = "Diese Einladung zur Mathematik besteht aus 14
Beitr{\"a}gen, viele davon von weltweit f{\"u}hrenden
Mathematikern geschrieben, die die Leser in spannende
Aspekte aktueller mathematischer Forschung
einf{\"u}hren. Die Artikel sind so vielf{\"a}ltig wie
die Pers{\"o}nlichkeiten ihrer Autoren und zeigen, wie
reich und lebendig die Mathematik als Forschungsgebiet
ist. Das Buch richtet sich in erster Linie an
interessierte Sch{\"u}ler und junge Studierende, die
Mathematik aus der Schule oder von Wettbewerben kennen
und die aktuelle Forschungsmathematik kennenlernen
wollen. Zusammen mit einem Team junger 'Testleser'
haben d.",
acknowledgement = ack-nhfb,
language = "German",
remark = "German translation by Bertram Arnold, Robin Stoll, and
Marcel Oliver of \booktitle{An invitation to
mathematics: from competitions to research}, Springer,
2011.",
subject = "Mathematics; Engineering mathematics; Essays;
Pre-Calculus; Reference; Mathematics",
tableofcontents = "Vorwort: Was ist Mathematik? / G{\"u}nter M.
Ziegler / vii \\
Willkommen! / Eine Begr{\"u}{\ss}ung durch die
Herausgeber / ix \\
Struktur und Zuf{\"a}lligkeit der Primzahlen / Terence
Tao / 1 \\
1 Einleitung \\
2 Primzahlen finden \\
3 Primzahlen z{\"a}hlen \\
4 Primzahlen modellieren \\
5 Muster in den Primzahlen finden \\
Literaturverzeichnis \\
Wie man Diophantische Gleichungen l{\"o}st / Michael
Stoll / 9 \\
1 Diophantische Gleichungen \\
2 Die Beispielgleichung \\
3 Eine geometrische Interpretation \\
4 Nadeln im Heuhaufen \\
Literaturverzeichnis \\
Vom Kindergarten zu quadratischen Formen / Simon Norton
/ 21 \\
1 Einleitung \\
2 Vom Geschlecht zu Socken \\
3 Von Socken zu Dreiecken \\
4 Von Dreiecken zu quadratischen Formen \\
5 Negative Diskriminanten \\
6 Verschwindende Diskriminante \\
7 Positive Diskriminanten \\
8 Orbits von Tripeln \\
9 Quadratische Diskriminanten \\
10 Positive nichtquadratische Diskriminanten \\
11 Zusammenfassung \\
Literaturverzeichnis \\
Kleine Nenner: Zahlentheorie in dynamischen Systemen /
Jean-Christophe Yoccoz / 43 \\
1 Planetensysteme \\
2 Komplexe quadratische Polynome und Linearisierung \\
3 Diophantische N{\"a}herung \\
4 Weitere Ergebnisse und offene Fragen \\
5 Mehrere Freiheitsgrade \\
Literaturverzeichnis \\
Sind IMO-Aufgaben wie Forschungsprobleme? / W. Timothy
Gowers / 57 \\
1 Einleitung \\
2 Asymptotisches Verhalten der Ramseyzahlen \\
3 Was ist Ramseytheorie?4 Ein Ramseysatz {\"u}ber eine
unendliche Struktur \\
5 Von Kombinatorik zu unendlichdimensionaler Geometrie
\\
6 Ein wenig mehr {\"u}ber Banachr{\"a}ume \\
7 Ein schwacher Ramsey-artiger Satz f{\"u}r
Unterr{\"a}ume \\
8 Zusammenfassung \\
Weiterf{\"u}hrende Literatur \\
Sind Forschungsprobleme wie IMO-Aufgaben? / Stanislav
Smirnov / 73\\
1 L{\"o}sen Mathematiker Probleme? \\
2 Das F{\"u}nfeckspiel \\
3 Das Spiel des Lebens \\
4 Das Sandhaufenmodell \\
5 Kreuzungsfreie Wanderung \\
6 Zusammenfassung \\
Literaturverzeichnis \\
45 Jahre Graphentheorie / L{\'a}szl{\'o} Lov{\'a}sz \\
1 Einleitung \\
2 Diskrete Optimierung \\
3 Informatik \\
4 Die probabilistische Methode \\
5 Algebra, Topologie und Graphentheorie \\
6 Netzwerke, oder sehr gro{\ss}e Graphen \\
Literaturverzeichnis \\
Die Komplexit{\"a}t der Kommunikation / Alexander A.
Razborov / 99 \\
1 Einleitung \\
2 Das Grundmodell \\
3 Untere Schranken \\
4 Sind die Schranken scharf? \\
5 Probabilistische Modelle \\
6 Andere Varianten von Kommunikationskomplexit{\"a}t
\\
7 Zusammenfassung \\
Formelindex \\
Literaturverzeichnis \\
Zehnstellige Probleme / Lloyd N. Trefethen / 121 \\
1 Einleitung \\
2 Zwei W{\"u}rfel \\
3 F{\"u}nf M{\"u}nzen \\
4 Blow-Up \\
5 Die 100-Stellen-Herausforderung \\
6 Epilog \\
Literaturverzeichnis \\
Regul{\"a}r oder singul{\"a}r? Mathematische und
numerische R{\"a}tsel in der Str{\"o}mungsmechanik /
Robert M. Kerr und Marcel Oliver / 141 \\
1 Einleitung \\
2 Die Differentialgleichungen der Str{\"o}mungsmechanik
\\
3 Erhaltungss{\"a}tze \\
4 Das Clay-Milleniums-Problem \\
5 Regul{\"a}r oder nicht regul{\"a}r, das ist hier die
Frage \\
6 Wirbelschl{\"a}uche als Testfall \\
7 Numerische Fehler \\
8 Eine Einladung zur Forschung \\
Anhang A. Im Schnellschritt durch die Vektoranalysis
\\
Anhang B. Energieabsch{\"a}tzungen \\
Anhang C. Spektralund Pseudospektralmethoden \\
Literaturverzeichnis \\
{\"U}ber die Hardy-Ungleichung / Nader Masmoudi / 171
\\
1 Ungleichungen \\
2 Geschichte der Hardy-Ungleichung \\
3 Beweis der Hardy-Ungleichung \\
4 Varianten der Hardy-Ungleichung \\
5 Anwendungen \\
6 Fazit \\
Literaturverzeichnis \\
Der L{\"o}we und der Christ, und andere Verfolgungs und
Fluchtspiele / B{\'e}la Bollob{\'a}s / 187 \\
Drei mathematische Wettbewerbe / G{\"u}nter M. Ziegler
/ 201 \\
Komplexe Dynamik, die Mandelbrot-Menge und das
Newton-Verfahren -- oder: Von nutzloser und
n{\"u}tzlicher Mathematik /Dierk Schleicher / 213",
}
