% From cs.cornell.edu!cv Fri Oct 5 10:00:53 PDT 1990 % % Bibliography of the book "Matrix Computations", 2nd Edn., % by Gene H. Golub & Charles F. Van Loan, % The Joh ns Hopkins University Press, Baltimore, Maryland 21218, 1989. % The original bibliography prepared by Charles Van Loan % (Computer Science, Cornell University, Ithaca, NY 14583) % was corrected, edited and put in Bibtex format (September 1990) % by Chris Paige and Clement Pellerin % (Computer Science, McGill University, Montreal, PQ, Canada H3A 2A7). % email any corrections to Charlie Van Loan at cv'AT SIGN'cs.cornell.edu % % This is the BibTeX file, store it as, for example, gvl.bib % % USE: suppose you want the first reference only to appear, without % citing it. Store in a file called say egcite.tex (without the %s): % % \documentstyle[art12,fullpage]{article} % \begin{document} % \nocite{Aas71} % \bibliographystyle{unsrt} % \bibliography{gvl} % \end{document} % % Then run % latex egcite % bibtex egcite % latex egcite % latex egcite % and use the resulting egcite.dvi to give the required output. % Using \nocite{*} should give you all entries, but you may have to % \nocite half of them, then the rest, to do this. % % Some entries have a \cite in the Note field because they appear % both in a journal and in a book, Calling % latex; bibtex; latex; latex % fails if you cite one of these entries. % If this happens you should either call: % latex; bibtex; latex; bibtex; latex; latex % or else you should \nocite{WilR71} at the beginning of your document % but don't use \bibliographystyle{unsrt} because WilR71 will come first % Journals % First the Full Name is given, then the abbreviation used in the AMS Math % Reviews, with an indication if it could not be found there. % Note the 2nd overwrites the 1st, so swap them if you want the full name. %{AMS} @String{AMSTrans = "American Mathematical Society Translations" } @String{AMSTrans = "Amer. Math. Soc. Transl." } @String{BullAMS = "Bulletin of the American Mathematical Society" } @String{BullAMS = "Bull. Amer. Math. Soc." } @String{ProcAMS = "Proceedings of the American Mathematical Society" } @String{ProcAMS = "Proc. Amer. Math. Soc." } @String{TransAMS = "Transactions of the American Mathematical Society" } @String{TransAMS = "Trans. Amer. Math. Soc." } %ACM @String{CACM = "Communications of the {ACM}" } @String{CACM = "Comm. {ACM}" } @String{CompServ = "{ACM} Computing Surveys" } @String{CompServ = "Comput. Surveys" } @String{JACM = "Journal of the {ACM}" } @String{JACM = "J. Assoc. Comput. Mach." } @String{ACMMathSoft = "{ACM} Transactions on Mathematical Software" } @String{ACMMathSoft = "{ACM} Trans. Math. Software" } @String{SIGNUM = "{ACM} {SIGNUM} Newsletter" } @String{SIGNUM = "{ACM} {SIGNUM} Newslett." } @String{AmerSocio = "American Journal of Sociology" } @String{AmerSocio = "Amer. J. Sociology" } % didn't find in AMS MR @String{AmerStatAssoc = "Journal of the American Statistical Association" } @String{AmerStatAssoc = "J. Amer. Statist. Assoc." } @String{ApplMathComp = "Applied Mathematics and Computation" } @String{ApplMathComp = "Appl. Math. Comput." } @String{AmerMathMonthly = "American Mathematical Monthly" } @String{AmerMathMonthly = "Amer. Math. Monthly" } @String{BIT = "{BIT}" } @String{BIT = "{BIT}" } @String{BritStatPsych = "British Journal of Mathematical and Statistical Psychology" } @String{BritStatPsych = "Brit. J. Math. Statist. Psych." } @String{CanMathBull = "Canadian Mathematical Bulletin" } @String{CanMathBull = "Canad. Math. Bull." } @String{CompApplMath = "Journal of Computational and Applied Mathematics" } @String{CompApplMath = "J. Comput. Appl. Math." } @String{CompPhys = "Journal of Computational Physics" } @String{CompPhys = "J. Comput. Phys." } @String{CompStruct = "Computers and Structures" } @String{CompStruct = "Comput. \& Structures" } @String{CompJour = "The Computer Journal" } @String{CompJour = "Comput. J." } @String{CompSysSci = "Journal of Computer and System Sciences" } @String{CompSysSci = "J. Comput. System Sci." } @String{Computing = "Computing" } @String{Computing = "Computing" } @String{ContempMath = "Contemporary Mathematics" } @String{ContempMath = "Contemp. Math." } @String{Crelle = "Crelle's Journal" } @String{Crelle = "Crelle's J." } % didn't find in AMS MR. %% When will they get up to date? @String{GiornaleMath = "Giornale di Mathematiche" } @String{GiornaleMath = "Giorn. Mat." } % didn't find in AMS MR., ibid. %IEEE @String{Computer = "{IEEE} Computer" } @String{Computer = "{IEEE} Computer" } @String{IEEETransComp = "{IEEE} Transactions on Computers" } @String{IEEETransComp = "{IEEE} Trans. Comput." } @String{IEEETransAC = "{IEEE} Transactions on Automatic Control" } @String{IEEETransAC = "{IEEE} Trans. Automat. Control" } @String{IEEESpec = "{IEEE} Spectrum" } @String{IEEESpec = "{IEEE} Spectrum" } % didn't find in AMS MR @String{ProcIEEE = "Proceedings of the {IEEE}" } @String{ProcIEEE = "Proc. {IEEE}" } % didn't find in AMS MR @String{IEEETransAeroElec = "{IEEE} Transactions on Aerospace and Electronic Systems" } @String{IEEETransAeroElec = "{IEEE} Trans. Aerospace Electron. Systems" } @String{IMANumerAna = "{IMA} Journal of Numerical Analysis" } @String{IMANumerAna = "{IMA} J. Numer. Anal." } @String{InfProcLet = "Information Processing Letters" } @String{InfProcLet = "Inform. Process. Lett." } @String{InstMathApp = "Journal of the Institute of Mathematics and its Applications" } @String{InstMathApp = "J. Inst. Math. Appl." } @String{IntControl = "International Journal of Control" } @String{IntControl = "Internat. J. Control" } @String{IntNumerEng = "International Journal for Numerical Methods in Engineering" } @String{IntNumerEng = "Internat. J. Numer. Methods Engrg." } @String{IntSuper = "International Journal of Supercomputing Applications" } @String{IntSuper = "Internat. J. Supercomputing Applic." } % didn't find %% in AMS MR @String{Kibernetika = "Kibernetika" } @String{Kibernetika = "Kibernetika" } @String{JResNatBurStand = "Journal of Research of the National Bureau of Standards" } @String{JResNatBurStand = "J. Res. Nat. Bur. Standards" } @String{LinAlgApp = "Linear Algebra and its Applications" } @String{LinAlgApp = "Linear Algebra Appl." } @String{MathAnaAppl = "Journal of Mathematical Analysis and Applications" } @String{MathAnaAppl = "J. Math. Anal. Appl." } @String{MathAnnalen = "Mathematische Annalen" } @String{MathAnnalen = "Math. Ann." } @String{MathPhys = "Journal of Mathematical Physics" } @String{MathPhys = "J. Math. Phys." } @String{MathComp = "Mathematics of Computation" } @String{MathComp = "Math. Comp." } @String{MathScand = "Mathematica Scandinavica" } @String{MathScand = "Math. Scand." } @String{TablesAidsComp = "Mathematical Tables and Other Aids to Computation" } @String{TablesAidsComp = "Math. Tables Aids Comput." } @String{NumerMath = "Numerische Mathematik" } @String{NumerMath = "Numer. Math." } @String{PacificMath = "Pacific Journal of Mathematics" } @String{PacificMath = "Pacific J. Math." } @String{ParDistComp = "Journal of Parallel and Distributed Computing" } @String{ParDistComp = "J. Parallel and Distrib. Comput." } % didn't find %% in AMS MR @String{ParComputing = "Parallel Computing" } @String{ParComputing = "Parallel Comput." } @String{PhilMag = "Philosophical Magazine" } @String{PhilMag = "Philos. Mag." } @String{ProcNAS = "Proceedings of the National Academy of Sciences of the USA" } @String{ProcNAS = "Proc. Nat. Acad. Sci. U.S.A." } @String{Psychometrika = "Psychometrika" } @String{Psychometrika = "Psychometrika" } @String{QuartMath = "Quarterly Journal of Mathematics, Oxford, Series (2)" } @String{QuartMath = "Quart. J. Math. Oxford Ser. (2)" } @String{QuartApplMath = "Quarterly of Applied Mathematics" } @String{QuartApplMath = "Quart. Appl. Math." } @String{RevueInstStat = "Review of the International Statisical Institute" } @String{RevueInstStat = "Rev. Inst. Internat. Statist." } %SIAM @String{JSIAM = "Journal of the Society for Industrial and Applied Mathematics" } @String{JSIAM = "J. Soc. Indust. Appl. Math." } @String{JSIAMB = "Journal of the Society for Industrial and Applied Mathematics, Series B, Numerical Analysis" } @String{JSIAMB = "J. Soc. Indust. Appl. Math. Ser. B Numer. Anal." } @String{SIAMAlgMeth = "{SIAM} Journal on Algebraic and Discrete Methods" } @String{SIAMAlgMeth = "{SIAM} J. Algebraic Discrete Methods" } @String{SIAMAppMath = "{SIAM} Journal on Applied Mathematics" } @String{SIAMAppMath = "{SIAM} J. Appl. Math." } @String{SIAMComp = "{SIAM} Journal on Computing" } @String{SIAMComp = "{SIAM} J. Comput." } @String{SIAMMatrix = "{SIAM} Journal on Matrix Analysis and Applications" } @String{SIAMMatrix = "{SIAM} J. Matrix Anal. Appl." } @String{SIAMNumAnal = "{SIAM} Journal on Numerical Analysis" } @String{SIAMNumAnal = "{SIAM} J. Numer. Anal." } @String{SIAMReview = "{SIAM} Review" } @String{SIAMReview = "{SIAM} Rev." } @String{SIAMSciStat = "{SIAM} Journal on Scientific and Statistical Computing" } @String{SIAMSciStat = "{SIAM} J. Sci. Statist. Comput." } @String{SoftPracExp = "Software Practice and Experience" } @String{SoftPracExp = "Software Prac. Experience" } % didn't find in AMS MR @String{StatScience = "Statistical Science" } @String{StatScience = "Statist. Sci." } @String{Techno = "Technometrics" } @String{Techno = "Technometrics" } @String{USSRCompMathPhys = "{USSR} Computational Mathematics and Mathematical Physics" } @String{USSRCompMathPhys = "{U.S.S.R.} Comput. Math. and Math. Phys." } @String{VLSICompSys = "Journal of {VLSI} and Computer Systems" } @String{VLSICompSys = "J. {VLSI} Comput. Syst." } @String{ZAngewMathMech = "Zeitschrift fur Angewandte Mathematik und Mechanik" } @String{ZAngewMathMech = "Z. Angew. Math. Mech." } @String{ZAngewMathPhys = "Zeitschrift fur Angewandte Mathematik und Physik" } @String{ZAngewMathPhys = "Z. Angew. Math. Phys." } % Publishers @String{Academic = "Academic Press" } @String{ACMPress = "{ACM} Press" } @String{AdamHilger = "Adam Hilger" } @String{AddisonWesley = "Addison-Wesley" } @String{AllynBacon = "Allyn and Bacon" } @String{AMS = "American Mathematical Society" } @String{Birkhauser = "Birkha{\"u}ser" } @String{CambridgePress = "Cambridge University Press" } @String{Chelsea = "Chelsea" } @String{ClaredonPress = "Claredon Press" } @String{DoverPub = "Dover Publications" } @String{Eyolles = "Eyolles" } @String{HoltRinehartWinston = "Holt, Rinehart and Winston" } @String{Interscience = "Interscience" } @String{JohnsHopkinsPress = "The Johns Hopkins University Press" } @String{JohnWileySons = "John Wiley and Sons" } @String{Macmillan = "Macmillan" } @String{MathWorks = "The Math Works Inc." } @String{McGrawHill = "McGraw-Hill" } @String{NatBurStd = "National Bureau of Standards" } @String{NorthHolland = "North-Holland" } @String{OxfordPress = "Oxford University Press" } %address Oxford or London? @String{PergamonPress = "Pergamon Press" } @String{PlenumPress = "Plenum Press" } @String{PrenticeHall = "Prentice-Hall" } @String{SIAMPub = "{SIAM} Publications" } @String{Springer = "Springer-Verlag" } @String{TexasPress = "University of Texas Press" } @String{VanNostrand = "Van Nostrand" } @String{WHFreeman = "W.H. Freeman and Co." } %Entries @Article{ Aas71, Author = "J.O. Aasen", Year = 1971, Title = "On the Reduction of a Symmetric Matrix to Tridiagonal Form", Journal = BIT, Volume = 11, Pages = "233--242" } @Article{ Abd71, Author = "N.N. Abdelmalek", Year = 1971, Title = "Roundoff Error Analysis for {G}ram-{S}chmidt Method and Solution of Linear Least Squares Problems", Journal = BIT, Volume = 11, Pages = "1345--1368" } @Article{ Ada85, Author = "L. Adams", Year = 1985, Title = "{m}-step Preconditioned Conjugate Gradient Methods", Journal = SIAMSciStat, Volume = 6, Pages = "452--463" } @Article{ AdaC84, Author = "L. Adams and T. Crockett", Year = 1984, Title = "Modelling Algorithm Execution Time on Processor Arrays", Journal = Computer, Volume = 17, Pages = "38--43" } @Article{ AlePP88, Author = "S.T. Alexander and C.T. Pan and R.J. Plemmons", Year = 1988, Title = "Analysis of a Recursive Least Squares Hyperbolic Rotation Algorithm for Signal Processing", Journal = LinAlgApp, Volume = 98, Pages = "3--40" } @Article{ All73, Author = "E.L. Allgower", Year = 1973, Title = "Exact Inverses of Certain Band Matrices", Journal = NumerMath, Volume = 21, Pages = "279--284" } @TechReport{ AmiM65, Author = "A.R. Amir-Moez", Year = 1965, Title = "Extremal Properties of Linear Transformations and Geometry of Unitary Spaces", Institution = "Texas Tech University", type = "Mathematics Series", number = 243, Address = "Lubbock, TX" } @Article{ AndK75, Author = "N. Anderson and I. Karasalo", Year = 1975, Title = "On Computing Bounds for the Least Singular Value of a Triangular Matrix", Journal = BIT, Volume = 15, Pages = "1--4" } @Article{ AndL73, Author = "P. Anderson and G. Loizou", Year = 1973, Title = "On the Quadratic Convergence of an Algorithm that Diagonalizes a Complex Symmetric Matrix", Journal = InstMathApp, Volume = 12, Pages = "261--271" } @Article{ AndL76, Author = "P. Anderson and G. Loizou", Year = 1976, Title = "A {J}acobi-Type Method for Complex Symmetric Matrices ({H}andbook)", Journal = NumerMath, Volume = 25, Pages = "347--363" } @Article{ AndOU87, Author = "T.W. Anderson and I. Olkin and L.G. Underhill", Year = 1987, Title = "Generation of Random Orthogonal Matrices", Journal = SIAMSciStat, Volume = 8, Pages = "625--629" } @Article{ AndS83, Author = "G. Andrews and F.B. Schneider", Year = 1983, Title = "Concepts and Notations for Concurrent Programming", Journal = CompServ, Volume = 15, Pages = "1--43" } @Article{ Arn51, Author = "W.E. Arnoldi", Year = 1951, Title = "The Principle of Minimized Iterations in the Solution of the Matrix Eigenvalue Problem", Journal = QuartApplMath, Volume = 9, Pages = "17--29" } @TechReport{ ArbG87, Author = "P. Arbenz and G.H. Golub", Year = 1987, Title = "On the Spectral Decomposition of {H}ermitian Matrices Subject to Indefinite Low Rank Perturbations with Applications", Number = "NA 87-07", Institution = "Computer Science, Stanford University", Address = "Stanford, CA" } @Article{ ArbGG88, Author = "P. Arbenz and W. Gander and G.H. Golub", Year = 1988, Title = "Restricted Rank Modification of the Symmetric Eigenvalue Problem: Theoretical Considerations", Journal = LinAlgApp, Volume = 104, Pages = "75--95" } @Article{ ArbG88, Author = "P. Arbenz and G.H. Golub", Year = 1988, Title = "On the Spectral Decomposition of {H}ermitian Matrices Subject to Indefinite Low Rank Perturbations with Applications", Journal = SIAMMatrix, Volume = 9, Pages = "40--58" } @TechReport{ AriDD88, Author = "M. Arioli and J.W. Demmel and I.S. Duff", Year = 1988, Title = "Solving Sparse Linear Systems with Sparse Backward Error", Number = "CSS 214", Institution = "Computer Science and Systems Division, AERE Harwell", Address = "Didcot, England" } @Article{ AriR85, Author = "M. Arioli and F. Romani", Year = 1985, Title = "Relations Between Condition Numbers and the Convergence of the {J}acobi Method for Real Positive Definite Matrices", Journal = NumerMath, Volume = 46, Pages = "31--42" } @Article{ AriL85, Author = "M. Arioli and A. Laratta", Year = 1985, Title = "Error Analysis of an Algorithm for Solving an Underdetermined System", Journal = NumerMath, Volume = 46, Pages = "255--268" } @TechReport{ ArmC76, Author = "E.S. Armstrong and A.K. Caglayan", Year = 1976, Title = "An Algorithm for the Weighting Matrices in the Sample-Data Optimal Linear Regulator Problem", Number = "TN D-8372", Institution = "NASA" } @Article{ ArnL84, Author = "W.F. Arnold and A.J. Laub", Year = 1984, Title = "Generalized Eigenproblem Algorithms and Software for Algebraic {R}iccati Equations", Journal = ProcIEEE, Volume = 72, Pages = "1746--1754" } @PhDThesis{ Ash87, Author = "S.F. Ashby", Year = 1987, Title = "Polynomial Preconditioning for Conjugate Gradient Methods", School = "Computer Science, University of Illinois", Address = "ILL", } @TechReport{ AshMS88, Author = "S. Ashby and T.A. Manteuffel and P.E. Saylor", Year = 1988, Title = "A Taxonomy for Conjugate Gradient Methods", Number = "UCRL-98508", Institution = "Lawrence Livermore National Laboratory", Address = "Livermore, CA" } @Article{ Asp59, Author = "E. Asplund", Year = 1959, Title = "Inverse of Matrices {$\{a_{ij}\}$} Which Satisfy {$a_{ij} = 0$, $j > i+p$}", Journal = MathScand, Volume = 7, Pages = "57--60" } @InCollection{ Axe77, Author = "O. Axelsson", Year = 1977, Title = "Solution of Linear Systems of Equations: Iterative Methods", BookTitle = "Sparse Matrix Techniques: {C}openhagen, 1976", Editor = "V.A. Barker", Publisher = Springer, Address = "Berlin" } @Article{ Axe80, Author = "O. Axelsson", Year = 1980, Title = "Conjugate Gradient Type Methods for Unsymmetric and Inconsistent Systems of Linear Equations", Journal = LinAlgApp, Volume = 29, Pages = "1--66" } @Article{ Axe85, Author = "O. Axelsson", Year = 1985, Title = "A Survey of Preconditioned Iterative Methods for Linear Systems of Equations", Journal = BIT, Volume = 25, Pages = "166--187" } @Article{ AxeP86, Author = "O. Axelsson and B. Polman", Year = 1986, Title = "On Approximate Factorization Methods for Block Matrices Suitable for Vector and Parallel Processors", Journal = LinAlgApp, Volume = 77, Pages = "3--26" } @Article{ Bai88a, Author = "Z. Bai", Year = 1988, Title = "Note on the Quadratic Convergence of {K}ogbetliantz's Algorithm for Computing the Singular Value Decomposition", Journal = LinAlgApp, Volume = 104, Pages = "131--140" } @Article{ Bai88b, Author = "D. Bailey", Year = 1988, Title = "Extra High Speed Matrix Multiplication on the {C}ray-2", Journal = SIAMSciStat, Volume = 9, Pages = "603--607" } @Article{ BarI75, Author = "I.Y. Bar-Itzhack", Year = 1975, Title = "Iterative Optimal Orthogonalization of the Strapdown Matrix", Journal = IEEETransAeroElec, Volume = 11, Pages = "30--37" } @Article{ Bar87, Author = "J. L. Barlow", Year = 1987, Title = "On the Smallest Positive Singular Value of an {$M$}-Matrix with Applications to Ergodic {M}arkov Chains", Journal = SIAMAlgMeth, Volume = 7, Pages = "414--424" } @Article{ BarNP88, Author = "J.L. Barlow and N.K. Nichols and R.J. Plemmons", Year = 1988, Title = "Iterative Methods for Equality Constrained Least Squares Problems", Journal = SIAMSciStat, Volume = 9, Pages = "892--906" } @Article{ BarS68, Author = "S. Barnett and C. Storey", Year = 1968, Title = "Some Applications of the {L}yapunov Matrix Equation", Journal = InstMathApp, Volume = 4, Pages = "33--42" } @Article{ BarP75a, Author = "I. Barrodale and C. Phillips", Year = 1975, Title = "Algorithm~495: Solution of an Overdetermined System of Linear Equations in the {C}hebychev Norm", Journal = ACMMathSoft, Volume = 1, Pages = "264--270" } @Article{ BarR73, Author = "I. Barrodale and F.D.K. Roberts", Year = 1973, Title = "An Improved Algorithm for Discrete {$L_{1}$} Linear Approximation", Journal = SIAMNumAnal, Volume = 10, Pages = "839--848" } @Article{ Bar71, Author = "R.H. Bartels", Year = 1971, Title = "A Stabilization of the Simplex Method", Journal = NumerMath, Volume = 16, Pages = "414--434" } @Article{ BarCC78, Author = "R.H. Bartels and A.R. Conn and C. Charalambous", Year = 1978, Title = "On {C}line's Direct Method for Solving Overdetermined Linear Systems in the {$L_{\infty}$} Sense", Journal = SIAMNumAnal, Volume = 15, Pages = "255--270" } @Article{ BarCS78, Author = "R.H. Bartels and A.R. Conn and J.W. Sinclair", Year = 1978, Title = "Minimization Techniques for Piecewise Differentiable Functions: The {$L_{1}$} Solution to an Overdetermined Linear System", Journal = SIAMNumAnal, Volume = 15, Pages = "224--241" } @Article{ BarS72, Author = "R.H. Bartels and G.W. Stewart", Year = 1972, Title = "Solution of the Equation {$AX + XB = C$}", Journal = CACM, Volume = 15, Pages = "820--826" } @Article{ BarMW67, Author = "W. Barth and R.S. Martin and J.H. Wilkinson", Year = 1967, Title = "Calculation of the Eigenvalues of a Symmetric Tridiagonal Matrix by the Method of Bisection", Journal = NumerMath, Volume = 9, Pages = "386-393", Note = "Also in \cite[pages 249--256]{WilR71}" } @Article{ BarG76, Author = "V. Barwell and J.A. George", Year = 1976, Title = "A Comparison of Algorithms for Solving Symmetric Indefinite Systems of Linear Equations", Journal = ACMMathSoft, Volume = 2, Pages = "242--251" } @Article{ BatW73, Author = "K.J. Bathe and E.L. Wilson", Year = 1973, Title = "Solution Methods for Eigenvalue Problems in Structural Mechanics", Journal = IntNumerEng, Volume = 6, Pages = "213--226" } @Article{ BauF60a, Author = "F.L. Bauer and C.T. Fike", Year = 1960, Title = "Norms and Exclusion Theorems", Journal = NumerMath, Volume = 2, Pages = "137--144" } @Article{ Bau63, Author = "F.L. Bauer", Year = 1963, Title = "Optimally Scaled Matrices", Journal = NumerMath, Volume = 5, Pages = "73--87" } @Article{ Bau65, Author = "F.L. Bauer", Year = 1965, Title = "Elimination with Weighted Row Combinations for Solving Linear Equations and Least Squares Problems", Journal = NumerMath, Volume = 7, Pages = "338--352", Note = "Also in \cite[pages 119--133]{WilR71}" } @Article{ BauF60b, Author = "F.L. Bauer and C.T. Fike", Year = 1960, Title = "Norms and Exclusion Theorems", Journal = NumerMath, Volume = 2, Pages = "137--144" } @Article{ BauR68, Author = "F.L. Bauer and C. Reinsch", Year = 1968, Title = "Rational {QR} Transformation with {N}ewton Shift for Symmetric Tridiagonal Matrices", Journal = NumerMath, Volume = 11, Pages = "264--272", Note = "Also in \cite[pages 257--265]{WilR71}" } @InCollection{ BauR70, Author = "F.L. Bauer and C. Reinsch", Year = 1970, Title = "Inversion of Positive Definite Matrices by the {G}auss-{J}ordan Methods", BookTitle = "Handbook for Automatic Computation Vol. 2: Linear Algebra", Editor = "J.H. Wilkinson and C. Reinsch", Publisher = Springer, Address = "New York", Pages = "45--49" } @Article{ BavS79, Author = "C. Bavely and G.W. Stewart", Year = 1979, Title = "An Algorithm for Computing Reducing Subspaces by Block Diagonalization", Journal = SIAMNumAnal, Volume = 16, Pages = "359--367" } @Book{ Bel70, Author = "R. Bellman", Year = 1970, Title = "Introduction to Matrix Analysis", Edition = "second", Publisher = McGrawHill, Address = "New York, NY" } @Article{ Bel73, Author = "E. Beltrami", Year = 1873, Title = "Sulle Funzioni Bilineari", Journal = GiornaleMath, Volume = 11, Pages = "98--106" } @Article{ BenS70, Author = "C.F. Bender and I. Shavitt", Year = 1970, Title = "An Iterative Procedure for the Calculation of the Lowest Real Eigenvalue and Eigenvector of a Non-Symmetric Matrix", Journal = CompPhys, Volume = 6, Pages = "146--149" } @Article{ BerBI71, Author = "A. Berman and A. Ben-Israel", Year = 1971, Title = "A Note on Pencils of {H}ermitian of Symmetric Matrices", Journal = SIAMAppMath, Volume = 21, Pages = "51--54" } @Article{ BerV68, Author = "M.J.M. Bernal and J.H. Verner", Year = 1968, Title = "On Generalizations of the Theory of Consistent Orderings for Successive Over-Relaxation Methods", Journal = NumerMath, Volume = 12, Pages = "215--222" } @InProceedings{ BerS86, Author = "M. Berry and A. Sameh", Year = 1986, Title = "Multiprocessor {J}acobi Algorithms for Dense Symmetric Eigenvalue and Singular Value Decompositions", BookTitle = "Proceedings International Conference on Parallel Processing", Pages = "433--440" } @InCollection{ Bis87, Author = "C.H. Bischof", Year = 1987, Title = "The Two-Sided Block {J}acobi Method on Hypercube Architectures", Booktitle = "Hypercube Multiprocessors", Editor = "M.T. Heath", Publisher = SIAMPub, Address = "Philadelphia" } @TechReport{ Bis88a, Author = "C.H. Bischof", Year = 1988, Title = "Computing the Singular Value Decomposition on a Distributed System of Vector Processors", Number = "87 869", Institution = "Computer Science, Cornell University", Address = "Ithaca, NY" } @PhDThesis{ Bis88b, Author = "C.H. Bischof", Year = 1988, Title = "{QR} Factorization Algorithms for Coarse Grain Distributed Systems", School = "Computer Science, Cornell University", Address = "Ithaca, NY" } @InCollection{ BisL86, Author = "C.H. Bischof and Van Loan, C.", Year = 1986, Title = "Computing the {SVD} on a Ring of Array Processors", BookTitle = "Large Scale Eigenvalue Problems", Editor = "J. Cullum and R. Willoughby", Publisher = NorthHolland, Pages = "51--66" } @Article{ BisL87, Author = "C.H. Bischof and Van Loan, C.", Year = 1987, Title = "The {WY} Representation for Products of {H}ouseholder Matrices", Journal = SIAMSciStat, Volume = 8, Pages = "s2--s13" } @Article{ Bjo67a, Author = "{\AA}. Bj{\"o}rck", Year = 1967, Title = "Iterative Refinement of Linear Least Squares Solution~{I}", Journal = BIT, Volume = 7, Pages = "257--278" } @Article{ Bjo67b, Author = "{\AA}. Bj{\"o}rck", Year = 1967, Title = "Solving Linear Least Squares Problems by {G}ram-{S}chmidt Orthogonalization", Journal = BIT, Volume = 7, Pages = "1--21" } @Article{ Bjo68, Author = "{\AA}. Bj{\"o}rck", Year = 1968, Title = "Iterative Refinement of Linear Least Squares Solution {II}", Journal = BIT, Volume = 8, Pages = "8--30" } @Article{ Bjo84, Author = "{\AA}. Bj{\"o}rck", Year = 1984, Title = "A General Updating Algorithm for Constrained Linear Least Squares Problems", Journal = SIAMSciStat, Volume = 5, Pages = "394--402" } @Article{ Bjo87, Author = "{\AA}. Bj{\"o}rck", Year = 1987, Title = "Stability Analysis of the Method of Seminormal Equations", Journal = LinAlgApp, Volume = "88/89", Pages = "31--48" } @Book{ Bjo88, Author = "{\AA}. Bj{\"o}rck", Year = 1988, Title = "Solution of Equations in {$R^N$}", Series = "Least Squares Methods: Handbook of Numerical Analysis", Volume = 1, Publisher = NorthHolland } @Article{ BjoB71, Author = "{\AA}. Bj{\"o}rck and C. Bowie", Year = 1971, Title = "An Iterative Algorithm for Computing the Best Estimate of an Orthogonal Matrix", Journal = SIAMNumAnal, Volume = 8, Pages = "358--364" } @Article{ BjoE73, Author = "{\AA}. Bj{\"o}rck and T. Elfving", Year = 1973, Title = "Algorithms for Confluent {V}andermonde Systems", Journal = NumerMath, Volume = 21, Pages = "130--137" } @Article{ BjoG67, Author = "{\AA}. Bj{\"o}rck and G.H. Golub", Year = 1967, Title = "Iterative Refinement of Linear Least Squares Solutions by {H}ouseholder Transformation", Journal = BIT, Volume = 7, Pages = "322--337" } @Article{ BjoG73, Author = "{\AA}. Bj{\"o}rck and G.H. Golub", Year = 1973, Title = "Numerical Methods for Computing Angles Between Linear Subspaces", Journal = MathComp, Volume = 27, Pages = "579--594" } @Article{ BjoP70, Author = "{\AA}. Bj{\"o}rck and V. Pereyra", Year = 1970, Title = "Solution of {V}andermonde Systems of Equations", Journal = MathComp, Volume = 24, Pages = "893--903" } @Book{ BjoPS81, Author = "{\AA}. Bj{\"o}rck and R.J. Plemmons and H. Schneider", Year = 1981, Title = "Large-Scale Matrix Problems", Publisher = NorthHolland, Address = "New York, NY" } @Article{ BjoH83, Author = "{\AA}. Bj{\"o}rck and S. Hammarling", Year = 1983, Title = "A {S}chur Method for the Square Root of a Matrix", Journal = LinAlgApp, Volume = "52/53", Pages = "127--140" } @Article{ Blu78, Author = "J.M. Blue", Year = 1978, Title = "A Portable {F}ortran Program to Find the {E}uclidean Norm of a Vector", Journal = ACMMathSoft, Volume = 4, Pages = "15--23" } @Article{ Boh75, Author = "Z. Bohte", Year = 1975, Title = "Bounds for Rounding Errors in the {G}aussian Elimination for Band Systems", Journal = InstMathApp, Volume = 16, Pages = "133--142" } @Article{ BojBdH86, Author = "A.W. Bojanczyk and R.P. Brent and de Hoog, F.R.", Year = 1986, Title = "{QR} Factorization of {T}oeplitz Matrices", Journal = NumerMath, Volume = 49, Pages = "81--94" } @Article{ BojBDdH87, Author = "A.W. Bojanczyk and R.P. Brent and Van Dooren, P. and de Hoog, F.R.", Year = 1987, Title = "A Note on Downdating the {C}holesky Factorization", Journal = SIAMSciStat, Volume = 8, Pages = "210--221" } @InProceedings{ BolG78, Author = "D.L. Boley and G.H. Golub", Year = 1978, Title = "The Matrix Inverse Eigenvalue Problem for Periodic {J}acobi Matrices", BookTitle = "Proceedings Fourth Symposium on Basic Problems of Numerical Mathematics, {P}rague", Pages = "63--76" } @Article{ BolG84a, Author = "D. Boley and G.H. Golub", Year = 1984, Title = "A Modified Method for Restructuring Periodic {J}acobi Matrices", Journal = MathComp, Volume = 42, Pages = "143--150" } @Article{ BooE68, Author = "J. Boothroyd and P.J. Eberlein", Year = 1968, Title = "Solution to the Eigenproblem by a Norm-Reducing {J}acobi-Type Method (Handbook)", Journal = NumerMath, Volume = 11, Pages = "1--12", Note = "Also in \cite[pages 327--338]{WilR71}" } @Article{ BowMPW66, Author = "H.J. Bowdler and R.S. Martin and G. Peters and J.H. Wilkinson", Year = 1966, Title = "Solution of Real and Complex Systems of Linear Equations", Journal = NumerMath, Volume = 8, Pages = "217-234", Note = "Also in \cite[pages 93--110]{WilR71}" } @Article{ BowMRW68, Author = "H. Bowdler and R.S. Martin and C. Reinsch and J.H. Wilkinson", Year = 1968, Title = "The {QR} and {QL} Algorithms for Symmetric Matrices", Journal = NumerMath, Volume = 11, Pages = "293-306", Note = "Also in \cite[pages 227--240]{WilR71}" } @Book{ BoyBD+87, Author = "J. Boyle and R. Butler and T. Disz and B. Glickfield and E. Lusk and R. Overbeek and J. Patterson and R. Stevens", Year = 1987, Title = "Portable Programs for Parallel Processors", Publisher = HoltRinehartWinston } @Article{ BraPS86a, Author = "J.H. Bramble and J.E. Pasciak and A.H. Schatz", Year = 1986, Title = "The construction of Preconditioners for Elliptic Problems by Substructuring {I}", Journal = MathComp, Volume = 47, Pages = "103--134" } @Article{ BraPS86b, Author = "J.H. Bramble and J.E. Pasciak and A.H. Schatz", Year = 1986, Title = "The construction of Preconditioners for Elliptic Problems by Substructuring {II}", Journal = MathComp, Volume = 49, Pages = "1--17" } @Article{ Bre70, Author = "R.P. Brent", Year = 1970, Title = "Error Analysis of Algorithms for Matrix Multiplication and Triangular Decomposition Using {W}inograd's Identity", Journal = NumerMath, Volume = 16, Pages = "145--156" } @Article{ BreL85, Author = "R.P. Brent and F.T. Luk", Year = 1985, Title = "The Solution of Singular Value and Symmetric Eigenvalue Problems on Multiprocessor Arrays", Journal = SIAMSciStat, Volume = 6, Pages = "69--84" } @Article{ BreLL85, Author = "R.P. Brent and F.T. Luk and Van Loan, C.", Year = 1985, Title = "Computation of the Singular Value Decomposition Using Mesh Connected Processors", Journal = VLSICompSys, Volume = 1, Pages = "242--270" } @Article{ BroP75b, Author = "K.W. Brodlie and M.J. D. Powell", Year = 1975, Title = "On the Convergence of Cyclic {J}acobi Methods", Journal = InstMathApp, Volume = 15, Pages = "279--287" } @Article{ Bro73, Author = "C.G. Broyden", Year = 1973, Title = "Some Condition Number Bounds for the {G}aussian Elimination Process", Journal = InstMathApp, Volume = 12, Pages = "273--286" } @Article{ Buc74, Author = "A. Buckley", Year = 1974, Title = "A Note on Matrices {$A = 1 + H$}, {$H$} Skew-Symmetric", Journal = ZAngewMathMech, Volume = 54, Pages = "125--126" } @Article{ Buc77, Author = "A. Buckley", Year = 1977, Title = "On the Solution of Certain Skew-Symmetric Linear Systems", Journal = SIAMNumAnal, Volume = 14, Pages = "566--570" } @Article{ Bun71a, Author = "J.R. Bunch", Year = 1971, Title = "Analysis of the Diagonal Pivoting Method", Journal = SIAMNumAnal, Volume = 8, Pages = "656--680" } @Article{ Bun71b, Author = "J.R. Bunch", Year = 1971, Title = "Equilibration of Symmetric Matrices in the Max-Norm", Journal = JACM, Volume = 18, Pages = "566--572" } @Article{ Bun74, Author = "J.R. Bunch", Year = 1974, Title = "Partial Pivoting Strategies for Symmetric Matrices", Journal = SIAMNumAnal, Volume = 11, Pages = "521--528" } @InCollection{ Bun76, Author = "J.R. Bunch", Year = 1976, Title = "Block Methods for Solving Sparse Linear Systems", BookTitle = "Sparse Matrix Computations", Editor = "J.R. Bunch and D.J. Rose", Publisher = Academic, Address = "New York, NY" } @Article{ BunK77, Author = "J.R. Bunch and K. Kaufman", Year = 1977, Title = "Some Stable Methods for Calculating Inertia and Solving Symmetric Linear Systems", Journal = MathComp, Volume = 31, Pages = "162--179" } @Article{ BunKP76, Author = "J.R. Bunch and K. Kaufman and B.N. Parlett", Year = 1976, Title = "Decomposition of a Symmetric Matrix", Journal = NumerMath, Volume = 27, Pages = "95--109" } @Article{ BunNS78, Author = "J.R. Bunch and C.P. Nielsen and D.C. Sorensen", Year = 1978, Title = "Rank-One Modification of the Symmetric Eigenproblem", Journal = NumerMath, Volume = 31, Pages = "31--48" } @Article{ BunP71, Author = "J.R. Bunch and B.N. Parlett", Year = 1971, Title = "Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations", Journal = SIAMNumAnal, Volume = 8, Pages = "639--655" } @Book{ BunR76, Editor = "J.R. Bunch and D.J. Rose", Year = 1976, Title = "Sparse Matrix Computations", Publisher = Academic, Address = "New York", } @Article{ Bun82, Author = "J.R. Bunch", Year = 1982, Title = "A Note on the Stable Decomposition of Skew Symmetric Matrices", Journal = MathComp, Volume = 158, Pages = "475--480" } @Article{ Bun85, Author = "J.R. Bunch", Year = 1985, Title = "Stability of Methods for Solving {T}oeplitz Systems of Equations", Journal = SIAMSciStat, Volume = 6, Pages = "349--364" } @Article{ Bun87, Author = "J.R. Bunch", Year = 1987, Title = "The Weak and Strong Stability of Algorithms in Numerical Linear Algebra", Journal = LinAlgApp, Volume = "88/89", Pages = "49--66" } @TechReport{ Bun69, Author = "O. Buneman", Year = 1969, Title = "A Compact Non-Iterative {P}oisson Solver", Institution = "Institute for Plasma Research", Address = "Stanford University, Stanford, CA", Number = 294 } @Article{ BunG84b, Author = "A. Bunse-Gerstner", Year = 1984, Title = "An Algorithm for the Symmetric Generalized Eigenvalue Problem", Journal = LinAlgApp, Volume = 58, Pages = "43--68" } @Article{ BunGG88, Author = "A. Bunse-Gerstner and W.B. Gragg", Year = 1988, Title = "Singular Value Decompositions of Complex Symmetric Matrices", Journal = CompApplMath, Volume = 21, Pages = "41--54" } @Article{ Bus68, Author = "P.A. Businger", Year = 1968, Title = "Matrices Which Can be Optimally Scaled", Journal = NumerMath, Volume = 12, Pages = "346--348" } @Article{ Bus69, Author = "P.A. Businger", Year = 1969, Title = "Reducing a Matrix to {H}essenberg Form", Journal = MathComp, Volume = 23, Pages = "819--821" } @Article{ Bus71a, Author = "P.A. Businger", Year = 1971, Title = "Monitoring the Numerical Stability of {G}aussian Elimination", Journal = NumerMath, Volume = 16, Pages = "360--361" } @Article{ Bus71b, Author = "P.A. Businger", Year = 1971, Title = "Numerically Stable Deflation of {H}essenberg and Symmetric Tridiagonal Matrices", Journal = BIT, Volume = 11, Pages = "262--270" } @Article{ BusG65, Author = "P.A. Businger and G.H. Golub", Year = 1965, Title = "Linear Least Squares Solutions by {H}ouseholder Transformations", Journal = NumerMath, Volume = 7, Pages = "269--276", Note = "Also in \cite[pages 111--118]{WilR71}" } @Article{ BusG69, Author = "P.A. Businger and G.H. Golub", Year = 1969, Title = "Algorithm~358: Singular Value Decomposition of a Complex Matrix", Journal = CACM, Volume = 12, Pages = "564--565" } @Article{ BuzD74, Author = "B.L. Buzbee and F.W. Dorr", Year = 1974, Title = "The Direct Solution of the Biharmonic Equation on Rectangular Regions and the {P}oisson Equation on Irregular Regions", Journal = SIAMNumAnal, Volume = 11, Pages = "753--763" } @Article{ BuzDGG71, Author = "B.L. Buzbee and F.W. Dorr and J.A. George and G.H. Golub", Year = 1971, Title = "The Direct Solution of the Discrete {P}oisson Equation on Irregular Regions", Journal = SIAMNumAnal, Volume = 8, Pages = "722--736" } @Article{ BuzGN70, Author = "B.L. Buzbee and G.H. Golub and C.W. Nielson", Year = 1970, Title = "On Direct Methods for Solving {P}oisson's Equations", Journal = SIAMNumAnal, Volume = 7, Pages = "627--656" } @Article{ Buz86, Author = "B.L. Buzbee", Year = 1986, Title = "A Strategy for Vectorization", Journal = ParComputing, Volume = 3, Pages = "187--192" } @PhDThesis{ Bye83, Author = "R. Byers", Year = 1983, Title = "{H}amiltonian and Symplectic Algorithms for the Algebraic {R}iccati Equation", School = "Center for Applied Mathematics, Cornell University", Address = "Ithaca, NY", } @Article{ Bye84, Author = "R. Byers", Year = 1984, Title = "A {L}inpack-Style Condition Estimator for the Equation {$AX - XB^{T} = C$}", Journal = IEEETransAC, Volume = "AC-29", Pages = "926--928" } @Article{ Bye86, Author = "R. Byers", Year = 1986, Title = "A {H}amiltonian {QR} Algorithm", Journal = SIAMSciStat, Volume = 7, Pages = "212--229" } @Article{ ByeN87, Author = "R. Byers and S.G. Nash", Year = 1987, Title = "On the Singular Vectors of the {L}yapunov Operator", Journal = SIAMAlgMeth, Volume = 8, Pages = "59--66" } @InProceedings{ Cal86, Author = "D.A. Calihan", Year = 1986, Title = "Block-Oriented, Local-Memory-Based Linear Equation Solution on the {C}ray-2: Uniprocessor Algorithms", BookTitle = "Proceedings of the 1986 Conference on Parallel Processing", Pages = "375--378" } @Article{ ChaP77, Author = "S.P. Chan and B.N. Parlett", Year = 1977, Title = "Algorithm~517: A Program for Computing the Condition Numbers of Matrix Eigenvalues without Computing Eigenvectors", Journal = ACMMathSoft, Volume = 3, Pages = "186--203" } @Article{ Cha82b, Author = "T.F. Chan", Year = 1982, Title = "An Improved Algorithm for Computing the Singular Value Decomposition", Journal = ACMMathSoft, Volume = 8, Pages = "72--83" } @Article{ Cha82a, Author = "T.F. Chan", Year = 1982, Title = "Algorithm~581: An Improved Algorithm for Computing the Singular Value Decomposition", Journal = ACMMathSoft, Volume = 8, Pages = "84--88" } @Article{ Cha84, Author = "T.F. Chan", Year = 1984, Title = "Deflated Decomposition Solutions of Nearly Singular Systems", Journal = SIAMNumAnal, Volume = 21, Pages = "738--754" } @Article{ Cha85, Author = "T.F. Chan", Year = 1985, Title = "On the Existence and Computation of {LU} Factorizations with small pivots", Journal = MathComp, Volume = 42, Pages = "535--548" } @Article{ Cha87, Author = "T.F. Chan", Year = 1987, Title = "Rank-Revealing {QR} Factorizations", Journal = LinAlgApp, Volume = "88/89", Pages = "67--82" } @Article{ Cha88, Author = "T.F. Chan", Year = 1988, Title = "An Optimal Circulant Preconditioner for {T}oeplitz Systems", Journal = SIAMSciStat, Volume = 9, Pages = "766--771" } @Article{ ChaJZ83, Author = "T.F. Chan and K.R. Jackson and B. Zhu", Year = 1983, Title = "Alternating Direction Incomplete Factorizations", Journal = SIAMNumAnal, Volume = 20, Pages = "239--257" } @Article{ ChaM88, Author = "H.Y. Chang and M.Salama", Year = 1988, Title = "A Parallel {H}ouseholder Tridiagonalization Stratagem Using Scattered Square Decomposition", Journal = ParComputing, Volume = 6, Pages = "297--312" } @Article{ ChaVD88, Author = "J.P. Charlier and M. Vanbegin and Van Dooren, P.", Year = 1988, Title = "On Efficient Implementation of {K}ogbetliantz's Algorithm for Computing the Singular Value Decomposition", Journal = NumerMath, Volume = 52, Pages = "279--300" } @Article{ ChaD87, Author = "J.P. Charlier and Van Dooren, P.", Year = 1987, Title = "On {K}ogbetliantz's {SVD} Algorithm in the Presence of Clusters", Journal = LinAlgApp, Volume = 95, Pages = "135--160" } @Article{ CheDH84, Author = "S. Chen and J. Dongarra and C. Hsuing", Title = "Multiprocessing Linear Algebra Algorithms on the {Cray X-MP-2}: Experiences with Small Granularity", Year = 1984, Journal = ParDistComp, Volume = 1, Pages = "22--31" } @Article{ CheKS78, Author = "S. Chen and D. Kuck and A. Sameh", Year = 1978, Title = "Practical Parallel Band Triangular Systems Solvers", Journal = ACMMathSoft, Volume = 4, Pages = "270--277" } @Article{ CheS87, Author = "K.H. Cheng and S. Sahni", Year = 1987, Title = "{VLSI} Systems for Band Matrix Multiplication", Journal = ParComputing, Volume = 4, Pages = "239--258" } @Article{ ChiMdP84, Author = " R.C. Chin and T.A. Manteuffel and de Pillis, J.", Year = 1984, Title = "{ADI} as a Preconditioning for Solving the Convection-Diffusion Equation", Journal = SIAMSciStat, Volume = 5, Pages = "281--299" } @Article{ Cli73, Author = "A.K. Cline", Year = 1973, Title = "An Elimination Method for the Solution of Linear Least Squares Problems", Journal = SIAMNumAnal, Volume = 10, Pages = "283--289" } @Article{ Cli76a, Author = "A.K. Cline", Year = 1976, Title = "A Descent Method for the Uniform Solution to Overdetermined Systems of Equations", Journal = SIAMNumAnal, Volume = 13, Pages = "293--309" } @TechReport{ Cli76b, Author = "A.K. Cline", Year = 1976, Title = "Several observations on the Use of Conjugate Gradient Methods", Type = "report", Number = "76-22", Institution = "ICASE, NASA Langley Research Center", Address = "Hampton, VA" } @Article{ CliR83, Author = "A.K. Cline and R.K. Rew", Year = 1983, Title = "A Set of Counter examples to Three Condition Number Estimators", Journal = SIAMSciStat, Volume = 4, Pages = "602--611" } @InCollection{ CliCL82, Author = "A.K. Cline and A.R. Conn and Van Loan, C.", Year = 1982, Title = "Generalizing the {LINPACK} Condition Estimator", Booktitle = "Numerical Analysis", Editor = "J.P. Hennart", Series = "Lecture Notes in Mathematics 909", Publisher = Springer, Address = "New York, NY" } @InCollection{ CliGP76, Author = "A.K. Cline and G.H. Golub and G.W. Platzman", Year = 1976, Title = "Calculation of Normal Modes of Oceans Using a {L}anczos Method", BookTitle = "Sparse Matrix Computations", Editor = "J.R. Bunch and D.J. Rose", Publisher = Academic, Address = "New York", Pages = "409--426" } @Article{ CliMSW79, Author = "A.K. Cline and C.B. Moler and G.W. Stewart and J.H. Wilkinson", Year = 1979, Title = "An Estimate for the Condition Number of a Matrix", Journal = SIAMNumAnal, Volume = 16, Pages = "368--375" } @Article{ CliP76, Author = "R.E. Cline and R.J. Plemmons", Year = 1976, Title = "{$L_{1}$}-Solutions to Underdetermined Linear Systems", Journal = SIAMReview, Volume = 18, Pages = "92--106" } @Article{ CliJ70, Author = "M. Clint and A. Jennings", Year = 1970, Title = "The Evaluation of Eigenvalues and Eigenvectors of Real Symmetric Matrix by Simultaneous Iteration", Journal = CompJour, Volume = 13, Pages = "76--80" } @Article{ CliJ71, Author = "M. Clint and A. Jennings", Year = 1971, Title = "A Simultaneous Iteration Method for the Unsymmetric Eigenvalue Problem", Journal = InstMathApp, Volume = 8, Pages = "111--121" } @Article{ Coc68, Author = "W.G. Cochrane", Year = 1968, Title = "Errors of Measurement in Statistics", Journal = Techno, Volume = 10, Pages = "637--666" } @Article{ Coh74, Author = "A.M. Cohen", Year = 1974, Title = "A Note on Pivot Size in {G}aussian Elimination", Journal = LinAlgApp, Volume = 8, Pages = "361--368" } @Book{ ColL88, Author = "T. Coleman and Van Loan, C.", Year = 1988, Title = "Handbook for Matrix Computations", Publisher = SIAMPub, Address = "Philadelphia, PA" } @Article{ ConG73, Author = "P. Concus and G.H. Golub", Year = 1973, Title = "Use of Fast Direct Methods for the Efficient Numerical Solution of Nonseparable Elliptic Equations", Journal = SIAMNumAnal, Volume = 10, Pages = "1103--1120" } @Article{ ConGM85, Author = "P. Concus and G.H. Golub and G. Meurant", Year = 1985, Title = "Block Preconditioning for the Conjugate Gradient Method", Journal = SIAMSciStat, Volume = 6, Pages = "220--252" } @InCollection{ ConGO76, Author = "P. Concus and G.H. Golub and D.P. O'Leary", Year = 1976, Title = "A Generalized Conjugate Gradient Method for the Numerical Solution of Elliptic Partial Differential Equations", Booktitle = "Sparse Matrix Computations", Editor = "J.R. Bunch and D.J. Rose", Publisher = Academic, Address = "New York, NY" } @Book{ CdB80, Author = "S.D. Conte and de Boor, C.", Year = 1980, Title = "Elementary Numerical Analysis: An Algorithmic Approach", Publisher = McGrawHill, Address = "New York, NY", Edition = "third" } @Article{ CopR79, Author = "J.E. Cope and B.W. Rust", Year = 1979, Title = "Bounds on Solutions of Systems with Inaccurate Data", Journal = SIAMNumAnal, Volume = 16, Pages = "950--963" } @Article{ CosMR86, Author = "M. Costnard and J.M. Muller and Y. Robert", Year = 1986, Title = "Parallel {QR} Decomposition of a Rectangular Matrix", Journal = NumerMath, Volume = 48, Pages = "239--250" } @Article{ CosMR88, Author = "M. Costnard and M. Marrakchi and Y. Robert", Year = 1988, Title = "Parallel {G}aussian Elimination on an {MIMD} Computer", Journal = ParComputing, Volume = 6, Pages = "275--296" } @Article{ Cot74, Author = "R.W. Cottle", Year = 1974, Title = "Manifestations of the {S}chur Complement", Journal = LinAlgApp, Volume = 8, Pages = "189--211" } @Article{ Cox81, Author = "M.G. Cox", Year = 1981, Title = "The Least Squares Solution of Overdetermined Linear Equations having Band or Augmented Band Structure", Journal = IMANumerAna, Volume = 1, Pages = "3--22" } @Article{ Cra73, Author = "C.R. Crawford", Year = 1973, Title = "Reduction of a Band Symmetric Generalized Eigenvalue Problem", Journal = CACM, Volume = 16, Pages = "41--44" } @Article{ Cra76, Author = "C.R. Crawford", Year = 1976, Title = "A Stable Generalized Eigenvalue Problem", Journal = SIAMNumAnal, Volume = 13, Pages = "854--860" } @Article{ Cra86, Author = "C.R. Crawford", Year = 1986, Title = "Algorithm~646 {PDFIND}: A Routine to Find a Positive Definite Linear Combination of Two Real Symmetric Matrices", Journal = ACMMathSoft, Volume = 12, Pages = "278--282" } @Article{ CraM83, Author = "C.R. Crawford and Y.S. Moon", Year = 1983, Title = "Finding a Positive Definite Linear Combination of Two {H}ermitian Matrices", Journal = LinAlgApp, Volume = 51, Pages = "37--48" } @Article{ Cry68, Author = "C.W. Cryer", Year = 1968, Title = "Pivot Size in {G}aussian Elimination", Journal = NumerMath, Volume = 12, Pages = "335--345" } @Article{ Cul78, Author = "J. Cullum", Year = 1978, Title = "The Simultaneous Computation of a Few of the Algebraically Largest and Smallest Eigenvalues of a Large Sparse Symmetric Matrix", Journal = BIT, Volume = 18, Pages = "265--275" } @InProceedings{ CulD74, Author = "J. Cullum and W.E. Donath", Year = 1974, Title = "A Block {L}anczos Algorithm for Computing the {Q} Algebraically Largest Eigenvalues and a Corresponding Eigenspace of Large, Sparse Real Symmetric Matrices", BookTitle = "Proceedings of the 1974 IEEE Conference on Decision and Control, {Phoenix, AZ}", Pages = "505--509" } @TechReport{ CulW77, Author = "J. Cullum and R.A. Willoughby", Year = 1977, Title = "The Equivalence of the {L}anczos and the Conjugate Gradient Algorithms", Number = "RC-6903", Institution = "IBM", Address = "Yorktown Heights, NY" } @InProceedings{ CulW79, Author = "J. Cullum and R.A. Willoughby", Year = 1979, Title = "{L}anczos and the Computation in Specified Intervals of the Spectrum of Large, Sparse Real Symmetric Matrices", Booktitle = "Sparse Matrix Proceedings 1978", Editor = "I.S. Duff and G.W. Stewart", Publisher = SIAMPub, Address = "Philadelphia, PA" } @Article{ CulW80, Author = "J. Cullum and R.A. Willoughby", Year = 1980, Title = "The {L}anczos Phenomena: An Interpretation Based on Conjugate Gradient Optimization", Journal = LinAlgApp, Volume = 29, Pages = "63--90" } @Book{ CulW85b, Author = "J. Cullum and R.A. Willoughby", Year = 1985, Title = "{L}anczos Algorithms for Large Symmetric Eigenvalue Computations, Volume 1: Theory", Publisher = Birkhauser, Address = "Boston" } @Book{ CulW85a, Author = "J. Cullum and R.A. Willoughby", Year = 1985, Title = "{L}anczos Algorithms for Large Symmetric Eigenvalue Computations, Volume 2: Programs", Publisher = Birkhauser, Address = "Boston" } @Book{ CulW86, Editor = "J. Cullum and R.A. Willoughby", Year = 1986, Title = "Large Scale Eigenvalue Problems", Publisher = NorthHolland, } @Article{ CulWL83, Author = "J. Cullum and R.A. Willoughby and M. Lake", Year = 1983, Title = "A {L}anczos Algorithm for Computing Singular Values and Vectors of Large Matrices", Journal = SIAMSciStat, Volume = 4, Pages = "197--215" } @Article{ Cup81, Author = "J.J.M. Cuppen", Year = 1981, Title = "A Divide and Conquer Method for the Symmetric Eigenproblem", Journal = NumerMath, Volume = 36, Pages = "177--195" } @Article{ Cup83, Author = "J.J.M. Cuppen", Year = 1983, Title = "The Singular Value Decomposition in Product Form", Journal = SIAMSciStat, Volume = 4, Pages = "216--222" } @Article{ Cup84, Author = "J.J.M. Cuppen", Year = 1984, Title = "On Updating Triangular Products of {H}ouseholder Matrices", Journal = NumerMath, Volume = 45, Pages = "403--410" } @InCollection{ Cut72, Author = "E. Cuthill", Year = 1972, Title = "Several Strategies for Reducing the Bandwidth of Matrices", BookTitle = "Sparse Matrices and Their Applications", Editor = "D.J. Rose and R.A. Willoughby", Publisher = PlenumPress, Address = "New York" } @PhDThesis{ Cyb78, Author = "G. Cybenko", Year = 1978, Title = "Error Analysis of Some Signal Processing Algorithms", School = "Princeton University", Address = "Princeton, NJ" } @Article{ Cyb80, Author = "G. Cybenko", Year = 1980, Title = "The Numerical Stability of the {L}evinson-{D}urbin Algorithm for {T}oeplitz Systems of Equations", Journal = SIAMSciStat, Volume = 1, Pages = "303--310" } @Article{ Cyb84, Author = "G. Cybenko", Year = 1984, Title = "The Numerical Stability of the Lattice Algorithm for Least Squares Linear Prediction Problems", Journal = BIT, Volume = 24, Pages = "441--455" } @Article{ CybL86, Author = "G. Cybenko and Van Loan, C.", Year = 1986, Title = "Computing the Minimum Eigenvalue of a Symmetric Positive Definite {T}oeplitz Matrix", Journal = SIAMSciStat, Volume = 7, Pages = "123--131" } @Article{ DanGKS76, Author = "J. Daniel and W.B. Gragg and L. Kaufman and G.W. Stewart", Year = 1976, Title = "Reorthogonalization and Stable Algorithms for Updating the {G}ram-{S}chmidt {QR} Factorization", Journal = MathComp, Volume = 30, Pages = "772--795" } @Article{ Dav73, Author = "C. Davis", Year = 1973, Title = "Explicit Functional Calculus", Journal = LinAlgApp, Volume = 6, Pages = "193--199" } @Book{ DatJK+88, Author = "B.N. Datta and C.R. Johnson and M.A. Kaashoek and R. Plemmons and E.D. Sontag", Year = 1988, Title = "Linear Algebra in Signals, Systems, and Control", Publisher = SIAMPub, Address = "Philadelphia" } @Article{ Dav86, Author = "G.J. Davis", Year = 1986, Title = "Column {LU} Pivoting on a Hypercube Multiprocessor", Journal = SIAMAlgMeth, Volume = 7, Pages = "538--550" } @Article{ DavK70, Author = "C. Davis and W.M. Kahan", Year = 1970, Title = "The Rotation of Eigenvectors by a Perturbation {III}", Journal = SIAMNumAnal, Volume = 7, Pages = "1--46" } @Article{ DaxK77, Author = "A. Dax and S. Kaniel", Year = 1977, Title = "Pivoting Techniques for Symmetric {G}aussian Elimination", Journal = NumerMath, Volume = 28, Pages = "221--242" } @Article{ DayP88, Author = "J. Day and B. Peterson", Year = 1988, Title = "Growth in {G}aussian Elimination", Journal = AmerMathMonthly, Volume = 95, Pages = "489--513" } @TechReport{ DayD88, Author = "M.J. Dayde and I.S. Duff", Year = 1988, Title = "Use of Level-3 {BLAS} in {LU} Factorization on the {C}ray-2, the {ETA-10P}, and the {IBM 3090-200/VF}", Number = "CSS-229", Institution = "Computer Science and Systems Division, Harwell Laboratory", Address = "Oxon OX11 ORA, England" } @Article{ dBooP77, Author = "de Boor, C. and A. Pinkus", Year = 1977, Title = "A Backward Error Analysis for Totally Positive Linear Systems", Journal = NumerMath, Volume = 27, Pages = "485--490" } @Article{ DeiNT83, Author = "P. Deift and T. Nande and C. Tome", Year = 1983, Title = "Ordinary Differential Equations and the Symmetric Eigenvalue Problem", Journal = SIAMNumAnal, Volume = 20, Pages = "1--22" } @Article{ DekT71, Author = "T.J. Dekker and J.F. Traub", Year = 1971, Title = "The Shifted {QR} Algorithm for {H}ermitian Matrices", Journal = LinAlgApp, Volume = 4, Pages = "137--154" } @Article{ DelI86, Author = "J.M. Delosme and I.C.F. Ipsen", Year = 1986, Title = "Parallel Solution of Symmetric Positive Definite Systems with Hyperbolic Rotations", Journal = LinAlgApp, Volume = 77, Pages = "75--112" } @PhDThesis{ Dem83b, Author = "J.W. Demmel", Year = 1983, Title = "A Numerical Analyst's {J}ordan Canonical Form", School = "Univ. of California at Berkeley", Address = "Berkeley, CA" } @Article{ Dem83a, Author = "J.W. Demmel", Year = 1983, Title = "The Condition Number of Equivalence Transformations that Block Diagonalize Matrix Pencils", Journal = SIAMNumAnal, Volume = 20, Pages = "599--610" } @Article{ Dem84, Author = "J.W. Demmel", Year = 1984, Title = "Underflow and the Reliability of Numerical Software", Journal = SIAMSciStat, Volume = 5, Pages = "887--919" } @Article{ Dem87b, Author = "J.W. Demmel", Year = 1987, Title = "On the Distance to the Nearest Ill-Posed Problem", Journal = NumerMath, Volume = 51, Pages = "251--289" } @Article{ Dem87a, Author = "J.W. Demmel", Year = 1987, Title = "A Counterexample for two Conjectures About Stability", Journal = IEEETransAC, Volume = "AC-32", Pages = "340--342" } @Article{ Dem87d, Author = "J.W. Demmel", Year = 1987, Title = "Three Methods for Refining Estimates of Invariant Subspaces", Journal = Computing, Volume = 38, Pages = "43--57" } @Article{ Dem87c, Author = "J.W. Demmel", Year = 1987, Title = "The smallest perturbation of a submatrix which lowers the rank and constrained total least squares problems", Journal = SIAMNumAnal, Volume = 24, Pages = "199--206" } @Article{ Dem88, Author = "J.W. Demmel", Year = 1988, Title = "The Probability that a Numerical Analysis Problem is Difficult", Journal = MathComp, Volume = 50, Pages = "449--480" } @Article{ DemK87, Author = "J.W. Demmel and B. K{\aa}gstr{\"o}m", Year = 1987, Title = "Computing Stable Eigendecompositions of Matrix Pencils", Journal = LinAlgApp, Volume = "88/89", Pages = "139--186" } @Article{ DemK88, Author = "J.W. Demmel and B. K{\aa}gstr{\"o}m", Year = 1988, Title = "Accurate Solutions of Ill-Posed Problems in Control Theory", Journal = SIAMMatrix, Pages = "126--145" } @Book{ DenS83, Author = "J.E. Dennis and R. Schnabel", Year = 1983, Title = "Numerical Methods for Unconstrained Optimization and Nonlinear Equations", Publisher = PrenticeHall, Address = "Englewood Cliffs, NJ" } @Article{ DenT87, Author = "J.E. Dennis Jr and K. Turner", Year = 1987, Title = "Generalized Conjugate Directions", Journal = LinAlgApp, Volume = "88/89", Pages = "187--209" } @Article{ Des63, Author = "J. Descloux", Year = 1963, Title = "Bounds for the Spectral Norm of Functions of Matrices", Journal = NumerMath, Volume = 5, Pages = "185--190" } @Article{ DiaF76, Author = "M.A. Diamond and D.L.V. Ferreira", Year = 1976, Title = "On a Cyclic Reduction Method for the Solution of {P}oisson's Equation", Journal = SIAMNumAnal, Volume = 13, Pages = "54--70" } @Article{ Don83, Author = "J.J. Dongarra", Year = 1983, Title = "Improving the Accuracy of Computed Singular Values", Journal = SIAMSciStat, Volume = 4, Pages = "712--719" } @Manual{ DonBMS78, Author = "J.J. Dongarra and J.R. Bunch and C.B. Moler and G.W. Stewart", Year = 1978, Title = "{LINPACK} Users Guide", Publisher = SIAMPub, Address = "Philadelphia, PA" } @TechReport{ DonCDH88, Author = "J.J. Dongarra and Du Croz, J. and I.S. Duff and S. Hammarling", Year = 1988, Title = "A Set of Level 3 {B}asic {L}inear {A}lgebra {S}ubprograms", Number = "ANL-MCS-TM-88", Institution = "Argonne National Laboratory", Address = "Argonne, ILL" } @Article{ DonCHH88b, Author = "J.J. Dongarra and Du Croz, J. and S. Hammarling and R.J. Hanson", Year = 1988, Title = "An Extended Set of {F}ortran {B}asic {L}inear {A}lgebra {S}ubprograms", Journal = ACMMathSoft, Volume = 14, Pages = "1--17" } @Article{ DonCHH88a, Author = "J.J. Dongarra and Du Croz, J. and S. Hammarling and R.J. Hanson", Year = 1988, Title = "Algorithm~656: An Extended Set of {F}ortran Basic Linear Algebra Subprograms: Model Implementation and Test Programs", Journal = ACMMathSoft, Volume = 14, Pages = "18--32" } @Article{ DonE84, Author = "J.J. Dongarra and S. Eisenstat", Year = 1984, Title = "Squeezing the Most Out of an Algorithm in {C}ray {F}ortran", Journal = ACMMathSoft, Volume = 10, Pages = "221--230" } @Article{ DonGK84, Author = "J.J. Dongarra and F.G. Gustavson and A. Karp", Year = 1984, Title = "Implementing Linear Algebra Algorithms for Dense Matrices on a Vector Pipeline Machine", Journal = SIAMReview, Volume = 26, Pages = "91--112" } @TechReport{ DonHS87, Author = "J.J. Dongarra and S. Hammarling and D.C. Sorensen", Year = 1987, Title = "Block Reduction of Matrices to Condensed form for Eigenvalue Computations", Number = "ANL-MCS-TM 99", Institution = "Argonne National Laboratory", Address = "Argonne, Illinois" } @Article{ DonH86, Author = "J. Dongarra and T. Hewitt", Year = 1986, Title = "Implementing Dense Linear Algebra Algorithms Using Multitasking on the {Cray X-MP-4} (or Approaching the Gigaflop)", Journal = SIAMSciStat, Volume = 7, Pages = "347--350" } @Article{ DonH79, Author = "J. Dongarra and A. Hinds", Year = 1979, Title = "Unrolling Loops in {F}ortran", Journal = SoftPracExp, Volume = 9, Pages = "219--229" } @Article{ DonH84, Author = "J.J. Dongarra and R.E. Hiromoto", Year = 1984, Title = "A Collection of Parallel Linear Equation Routines for the {D}enelcor {HEP}", Journal = ParComputing, Volume = 1, Pages = "133--142" } @Article{ DonKH86, Author = "J.J. Dongarra and L. Kaufman and S. Hammarling", Year = 1986, Title = "Squeezing the Most Out of Eigenvalue Solvers on High Performance Computers", Journal = LinAlgApp, Volume = 77, Pages = "113--136" } @Article{ DonMW83, Author = "J.J. Dongarra and C.B. Moler and J.H. Wilkinson", Year = 1983, Title = "Improving the Accuracy of Computed Eigenvalues and Eigenvectors", Journal = SIAMNumAnal, Volume = 20, Pages = "23--46" } @Article{ DonS84, Author = "J.J. Dongarra and A.H. Sameh", Year = 1984, Title = "On Some Parallel Banded System Solvers", Journal = ParComputing, Volume = 1, Pages = "223--235" } @Article{ DonSS86, Author = "J.J. Dongarra and A. Sameh and D. Sorensen", Year = 1986, Title = "Implementation of Some Concurrent Algorithms for Matrix Factorization", Journal = ParComputing, Volume = 3, Pages = "25--34" } @Article{ DonS86, Author = "J.J. Dongarra and D.C. Sorensen", Year = 1986, Title = "Linear Algebra on High Performance Computers", Journal = ApplMathComp, Volume = 20, Pages = "57--88" } @Article{ DonS87a, Author = "J.J. Dongarra and D.C. Sorensen", Year = 1987, Title = "A Fully Parallel Algorithm for the Symmetric Eigenvalue Problem", Journal = SIAMSciStat, Volume = 8, Pages = "s139-s154" } @Article{ DonS87b, Author = "J.J. Dongarra and D.C. Sorensen", Year = 1987, Title = "A Portable Environment for Developing Parallel Programs", Journal = ParComputing, Volume = 5, Pages = "175--186" } @Article{ Dor70, Author = "F.W. Dorr", Year = 1970, Title = "The Direct Solution of the Discrete {P}oisson Equation on a Rectangle", Journal = SIAMReview, Volume = 12, Pages = "248--263" } @Article{ Dor73, Author = "F.W. Dorr", Year = 1973, Title = "The Direct Solution of the Discrete {P}oisson Equation in {$O(n^{2})$} Operations", Journal = SIAMReview, Volume = 15, Pages = "412--415" } @Article{ DubGR79, Author = "P.F. Dubois and A. Greenbaum and G.H. Rodrigue", Year = 1979, Title = "Approximating the Inverse of a Matrix for Use on Iterative Algorithms on Vector Processors", Journal = Computing, Volume = 22, Pages = "257--268" } @Article{ Dub70, Author = "A. Dubrulle", Year = 1970, Title = "A Short Note on the Implicit {QL} Algorithm for Symmetric Tridiagonal Matrices", Journal = NumerMath, Volume = 15, Pages = "450" } @Article{ DubMW68, Author = "A. Dubrulle and R.S. Martin and J.H. Wilkinson", Year = 1968, Title = "The Implicit {QL} Algorithm", Journal = NumerMath, Volume = 12, Pages = "377--383", Note = "Also in \cite[pages 241--248]{WilR71}" } @Article{ Duf74, Author = "I.S. Duff", Year = 1974, Title = "Pivot Selection and Row Ordering in {G}ivens Reduction on Sparse Matrices", Journal = Computing, Volume = 13, Pages = "239--248" } @Article{ Duf77, Author = "I.S. Duff", Year = 1977, Title = "A Survey of Sparse Matrix Research", Journal = ProcIEEE, Volume = 65, Pages = "500--535" } @Article{ DufR75, Author = "I.S. Duff and J.K. Reid", Year = 1975, Title = "On the Reduction of Sparse Matrices to Condensed Forms by Similarity Transformations", Journal = InstMathApp, Volume = 15, Pages = "217--224" } @Article{ DufR76, Author = "I.S. Duff and J.K. Reid", Year = 1976, Title = "A Comparison of Some Methods for the Solution of Sparse Over-Determined Systems of Linear Equations", Journal = InstMathApp, Volume = 17, Pages = "267--280" } @Proceedings{ DufS78, Editor = "I.S. Duff and G.W. Stewart", Year = 1978, Title = "Sparse Matrix Proceedings", Publisher = SIAMPub, Address = "Philadelphia, PA" } @Book{ DufER86, Author = "I.S. Duff and A.M. Erisman and J.K. Reid", Year = 1986, Title = "Direct Methods for Sparse Matrices", Publisher = OxfordPress } @Book{ DunS58, Author = "N. Dunford and J. Schwartz", Year = 1958, Title = "Linear Operators, Part {I}", Publisher = Interscience, Address = "New York" } @Article{ Dur60, Author = "J. Durbin", Year = 1960, Title = "The Fitting of Time Series Models", Journal = RevueInstStat, Volume = 28, Pages = "233--243" } @Article{ Ebe65, Author = "P.J. Eberlein", Year = 1965, Title = "On Measures of Non-normality for Matrices", Journal = AmerMathMonthly, Volume = 72, Pages = "995--996" } @Article{ Ebe70, Author = "P.J. Eberlein", Year = 1970, Title = "Solution to the Complex Eigenproblem by a Norm-Reducing {J}acobi-Type Method", Journal = NumerMath, Volume = 14, Pages = "232--245", Note = "Also in \cite[pages 404--417]{WilR71}" } @Article{ Ebe71, Author = "P.J. Eberlein", Year = 1971, Title = "On the Diagonalization of Complex Symmetric Matrices", Journal = InstMathApp, Volume = 7, Pages = "377--383" } @InCollection{ Ebe87, Author = "P.J. Eberlein", Year = 1987, Title = "On Using the {J}acobi Method on a Hypercube", BookTitle = "Hypercube Multiprocessors", Editor = "M.T. Heath", Publisher = SIAMPub, Address = "Philadelphia" } @Article{ EckY39, Author = "C. Eckart and G. Young", Year = 1939, Title = "A Principal Axis Transformation for Non-{H}ermitian Matrices", Journal = BullAMS, Volume = 45, Pages = "118--121" } @Article{ EieN83, Author = "M. Eiermann and W. Niethammer", Year = 1983, Title = "On the Construction of Semi-iterative Methods", Journal = SIAMNumAnal, Volume = 20, Pages = "1153--1160" } @Article{ Eis84, Author = "S.C. Eisenstat", Year = 1984, Title = "Efficient Implementation of a Class of Preconditioned Conjugate Gradient Methods", Journal = SIAMSciStat, Volume = 2, Pages = "1--4" } @Article{ EisHHR88, Author = "S.C Eisenstat and M.T. Heath and C.S. Henkel and C.H. Romine", Year = 1988, Title = "Modified Cyclic Algorithms for Solving Triangular Systems on Distributed Memory Multiprocessors", Journal = SIAMSciStat, Volume = 9, Pages = "589--600" } @Article{ Eld77a, Author = "L. Eld{\`e}n", Year = 1977, Title = "Algorithms for the Regularization of Ill-Conditioned Least Squares Problems", Journal = BIT, Volume = 17, Pages = "134--145" } @PhDThesis{ Eld77b, Author = "L. Eld{\`e}n", Year = 1977, Title = "Numerical Analysis of Regularization and Constrained Least Square Methods", Number = 20, School = "Linkoping Studies in Science and Technology", Address = "Linkoping, Sweden" } @Article{ Eld80, Author = "L. Eld{\`e}n", Year = 1980, Title = "Perturbation Theory for the Least Squares Problem with Linear Equality Constraints", Journal = SIAMNumAnal, Volume = 17, Pages = "338--350" } @Article{ Eld83, Author = "L. Eld{\`e}n", Year = 1983, Title = "A Weighted Pseudoinverse, Generalized Singular Values, and Constrained Least Squares Problems", Journal = BIT, Volume = 22, Pages = "487--502" } @Article{ Eld84, Author = "L. Eld{\`e}n", Year = 1984, Title = "An Algorithm for the Regularization of Ill-Conditioned, Banded Least Squares Problems", Journal = SIAMSciStat, Volume = 5, Pages = "237--254" } @Article{ Eld85, Author = "L. Eld{\`e}n", Year = 1985, Title = "A Note on the Computation of the Generalized Cross-Validation Function for Ill-Conditioned Least Squares Problems", Journal = BIT, Volume = 24, Pages = "467--472" } @TechReport{ Eld88, Author = "L. Eld{\`e}n", Year = 1988, Title = "A Parallel {QR} Decomposition Algorithm", Number = "LiTh Mat R 1988-02", Institution = "Mathematics, Linkoping University", Address = "Sweden" } @Article{ EldS86, Author = "L. Eld{\`e}n and R. Schreiber", Year = 1986, Title = "An Application of Systolic Arrays to Linear Discrete Ill-Posed Problems", Journal = SIAMSciStat, Volume = 7, Pages = "892--903" } @Article{ Elm86, Author = "H. Elman", Year = 1986, Title = "A Stability Analysis of Incomplete {LU} Factorization", Journal = MathComp, Volume = 47, Pages = "191--218" } @Article{ ElsS82, Author = "L. Elsner and Guang Sun, J.", Year = 1982, Title = "Perturbation Theorems for the Generalized Eigenvalue Problem", Journal = LinAlgApp, Volume = 48, Pages = "341--357" } @InProceedings{ ElsR88, Author = "A. Elster and A.P. Reeves", Year = 1988, Title = "Block Matrix Operations Using Orthogonal Trees", BookTitle = "The Third Conference on Hypercube Concurrent Computers and Applications, Vol. {II}, Applications", Editor = "G. Fox", Publisher = ACMPress, Address = "New York", Pages = "1554--1561" } @Article{ Enr79, Author = "W. Enright", Year = 1979, Title = "On the Efficient and Reliable Numerical Solution of Large Linear Systems of {O.D.E.}'s", Journal = IEEETransAC, Volume = "AC-24", Pages = "905--908" } @Article{ Erd67, Author = "I. Erdelyi", Year = 1967, Title = "On the Matrix Equation {$Ax = \lambda Bx$}", Journal = MathAnaAppl, Volume = 17, Pages = "119--132" } @Article{ EriR80, Author = "T. Ericsson and A. Ruhe", Year = 1980, Title = "The Spectral Transformation {L}anczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems", Journal = MathComp, Volume = 35, Pages = "1251--1268" } @Article{ EriR74, Author = "A.M. Erisman and J.K. Reid", Year = 1974, Title = "Monitoring the Stability of the Triangular Factorization of a Sparse Matrix", Journal = NumerMath, Volume = 22, Pages = "183--186" } @Article{ Eva84, Author = "D.J. Evans", Year = 1984, Title = "Parallel {SOR} Iterative Methods", Journal = ParComputing, Volume = 1, Pages = "3--18" } @Article{ EvaD83, Author = "D.J. Evans and R. Dunbar", Year = 1983, Title = "The Parallel Solution of Triangular Systems of Equations", Journal = IEEETransComp, Volume = "C-32", Pages = "201--204" } @Article{ FabM84, Author = "V. Faber and T. Manteuffel", Year = 1984, Title = "Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method", Journal = SIAMNumAnal, Volume = 21, Pages = "352--362" } @Book{ FadF63, Author = "D.K. Faddeev and V.N. Faddeva", Year = 1963, Title = "Computational Methods of Linear Algebra", Publisher = WHFreeman, Address = "San Francisco, CA" } @Article{ FadF77, Author = "V. N. Fadeeva and D. K. Fadeev", Year = 1977, Title = "Parallel Calculations in Linear Algebra", Journal = Kibernetika, Volume = 6, Pages = "28--40" } @Article{ FaiL70, Author = "W. Fair and Y. Luke", Year = 1970, Title = "{P}ad{\'e} Approximations to the Operator Exponential", Journal = NumerMath, Volume = 14, Pages = "379--382" } @Article{ FeiV62, Author = "D.G. Feingold and R.S. Varga", Year = 1962, Title = "Block Diagonally Dominant Matrices and Generalizations of the {G}ershgorin Circle Theorem", Journal = "Pacific J. Math.", Volume = 12, Pages = "1241--1250" } @Article{ FenL74, Author = "T. Fenner and G. Loizou", Year = 1974, Title = "Some New Bounds on the Condition Numbers of Optimally Scaled Matrices", Journal = JACM, Volume = 1, Pages = "514--524" } @Article{ FisU69, Author = "C. Fischer and R.A. Usmani", Year = 1969, Title = "Properties of Some Tridiagonal Matrices and Their Application to Boundary Value Problems", Journal = SIAMNumAnal, Volume = 6, Pages = "127--142" } @Article{ FixH72, Author = "G. Fix and R. Heiberger", Year = 1972, Title = "An Algorithm for the Ill-Conditioned Generalized Eigenvalue Problem", Journal = SIAMNumAnal, Volume = 9, Pages = "78--88" } @Article{ Fle76, Author = "R. Fletcher", Year = 1976, Title = "Factorizing Symmetric Indefinite Matrices", Journal = LinAlgApp, Volume = 14, Pages = "257--272" } @Article{ For60, Author = "G.E. Forsythe", Year = 1960, Title = "Crout with Pivoting", Journal = CACM, Volume = 3, Pages = "507--508" } @Article{ ForG65, Author = "G.E. Forsythe and G.H. Golub", Year = 1965, Title = "On the Stationary Values of a Second-Degree Polynomial on the Unit Sphere", Journal = SIAMAppMath, Volume = 13, Pages = "1050--1068" } @Article{ ForH60, Author = "G.E. Forsythe and P. Henrici", Year = 1960, Title = "The Cyclic {J}acobi Method for Computing the Principal Values of a Complex Matrix", Journal = "Trans. Amer. Math. Soc.", Volume = 94, Pages = "1--23" } @Book{ ForMM77, Author = "G.E. Forsythe and M.A. Malcolm and C.B. Moler", Year = 1977, Title = "Computer Methods for Mathematical Computations", Publisher = PrenticeHall, Address = "Englewood Cliffs, NJ" } @Book{ ForM67, Author = "G.E. Forsythe and C.B. Moler", Year = 1967, Title = "Computer Solution of Linear Algebraic Systems", Publisher = PrenticeHall, Address = "Englewood Cliffs, NJ" } @Article{ Fos86, Author = "L.V. Foster", Year = 1986, Title = "Rank and Null Space Calculations Using Matrix Decomposition without Column Interchanges", Journal = LinAlgApp, Volume = 74, Pages = "47--71" } @Article{ Fou84, Author = "R. Fourer", Year = 1984, Title = "Staircase Matrices and Systems", Journal = SIAMReview, Volume = 26, Pages = "1--71" } @Book{ Fox64, Author = "L. Fox", Year = 1964, Title = "An Introduction to Numerical Linear Algebra", Publisher = OxfordPress, Address = "Oxford, England" } @Proceedings{ Fox88, Editor = "G. Fox", Year = 1988, Title = "Applications", Series = "The Third Conference on Hypercube Concurrent Computers and Applications", Volume = 2, Publisher = ACMPress, Address = "New York" } @Article{ FoxOH87, Author = "G. Fox and S.W. Otto and A.J. Hey", Year = 1987, Title = "Matrix Algorithms on a Hypercube {I}: Matrix Multiplication", Journal = ParComputing, Volume = 4, Pages = "17--31" } @Book{ FoxJL+88, Author = "G. Fox and M. Johnson and G. Lyzenga and S. Otto and J. Salmon and D. Walker", Year = 1988, Title = "On Concurrent Processors Vol {I}: General Techniques and Regular Problems", Publisher = PrenticeHall, Address = "Englewood Cliffs, NJ" } @Article{ Fra64a, Author = "J.S. Frame", Year = 1964, Title = "Matrix Functions and Applications, Part {II}", Journal = IEEESpec, Volume = 1, Month = apr, Pages = "102--108" } @Article{ Fra64b, Author = "J.S. Frame", Year = 1964, Title = "Matrix Functions and Applications, Part {IV}", Journal = IEEESpec, Volume = 1, Month = jun, Pages = "123--131" } @Article{ Fra61, Author = "J.G.F. Francis", Year = 1961, Title = "The {QR} Transformation: A Unitary Analogue to the {LR} Transformation, Parts~{I} and~{II}", Journal = CompJour, Volume = 4, Pages = "265-272, 332--345" } @Article{ Fri75, Author = "S. Friedland", Year = 1975, Title = "On Inverse Multiplicative Eigenvalue Problems for Matrices", Journal = LinAlgApp, Volume = 12, Pages = "127--138" } @Article{ Fri77, Author = "S. Friedland", Year = 1977, Title = "Inverse Eigenvalue Problems", Journal = LinAlgApp, Volume = 17, Pages = "15--52" } @Article{ FriNO87, Author = "S. Friedland and J. Nocedal and M.L. Overton", Year = 1987, Title = "The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems", Journal = SIAMNumAnal, Volume = 24, Pages = "634--667" } @Article{ Fro65, Author = "C.E. Froberg", Year = 1965, Title = "On Triangularization of Complex Matrices by Two-Dimen\-sional Unitary Transformations", Journal = BIT, Volume = 5, Pages = "230--234" } @Article{ FunG86, Author = "R.E. Funderlic and A. Geist", Year = 1986, Title = "Torus Data Flow for Parallel Computation of Missized Matrix Problems", Journal = LinAlgApp, Volume = 77, Pages = "149--164" } @Article{ FunNP82, Author = "R.E. Funderlic and M. Neuman and R.J. Plemmons", Year = 1982, Title = "Generalized Diagonally Dominant Matrices", Journal = NumerMath, Volume = 40, Pages = "57--70" } @Article{ GalP70, Author = "G. Galimberti and V. Pereyra", Year = 1970, Title = "Numerical Differentiation and the Solution of Multidimensional {V}andermonde Systems", Journal = MathComp, Volume = 24, Pages = "357--364" } @Article{ GalP71, Author = "G. Galimberti and V. Pereyra", Year = 1971, Title = "Solving Confluent {V}andermonde Systems of {H}ermite Type", Journal = NumerMath, Volume = 18, Pages = "44--60" } @Article{ GalJM87, Author = "K. Gallivan and W. Jalby and U. Meier", Year = 1987, Title = "The Use of {BLAS3} in Linear Algebra on a Parallel Processor with a Hierarchical Memory", Journal = SIAMSciStat, Volume = 8, Pages = "1079--1084" } @Article{ GalJMS88, Author = "K. Gallivan and W. Jalby and U. Meier and A.H. Sameh", Year = 1988, Title = "Impact of Hierarchical Memory Systems on Linear Algebra Algorithm Design", Journal = IntSuper, Volume = 2, Pages = "12--48" } @Article{ Gan81, Author = "W. Gander", Year = 1981, Title = "Least Squares with a Quadratic Constraint", Journal = NumerMath, Volume = 36, Pages = "291--307" } @Article{ GanR84, Author = "D. Gannon and Van Rosendale, J.", Year = 1984, Title = "On the Impact of Communication Complexity on the Design of Parallel Numerical Algorithms", Journal = IEEETransComp, Volume = "C-33", Pages = "1180--1194" } @Book{ Gan59a, Author = "F.R. Gantmacher", Year = 1959, Title = "The Theory of Matrices", Publisher = Chelsea, Address = "New York", Volume = 1, } @Book{ Gan59b, Author = "F.R. Gantmacher", Year = 1959, Title = "The Theory of Matrices", Publisher = Chelsea, Address = "New York", Volume = 2, } @Manual{ GarBDM72, Author = "B.S. Garbow and J.M. Boyle and J.J. Dongarra and C.B. Moler", Year = 1972, Title = "Matrix Eigensystem Routines: {EISPACK} Guide Extension", Publisher = Springer, Address = "New York" } @Article{ Gau75a, Author = "W. Gautschi", Year = 1975, Title = "Norm Estimates for Inverses of {V}andermonde Matrices", Journal = NumerMath, Volume = 23, Pages = "337--347" } @Article{ Gau75b, Author = "W. Gautschi", Year = 1975, Title = "Optimally Conditioned {V}andermonde Matrices", Journal = NumerMath, Volume = 24, Pages = "1--12" } @TechReport{ GeiH85, Author = "G.A. Geist and M.T. Heath", Year = 1985, Title = "Parallel {C}holesky Factorization on a Hypercube Multiprocessor", Number = "ORNL 6190", Institution = "Oak Ridge Laboratory", Address = "Oak Ridge, TN" } @InCollection{ GeiH86, Author = "G.A. Geist and M.T. Heath", Year = 1986, Title = "Matrix Factorization on a Hypercube", BookTitle = "Hypercube Multiprocessors", Editor = "M.T. Heath", Publisher = SIAMPub, Pages = "161--180" } @InProceedings{ GeiWDF88, Author = "G.A. Geist and R.C. Ward and G.J. Davis and R.E. Funderlic", Year = 1988, Title = "Finding Eigenvalues and Eigenvectors of Unsymmetric Matrices Using a Hypercube Multiprocessor", BookTitle = "The Third Conference on Hypercube Concurrent Computers and Applications, Vol. {II}, Applications", Editor = "G. Fox", Publisher = ACMPress, Address = "New York", Pages = "1577--1582" } @Article{ Gen73a, Author = "W.M. Gentleman", Year = 1973, Title = "Error Analysis of {QR} Decompositions by {G}ivens Transformations", Journal = LinAlgApp, Volume = 10, Pages = "189--197" } @Article{ Gen73b, Author = "W.M. Gentleman", Year = 1973, Title = "Least Squares Computations by {G}ivens Transformations Without Square Roots", Journal = InstMathApp, Volume = 12, Pages = "329--336" } @InProceedings{ GenK82, Author = "W.M. Gentleman and H.T. Kung", Year = 1982, Title = "Matrix Triangularization by Systolic Arrays", BookTitle = "{SPIE} Proceedings", Volume = 298, Pages = "19--26" } @Article{ Geo73, Author = "J.A. George", Year = 1973, Title = "Nested Dissection of a Regular Finite Element Mesh", Journal = SIAMNumAnal, Volume = 10, Pages = "345--363" } @Article{ Geo74, Author = "J.A. George", Year = 1974, Title = "On Block Elimination for Sparse Linear Systems", Journal = SIAMNumAnal, Volume = 11, Pages = "585--603" } @Article{ GeoH80, Author = "J.A. George and M.T. Heath", Year = 1980, Title = "Solution of Sparse Linear Least Squares Problems Using {G}ivens Rotations", Journal = LinAlgApp, Volume = 34, Pages = "69--83" } @Article{ GeoHL86, Author = "J.A. George and M.T. Heath and J. Liu", Year = 1986, Title = "Parallel {C}holesky Factorization on a Shared Memory Multiprocessor", Journal = LinAlgApp, Volume = 77, Pages = "165--187" } @Book{ GeoL81a, Author = "J.A. George and J.W. Liu", Year = 1981, Title = "Computer Solution of Large Sparse Positive Definite Systems", Publisher = PrenticeHall, Address = "Englewood Cliffs, NJ" } @Article{ GibWP74, Author = "N.E. Gibbs and W.G. Poole, Jr", Year = 1974, Title = "Tridiagonalization by Permutations", Journal = CACM, Volume = 17, Pages = "20--24" } @Article{ GibPS76b, Author = "N.E. Gibbs and W.G. Poole and P.K. Stockmeyer", Year = 1976, Title = "A Comparison of Several Bandwidth and Profile Reduction Algorithms", Journal = ACMMathSoft, Volume = 2, Pages = "322--330" } @Article{ GibPS76a, Author = "N.E. Gibbs and W.G. Poole and P.K. Stockmeyer", Year = 1976, Title = "An Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix", Journal = SIAMNumAnal, Volume = 13, Pages = "236--250" } @Article{ GilGMS74, Author = "P.E. Gill and G.H. Golub and W. Murray and M.A. Saunders", Year = 1974, Title = "Methods for Modifying Matrix Factorizations", Journal = MathComp, Volume = 28, Pages = "505--535" } @InCollection{ GilM76, Author = "P.E. Gill and W. Murray", Year = 1976, Title = "The Orthogonal Factorization of a Large Sparse Matrix", BookTitle = "Sparse Matrix Computations", Editor = "J.R. Bunch and D.J. Rose", Publisher = Academic, Address = "New York", Pages = "177--200" } @Article{ GilMS75, Author = "P.E. Gill and W. Murray and M.A. Saunders", Year = 1975, Title = "Methods for Computing and Modifying the {LDV} Factors of a Matrix", Journal = MathComp, Volume = 29, Pages = "1051--1077" } @InCollection{ Gin71, Author = "T. Ginsburg", Year = 1971, Title = "The Conjugate Gradient Method", BookTitle = "Handbook for Automatic Computation Vol. 2: Linear Algebra", Editor = "J.H. Wilkinson and C. Reinsch", Publisher = Springer, Address = "New York", Pages = "57--69" } @Article{ Giv58, Author = "W. Givens", Year = 1958, Title = "Computation of Plane Unitary Rotations Transforming a General Matrix to Triangular Form", Journal = SIAMAppMath, Volume = 6, Pages = "26--50" } @Book{ GohK69, Author = "I.C. Gohberg and M.G. Krein", Year = 1969, Title = "Introduction to the Theory of Linear Non-Self-Adjoint Operators", Publisher = AMS, Address = "Providence, RI" } @Book{ GohLR86, Author = "I.C. Gohberg and P. Lancaster and L. Rodman", Year = 1986, Title = "Invariant Subspaces of Matrices With Applications", Publisher = JohnWileySons, Address = "New York" } @Article{ GolH59, Author = "H.H. Goldstine and L.P. Horowitz", Year = 1959, Title = "A Procedure for the Diagonalization of Normal Matrices", Journal = JACM, Volume = 6, Pages = "176--195" } @Article{ Gol76, Author = "D. Goldfarb", Year = 1976, Title = "Factorized Variable Metric Methods for Unconstrained Optimization", Journal = MathComp, Volume = 30, Pages = "796--811" } @Article{ Gol65, Author = "G.H. Golub", Year = 1965, Title = "Numerical Methods for Solving Linear Least Squares Problems", Journal = NumerMath, Volume = 7, Pages = "206--216" } @InCollection{ Gol69, Author = "G.H. Golub", Year = 1969, Title = "Matrix Decompositions and Statistical Computation", BookTitle = "Statistical Computation", Editor = "R.C. Milton and J.A. Nelder", Publisher = Academic, Address = "New York", Pages = "365--397" } @Article{ Gol73, Author = "G.H. Golub", Year = 1973, Title = "Some Modified Matrix Eigenvalue Problems", Journal = SIAMReview, Volume = 15, Pages = "318--344" } @InCollection{ Gol74, Author = "G.H. Golub", Year = 1974, Title = "Some Uses of the {L}anczos Algorithm in Numerical Linear Algebra", BookTitle = "Topics in Numerical Analysis", Editor = "J.J.H. Miller", Publisher = Academic, Address = "New York" } @Article{ GolHW79, Author = "G.H. Golub and M. Heath and G. Wahba", Year = 1979, Title = "Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter", Journal = Techno, Volume = 21, Pages = "215--223" } @Article{ GolHS88, Author = "G.H. Golub and A. Hoffman and G.W. Stewart", Year = 1988, Title = "A Generalization of the {E}ckart-{Y}oung-{M}irsky Approximation Theorem", Journal = LinAlgApp, Volume = "88/89", Pages = "317--328" } @Article{ GolK65, Author = "G.H. Golub and W. Kahan", Year = 1965, Title = "Calculating the Singular Values and Pseudo-Inverse of a Matrix", Journal = JSIAMB, Volume = 2, Pages = "205--224" } @TechReport{ GolKS76, Author = "G.H. Golub and V. Klema and G.W. Stewart", Year = 1976, Title = "Rank Degeneracy and Least Squares Problems", Number = "TR-456", Institution = "Computer Science, University of Maryland", Address = "College Park, MD" } @Article{ GolLO81, Author = "G.H. Golub and F.T. Luk and M. Overton", Year = 1981, Title = "A Block {L}anczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix", Journal = ACMMathSoft, Volume = 7, Pages = "149--169" } @Book{ GolM83, Author = "G.H. Golub and G. Meurant", Year = 1983, Title = "R{\'e}solution Num{\'e}rique des Grands Syst{\`e}mes Lin{\'e}aires", Series = "Collection de la Direction des Etudes et Recherches de l'Electricit\'e de France", Volume = 49, Publisher = Eyolles, Address = "Paris" } @Article{ GolM86, Author = "G.H. Golub and C.D. Meyer", Year = 1986, Title = "Using the {QR} Factorization and Group Inversion to Compute, Differentiate, and estimate the Sensitivity of Stationary Probabilities for {M}arkov Chains", Journal = SIAMAlgMeth, Volume = 7, Pages = "273--281" } @Article{ GolNL79, Author = "G.H. Golub and S. Nash and Van Loan, C.", Year = 1979, Title = "A {H}essenberg-{S}chur Method for the Matrix Problem {$AX + XB = C$}", Journal = IEEETransAC, Volume = "AC-24", Pages = "909--913" } @Article{ GolO88, Author = "G.H. Golub and M. Overton", Year = 1988, Title = "The Convergence of Inexact {C}hebychev and {R}ichardson Iterative Methods for Solving Linear Systems", Journal = NumerMath, Volume = 53, Pages = "571--594" } @Article{ GolP73, Author = "G.H. Golub and V. Pereyra", Year = 1973, Title = "The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate", Journal = SIAMNumAnal, Volume = 10, Pages = "413--432" } @InCollection{ GolP76, Author = "G.H. Golub and V. Pereyra", Year = 1976, Title = "Differentiation of Pseudo-Inverses, Separable Nonlinear Least Squares Problems and Other Tales", BookTitle = "Generalized Inverses and Applications", Editor = "M.Z. Nashed", Publisher = Academic, Address = "New York", Pages = "303--324" } @Article{ GolR70, Author = "G.H. Golub and C. Reinsch", Year = 1970, Title = "Singular Value Decomposition and Least Squares Solutions", Journal = NumerMath, Volume = 14, Pages = "403-420", Note = "Also in \cite[pages 134--151]{WilR71}" } @Article{ GolT81, Author = "G.H. Golub and W.P. Tang", Year = 1981, Title = "The Block Decomposition of a {V}andermonde Matrix and Its Applications", Journal = BIT, Volume = 21, Pages = "505--517" } @Article{ GolU70, Author = "G.H. Golub and R. Underwood", Year = 1970, Title = "Stationary Values of the Ratio of Quadratic Forms Subject to Linear Constraints", Journal = ZAngewMathPhys, Volume = 21, Pages = "318--326" } @InCollection{ GolU77, Author = "G.H. Golub and R. Underwood", Year = 1977, Title = "The Block {L}anczos Method for Computing Eigenvalues", BookTitle = "Mathematical Software {III}", Editor = "J. Rice", Publisher = Academic, Address = "New York", Pages = "364--377" } @TechReport{ GolUW72, Author = "G.H. Golub and R. Underwood and J.H. Wilkinson", Year = 1972, Title = "The {L}anczos Algorithm for the Symmetric {$Ax = \lambda Bx$} Problem", Number = "STAN-CS-72-270", Institution = "Computer Science, Stanford University", Address = "Stanford, CA" } @Article{ GolL79, Author = "G.H. Golub and Van Loan, C.F.", Year = 1979, Title = "Unsymmetric Positive Definite Linear Systems", Journal = LinAlgApp, Volume = 28, Pages = "85--98" } @Article{ GolL80, Author = "G.H. Golub and Van Loan, C.F.", Year = 1980, Title = "An Analysis of the Total Least Squares Problem", Journal = SIAMNumAnal, Volume = 17, Pages = "883--893" } @Book{ GolL89, Author = "G.H. Golub and Van Loan, C.F.", Year = 1989, Title = "Matrix Computations", Edition = "second", Publisher = JohnsHopkinsPress, Address = "Baltimore, MD" } @Article{ GolV74, Author = "G.H. Golub and J.M. Varah", Year = 1974, Title = "On a Characterization of the Best {$L_{2}$}-Scaling of a Matrix", Journal = SIAMNumAnal, Volume = 11, Pages = "472--479" } @Article{ GolV61, Author = "G.H. Golub and R.S. Varga", Year = 1961, Title = "{C}hebychev Semi-Iterative Methods, Successive Over-Relaxation Iterative Methods, and Second-Order {R}ichardson Iterative Methods, Parts {I} and {II}", Journal = NumerMath, Volume = 3, Pages = "147--156, 157--168" } @Article{ GolW69, Author = "G.H. Golub and J.H. Welsch", Year = 1969, Title = "Calculation of {G}auss Quadrature Rules", Journal = MathComp, Volume = 23, Pages = "221--230" } @Article{ GolW66, Author = "G.H. Golub and J.H. Wilkinson", Year = 1966, Title = "Note on the Iterative Refinement of Least Squares Solution", Journal = NumerMath, Volume = 9, Pages = "139--148" } @Article{ GolW76, Author = "G.H. Golub and J.H. Wilkinson", Year = 1976, Title = "Ill-Conditioned Eigensystems and the Computation of the {J}ordan Canonical Form", Journal = SIAMReview, Volume = 18, Pages = "578--619" } @Article{ Gou70, Author = "A.R. Gourlay", Year = 1970, Title = "Generalization of Elementary {H}ermitian Matrices", Journal = CompJour, Volume = 13, Pages = "411--412" } @Article{ Gra86, Author = "W. B. Gragg", Year = 1986, Title = "The {QR} Algorithm for Unitary {H}essenberg Matrices", Journal = CompApplMath, Volume = 16, Pages = "1--8" } @Article{ GraH84, Author = "W.B. Gragg and W.J. Harrod", Year = 1984, Title = "The Numerically Stable Reconstruction of {J}acobi Matrices from Spectral Data", Journal = NumerMath, Volume = 44, Pages = "317--336" } @Article{ Gre52, Author = "B. Green", Year = 1952, Title = "The Orthogonal Approximation of an Oblique Structure in Factor Analysis", Journal = Psychometrika, Volume = 17, Pages = "429--440" } @TechReport{ Gre81, Author = "A. Greenbaum", Year = 1981, Title = "Behavior of the Conjugate Gradient Algorithm in Finite Precision Arithmetic", Number = "UCRL 85752", Institution = "Lawrence Livermore Laboratory", Address = "Livermore, CA" } @Article{ GriL81b, Author = "R.G. Grimes and J.G. Lewis", Year = 1981, Title = "Condition Number Estimation for Sparse Matrices", Journal = SIAMSciStat, Volume = 2, Pages = "384--388" } @Article{ GunWM76, Author = "R.F. Gunst and J.T. Webster and R.L. Mason", Year = 1976, Title = "A Comparison of Least Squares and Latent Root Regression Estimators", Journal = Techno, Volume = 18, Pages = "75--83" } @Article{ Gup72, Author = "K.K. Gupta", Year = 1972, Title = "Solution of Eigenvalue Problems by {S}turm Sequence Method", Journal = IntNumerEng, Volume = 4, Pages = "379--404" } @Book{ HagY81, Author = "L.A. Hageman and D.M. Young", Year = 1981, Title = "Applied Iterative Methods", Publisher = Academic, Address = "New York" } @Article{ Hag84, Author = "W. Hager", Year = 1984, Title = "Condition Estimates", Journal = SIAMSciStat, Volume = 5, Pages = "311--316" } @Book{ Hag88, Author = "W. Hager", Year = 1988, Title = "Applied Numerical Linear Algebra", Publisher = PrenticeHall, Address = "Englewood Cliffs, NJ" } @Book{ Hal58, Author = "P. Halmos", Year = 1958, Title = "Finite Dimensional Vector Spaces", Publisher = VanNostrand, Address = "New York" } @Article{ Ham74, Author = "S. Hammarling", Year = 1974, Title = "A Note on Modifications to the {G}ivens Plane Rotation", Journal = InstMathApp, Volume = 13, Pages = "215--218" } @Article{ Ham85, Author = "S.J. Hammarling", Year = 1985, Title = "The Singular Value Decomposition in Multivariate Statistics", Journal = SIGNUM, Volume = 20, Pages = "2--25" } @Article{ Han62, Author = "E.R. Hansen", Year = 1962, Title = "On Quasicyclic {J}acobi Methods", Journal = JACM, Volume = 9, Pages = "118--135" } @Article{ Han63, Author = "E.R. Hanson", Year = 1963, Title = "On Cyclic {J}acobi Methods", Journal = SIAMAppMath, Volume = 11, Pages = "448--459" } @Article{ Han87, Author = "P.C. Hansen", Year = 1987, Title = "The Truncated {SVD} as a Method for Regularization", Journal = BIT, Volume = 27, Pages = "534--553" } @InCollection{ Han88, Author = "P.C. Hansen", Year = 1988, Title = "Reducing the Number of Sweeps in {H}estenes Method", BookTitle = "Singular Value Decomposition and Signal Processing", Editor = "E.F. Deprettere", Publisher = NorthHolland } @Article{ HanL69, Author = "R.J. Hanson and C.L. Lawson", Year = 1969, Title = "Extensions and Applications of the {H}ouseholder Algorithm for Solving Linear Least Squares Problems", Journal = MathComp, Volume = 23, Pages = "787--812" } @Article{ HanN81, Author = "R.J. Hanson and M.J. Norris", Year = 1981, Title = "Analysis of Measurements Based on the Singular Value Decomposition", Journal = SIAMSciStat, Volume = 2, Pages = "363--374" } @Article{ Har82, Author = "V. Hari", Year = 1982, Title = "On the Global Convergence of the {E}berlein Method for Real Matrices", Journal = NumerMath, Volume = 39, Pages = "361--370" } @PhDThesis{ Hea78, Author = "M.T. Heath", Year = 1978, Title = "Numerical Algorithms for Nonlinearly Constrained Optimization", Number = "STAN-CS-78-656", School = "Computer Science, Stanford University", Address = "Stanford, CA" } @Proceedings{ Hea86, Editor = "M.T. Heath", Year = 1986, Title = "Proceedings of First {SIAM} Conference on Hypercube Multiprocessors", Publisher = SIAMPub, Address = "Philadelphia, PA" } @Proceedings{ Hea87, Editor = "M.T. Heath", Year = 1987, Title = "Hypercube Multiprocessors", Publisher = SIAMPub, Address = "Philadelphia, PA" } @Article{ HeaLPW86, Author = "M.T. Heath and A.J. Laub and C.C. Paige and R.C. Ward", Year = 1986, Title = "Computing the {SVD} of a Product of Two Matrices", Journal = SIAMSciStat, Volume = 7, Pages = "1147--1159" } @Article{ HeaR88, Author = "M.T. Heath and C.H. Romine", Year = 1988, Title = "Parallel Solution of Triangular Systems on Distributed Memory Multiprocessors", Journal = SIAMSciStat, Volume = 9, Pages = "558--588" } @Article{ HeaS86, Author = "M.T. Heath and D.C. Sorensen", Year = 1986, Title = "A Pipelined Method for Computing the {QR} Factorization of a Sparse Matrix", Journal = LinAlgApp, Volume = 77, Pages = "189--203" } @Article{ Hel76, Author = "D. Heller", Year = 1976, Title = "Some Aspects of the Cyclic Reduction Algorithm for Block Tridiagonal Linear Systems", Journal = SIAMNumAnal, Volume = 13, Pages = "484--496" } @Article{ Hel78, Author = "D. Heller", Year = 1978, Title = "A Survey of Parallel Algorithms in Numerical Linear Algebra", Journal = SIAMReview, Volume = 20, Pages = "740--777" } @Article{ HelI83, Author = "D.E. Heller and I.C.F. Ipsen", Year = 1983, Title = "Systolic Networks for Orthogonal Decompositions", Journal = SIAMSciStat, Volume = 4, Pages = "261--269" } @Article{ Hel68, Author = "B.W. Helton", Year = 1968, Title = "Logarithms of Matrices", Journal = ProcAMS, Volume = 19, Pages = "733--736" } @InProceedings{ HenHP88, Author = "C.S. Henkel and M.T. Heath and R.J. Plemmons", Year = 1988, Title = "{C}holesky Downdating on a Hypercube", BookTitle = "The Third Conference on Hypercube Concurrent Computers and Applications, Vol. {II}, Applications", Editor = "G. Fox", Publisher = ACMPress, Address = "New York", Pages = "1592--1598" } @Article{ Hen58, Author = "P. Henrici", Year = 1958, Title = "On the Speed of Convergence of Cyclic and Quasicyclic {J}acobi Methods for Computing the Eigenvalues of of {H}ermitian Matrices", Journal = SIAMAppMath, Volume = 6, Pages = "144--162" } @Article{ Hen62, Author = "P. Henrici", Year = 1962, Title = "Bounds for Iterates, Inverses, Spectral Variation, and Fields of Values of Non-Normal Matrices", Journal = NumerMath, Volume = 4, Pages = "24--40" } @Article{ HenZ68, Author = "P. Henrici and K. Zimmermann", Year = 1968, Title = "An Estimate for the Norms of Certain cyclic {J}acobi Operators", Journal = LinAlgApp, Volume = 1, Pages = "489--501" } @Book{ Hes80, Author = "M.R. Hestenes", Year = 1980, Title = "Conjugate Direction Methods in Optimization", Publisher = Springer, Address = "Berlin" } @Article{ HesS52, Author = "M.R. Hestenes and E. Stiefel", Year = 1952, Title = "Methods of Conjugate Gradients for Solving Linear Systems", Journal = JResNatBurStand, Volume = 49, Pages = "409--436" } @PhDThesis{ Hig85, Author = "N.J. Higham", Year = 1985, Title = "Nearness Problems in Numerical Linear Algebra", School = "University of Manchester", Address = "England" } @Article{ Hig86c, Author = "N.J. Higham", Year = 1986, Title = "{N}ewton's Method for the Matrix Square Root", Journal = MathComp, Volume = 46, Pages = "537--550" } @Article{ Hig86a, Author = "N.J. Higham", Year = 1986, Title = "Computing the Polar Decomposition with Applications", Journal = SIAMSciStat, Volume = 7, Pages = "1160--1174" } @Article{ Hig86b, Author = "N.J. Higham", Year = 1986, Title = "Efficient Algorithms for computing the condition number of a tridiagonal matrix", Journal = SIAMSciStat, Volume = 7, Pages = "150--165" } @Article{ Hig87c, Author = "N.J. Higham", Year = 1987, Title = "A Survey of Condition Number Estimation for Triangular Matrices", Journal = SIAMReview, Volume = 29, Pages = "575--596" } @Article{ Hig87b, Author = "N.J. Higham", Year = 1987, Title = "Error Analysis of the {B}j{\"o}rck-{P}ereyra Algorithms for Solving {V}andermonde Systems", Journal = NumerMath, Volume = 50, Pages = "613--632" } @Article{ Hig87a, Author = "N.J. Higham", Year = 1987, Title = "Computing Real Square Roots of a Real Matrix", Journal = LinAlgApp, Volume = "88/89", Pages = "405--430" } @TechReport{ Hig88f, Author = "N.J. Higham", Year = 1988, Title = "Matrix Nearness Problems and Applications", Number = 161, Institution = "Mathematics, University of Manchester", Address = "England", Note = "To appear in Proceedings of the IMA Conference on Applications of Matrix Theory, eds. S. Barnett and M.J.C. Gover" } @Article{ Hig88e, Author = "N.J. Higham", Year = 1988, Title = "{F}ortran Codes for Estimating the One-Norm of a Real or Complex Matrix, with Applications to Condition Estimation", Journal = ACMMathSoft, Volume = 14, Pages = "381--396" } @Article{ Hig88d, Author = "N.J. Higham", Year = 1988, Title = "The Symmetric {P}rocrustes Problem", Journal = BIT, Volume = 28, Pages = "133--143" } @Article{ Hig88c, Author = "N.J. Higham", Year = 1988, Title = "Fast Solution of {V}andermonde-like Systems Involving Orthogonal Polynomials", Journal = IMANumerAna, Volume = 8, Pages = "473--486" } @Article{ Hig88b, Author = "N.J. Higham", Year = 1988, Title = "Computing a Nearest Symmetric Positive Semidefinite Matrix", Journal = LinAlgApp, Volume = 103, Pages = "103--118" } @TechReport{ Hig88a, Author = "N.J. Higham", Year = 1988, Title = "The Accuracy of Solutions to Triangular Systems", Number = 158, Institution = "Mathematics, University of Manchester", Address = "England" } @InCollection{ Hig89, Author = "N.J. Higham", Year = 1989, Title = "Analysis of the {C}holesky Decomposition of a Semi-definite Matrix", BookTitle = "Reliable Numerical Computation", Editor = "M.G. Cox and S.J. Hammarling", Publisher = OxfordPress } @Article{ HigH89, Author = "N.J. Higham and D.J. Higham", Year = 1989, Title = "Large Growth Factors in {G}aussian Elimination with Pivoting", Journal = SIAMMatrix, Volume = 10, Pages = "155--164" } @TechReport{ HigS88, Author = "N.J. Higham and R.S. Schreiber", Year = 1988, Title = "Fast Polar Decomposition of an Arbitrary Matrix", Number = "88-942", Institution = "Computer Science, Cornell University", Address = "Ithaca, NY 14853" } @InCollection{ Hoa77, Author = "D. Hoaglin", Year = 1977, Title = "Mathematical Software and Exploratory Data Analysis", BookTitle = "Mathematical Software {III}", Editor = "John Rice", Publisher = Academic, Address = "New York", Pages = "139--159" } @Article{ Hoc65, Author = "R.W. Hockney", Year = 1965, Title = "A Fast Direct Solution of {P}oisson's Equation Using {F}ourier Analysis", Journal = JACM, Volume = 12, Pages = "95--113" } @Article{ Hoc83, Author = "R. Hockney", Year = 1983, Title = "Characterizing Computers and Optimizing the {FACR($\ell$)} {P}oisson Solver on Parallel Unicomputers", Journal = IEEETransComp, Volume = "C-32", Pages = "933--941" } @Book{ HocJ88, Author = "R.W. Hockney and C.R. Jesshope", Year = 1988, Title = "Parallel Computers 2", Publisher = AdamHilger, Address = "Bristol and Philadelphia" } @Article{ HofP78, Author = "W. Hoffmann and B.N. Parlett", Year = 1978, Title = "A New Proof of Global Convergence for the Tridiagonal {QL} Algorithm", Journal = SIAMNumAnal, Volume = 15, Pages = "929--937" } @Article{ Hot57, Author = "H. Hotelling", Year = 1957, Title = "The Relations of the Newer Multivariate Statistical Methods to Factor Analysis", Journal = BritStatPsych, Volume = 10, Pages = "69--79" } @Article{ Hou58, Author = "A.S. Householder", Year = 1958, Title = "Unitary Triangularization of a Nonsymmetric Matrix", Journal = JACM, Volume = 5, Pages = "339--342" } @Article{ Hou68, Author = "A.S. Householder", Year = 1968, Title = "Moments and Characteristic Roots {II}", Journal = NumerMath, Volume = 11, Pages = "126--128" } @Book{ Hou74, Author = "A.S. Householder", Year = 1974, Title = "The Theory of Matrices in Numerical Analysis", Publisher = DoverPub, Address = "New York" } @Article{ Hua75, Author = "C.P. Huang", Year = 1975, Title = "A {J}acobi-Type Method for Triangularizing an Arbitrary Matrix", Journal = SIAMNumAnal, Volume = 12, Pages = "566--570" } @Article{ Hua81, Author = "C.P. Huang", Year = 1981, Title = "On the Convergence of the {QR} Algorithm with Origin Shifts for Normal Matrices", Journal = IMANumerAna, Volume = 1, Pages = "127--133" } @Article{ HulS66, Author = "T.E. Hull and J.R. Swenson", Year = 1966, Title = "Tests of Probabilistic Models for Propagation of Roundoff Errors", Journal = CACM, Volume = 9, Pages = "108--113" } @Article{ Ike79, Author = "Y. Ikebe", Year = 1979, Title = "On Inverses of {H}essenberg Matrices", Journal = LinAlgApp, Volume = 24, Pages = "93--97" } @Article{ IpsSS86, Author = "I.C.F. Ipsen and Y. Saad and M. Schultz", Year = 1986, Title = "Dense Linear Systems on a Ring of Processors", Journal = LinAlgApp, Volume = 77, Pages = "205--239" } @Book{ IseP87, Editor = "A. Iserles and M.J.D. Powell", Year = 1987, Title = "The State of the Art in Numerical Analysis", Publisher = OxfordPress } @Article{ Jac46, Author = "C.G.J. Jacobi", Year = 1846, Title = "{\"U}ber ein leichtes Verfahren die in der Theorie der S{\"a}cul{\"a}rst{\"o}rungen vorkommenden Gleichungen numerisch aufzul{\"o}sen", Journal = Crelle, Volume = 30, Pages = "51--94" } @Article{ JanW77, Author = "M. Jankowski and M. Wozniakowski", Year = 1977, Title = "Iterative Refinement Implies Numerical Stability", Journal = BIT, Volume = 17, Pages = "303--311" } @Article{ JeaY83, Author = "K.C. Jea and D.M. Young", Year = 1983, Title = "On the Simplification of Generalized Conjugate Gradient Methods for Nonsymmetrizable Linear Systems", Journal = LinAlgApp, Volume = "52/53", Pages = "399--417" } @Article{ Jen77a, Author = "A. Jennings", Year = 1977, Title = "Influence of the Eigenvalue Spectrum on the Convergence Rate of the Conjugate Gradient Method", Journal = InstMathApp, Volume = 20, Pages = "61--72" } @Book{ Jen77b, Author = "A. Jennings", Year = 1977, Title = "Matrix Computation for Engineers and Scientists", Publisher = JohnWileySons, Address = "New York" } @Article{ JenO71, Author = "A. Jennings and D.R.L. Orr", Year = 1971, Title = "Application of the Simultaneous Iteration Method to Undamped Vibration Problems", Journal = IntNumerEng, Volume = 3, Pages = "13--24" } @Article{ JenO77, Author = "A. Jennings and M.R. Osborne", Year = 1977, Title = "Generalized Eigenvalue Problems for Certain Unsymmetric Band Matrices", Journal = LinAlgApp, Volume = 29, Pages = "139--150" } @Article{ JenS75, Author = "A. Jennings and W.J. Stewart", Year = 1975, Title = "Simultaneous Iteration for the Partial Eigensolution of Real Matrices", Journal = InstMathApp, Volume = 15, Pages = "351--362" } @Article{ JenO74, Author = "L.S. Jennings and M.R. Osborne", Year = 1974, Title = "A Direct Error Analysis for Least Squares", Journal = NumerMath, Volume = 22, Pages = "322--332" } @Article{ Jen72, Author = "P.S. Jenson", Year = 1972, Title = "The Solution of Large Symmetric Eigenproblems by Sectioning", Journal = SIAMNumAnal, Volume = 9, Pages = "534--545" } @Article{ JohP71, Author = "J. Johnson and C.L. Phillips", Year = 1971, Title = "An Algorithm for the Computation of the Integral of the State Transition Matrix", Journal = IEEETransAC, Volume = "AC-16", Pages = "204--205" } @Article{ JohMP83, Author = "O.G. Johnson and C.A. Micchelli and G. Paul", Year = 1983, Title = "Polynomial Preconditioners for Conjugate Gradient Calculations", Journal = SIAMNumAnal, Volume = 20, Pages = "362--376" } @TechReport{ Joh84, Author = "S.L. Johnsson", Year = 1984, Title = "Odd-Even Cyclic Reduction on Ensemble Architectures and the Solution of Tridiagonal Systems of Equations", Number = "YALEU DCS RR-339", Institution = "Computer Science, Yale University", Address = "New Haven, CT" } @Article{ Joh85, Author = "S.L. Johnsson", Year = 1985, Title = "Solving Narrow Banded Systems on Ensemble Architectures", Journal = ACMMathSoft, Volume = 11, Pages = "271--288" } @InCollection{ Joh86, Author = "S.L. Johnsson", Year = 1986, Title = "Band Matrix System Solvers on Ensemble Architectures", BookTitle = "Supercomputers: Algorithms, Architectures, and Scientific Computation", Editor = "F.A. Matsen and T. Tajima", Publisher = TexasPress, Address = "Austin, TX", Pages = "196--216" } @Article{ Joh87b, Author = "S.L. Johnsson", Year = 1987, Title = "Solving Tridiagonal Systems on Ensemble Architectures", Journal = SIAMSciStat, Volume = 8, Pages = "354--392" } @Article{ Joh87a, Author = "S.L. Johnsson", Year = 1987, Title = "Communication Efficient Basic Linear Algebra Computations on Hypercube Multiprocessors", Journal = ParDistComp, Volume = 4, Pages = "133--172" } @TechReport{ JohH87c, Author = "S.L. Johnsson and C.T. Ho", Year = 1987, Title = "Multiple Tridiagonal Systems, the Alternating Direction Methods, and {B}oolean Cube Configured Multiprocessors", Number = "YALEU DCS RR-532", Institution = "Computer Science, Yale University", Address = "New Haven, CT" } @TechReport{ JohH87, Author = "S.L. Johnsson and C.T. Ho", Year = 1987, Title = "Algorithms for Multiplying Matrices of Arbitrary Shapes Using Shared Memory Primatives on a {B}oolean Cube", Number = "YALEU DCS RR-569", Institution = "Computer Science, Yale University", Address = "New Haven, CT" } @Article{ JohH88, Author = "S.L. Johnsson and C.T. Ho", Year = 1988, Title = "Algorithms for Matrix Transposition on {B}oolean {$N$}-Cube Configured Ensemble Architectures", Journal = SIAMMatrix, Volume = 9, Pages = "419--454" } @Article{ Joh71, Author = "R.L. Johnston", Year = 1971, Title = "{G}ershgorin Theorems for Partitioned Matrices", Journal = LinAlgApp, Volume = 4, Pages = "205--220" } @Article{ Jor87, Author = "H. Jordan", Year = 1987, Title = "Interpreting Parallel Processor Performance Measurements", Journal = SIAMSciStat, Volume = 8, Pages = "s220--s226" } @InProceedings{ Jor84, Author = "T. Jordan", Year = 1984, Title = "Conjugate Gradient Preconditioners for Vector and Parallel Processors", BookTitle = "Proceedings of the Conference on Elliptic Problem Solvers", Editor = "G. Birkoff and A. Schoenstadt", Publisher = Academic, Address = "New York" } @Article{ Kag77a, Author = "B. K{\aa}gstr{\"o}m", Year = 1977, Title = "Bounds and Perturbation Bounds for the Matrix Exponential", Journal = BIT, Volume = 17, Pages = "39--57" } @TechReport{ Kag77b, Author = "B. K{\aa}gstr{\"o}m", Year = 1977, Title = "Numerical Computation of Matrix Functions", Number = "UMINF-58.77", Institution = "Information Processing, University of Ume{\aa}", Address = "Ume{\aa}, Sweden" } @Article{ KagR80b, Author = "B. K{\aa}gstr{\"o}m and A. Ruhe", Year = 1980, Title = "An Algorithm for Numerical Computation of the {J}ordan Normal Form of a Complex Matrix", Journal = ACMMathSoft, Volume = 6, Pages = "398--419" } @Article{ KagR80a, Author = "B. K{\aa}gstr{\"o}m and A. Ruhe", Year = 1980, Title = "Algorithm~560~{JNF}: An Algorithm for Numerical Computation of the {J}ordan Normal Form of a Complex Matrix", Journal = ACMMathSoft, Volume = 6, Pages = "437--443" } @Article{ Kag85, Author = "B. K{\aa}gstr{\"o}m", Year = 1985, Title = "The Generalized Singular Value Decomposition and the General {$A - \lambda B$} Problem", Journal = BIT, Volume = 24, Pages = "568--583" } @Article{ Kag86, Author = "B. K{\aa}gstr{\"o}m", Year = 1986, Title = "{RGSVD}: An Algorithm for Computing the {K}ronecker Structure and Reducing Subspaces of Singular {$A - \lambda B$} Pencils", Journal = SIAMSciStat, Volume = 7, Pages = "185--211" } @TechReport{ KagL88, Author = "B. K{\aa}gstr{\"o}m and P. Ling", Year = 1988, Title = "Level 2 and 3 {BLAS} Routines for the {IBM 3090 VF/400}: Implementation and Experiences", Number = "UMINF-154.88", Institution = "Information Processing, University of Ume{\aa}", Address = "S-901 87 Ume{\aa}, Sweden" } @TechReport{ KagNP87, Author = "B. K{\aa}gstr{\"o}m and L. Nystr{\"o}m and P. Poromaa", Year = 1987, Title = "Parallel Algorithms for Solving the Triangular {S}ylvester Equation on a Hypercube Multiprocessor", Number = "UMINF-136.87", Institution = "Information Processing, University of Ume{\aa}", Address = "S-901 87 Ume{\aa}, Sweden" } @TechReport{ KagNP88, Author = "B. K{\aa}gstr{\"o}m and L. Nystr{\"o}m and P. Poromaa", Year = 1988, Title = "Parallel Shared Memory Algorithms for Solving the Triangular {S}ylvester Equation", Number = "UMINF-155.88", Institution = "Information Processing, University of Ume{\aa}", Address = "S-901 87 Ume{\aa}, Sweden" } @Proceedings{ KagR83, Editor = "B. K{\aa}gstr{\"o}m and A. Ruhe", Year = 1983, Title = "Proceedings of the Conference on Matrix Pencils, {P}ite {H}avsbad 1982", Series = "Lecture Notes in Mathematics", Volume = 973, Publisher = Springer, Address = "New York and Berlin" } @TechReport{ KagW87, Author = "B. K{\aa}gstr{\"o}m and L. Westin", Year = 1987, Title = "{GSYLV}- {F}ortran Routines for the Generalized {S}chur Method with dif$^{-1}$ estimators for Solving the Generalized {S}ylvester Equation", Number = "UMINF-132.86", Institution = "Information Processing, University of Ume{\aa}", Address = "S-901 87 Ume{\aa}, Sweden" } @Article{ Kah66, Author = "W. Kahan", Year = 1966, Title = "Numerical Linear Algebra", Journal = CanMathBull, Volume = 9, Pages = "757--801" } @TechReport{ Kah67, Author = "W. Kahan", Year = 1967, Title = "Inclusion Theorems for Clusters of Eigenvalues of {H}ermitian Matrices", Type = "report", Institution = "Computer Science, University of Toronto", Address = "Toronto, Canada" } @Article{ Kah75, Author = "W. Kahan", Year = 1975, Title = "Spectra of Nearly {H}ermitian Matrices", Journal = ProcAMS, Volume = 48, Pages = "11--17" } @TechReport{ KahP74, Author = "W. Kahan and B.N. Parlett", Year = 1974, Title = "An Analysis of {L}anczos Algorithms for Symmetric Matrices", Number = "ERL-M467", Institution = "University of California, Berkeley", Address = "Berkeley, CA" } @InCollection{ KahP76, Author = "W. Kahan and B.N. Parlett", Year = 1976, Title = "How Far Should You Go with the {L}anczos Process?", BookTitle = "Sparse Matrix Computations", Editor = "J. Bunch and D. Rose", Publisher = Academic, Address = "New York", Pages = "131--144" } @Article{ KahPJ82, Author = "W. Kahan and B.N. Parlett and E. Jiang", Year = 1982, Title = "Residual Bounds on Approximate Eigensystems of Nonnormal Matrices", Journal = SIAMNumAnal, Volume = 19, Pages = "470--484" } @Book{ KahMN88, Author = "D. Kahaner and C.B. Moler and S. Nash", Year = 1988, Title = "Numerical Methods and Software", Publisher = PrenticeHall, Address = "Englewood Cliffs, NJ" } @Article{ Kan66, Author = "S. Kaniel", Year = 1966, Title = "Estimates for Some Computational Techniques in Linear Algebra", Journal = MathComp, Volume = 20, Pages = "369--378" } @Article{ KapB84, Author = "R.N. Kapur and J.C. Browne", Year = 1984, Title = "Techniques for Solving Block Tridiagonal Systems on Reconfigurable Array Computers", Journal = SIAMSciStat, Volume = 5, Pages = "701--719" } @Article{ Kar74, Author = "I. Karasalo", Year = 1974, Title = "A Criterion for Truncation of the {QR} Decomposition Algorithm for the Singular Linear Least Squares Problem", Journal = BIT, Volume = 14, Pages = "156--166" } @Book{ Kat66, Author = "T. Kato", Year = 1966, Title = "Perturbation Theory for Linear Operators", Publisher = Springer, Address = "New York, NY" } @Article{ Kau74, Author = "L. Kaufman", Year = 1974, Title = "The {LZ} Algorithm to Solve the Generalized Eigenvalue Problem", Journal = SIAMNumAnal, Volume = 11, Pages = "997--1024" } @Article{ Kau77, Author = "L. Kaufman", Year = 1977, Title = "Some Thoughts on the {QZ} Algorithm for Solving the Generalized Eigenvalue Problem", Journal = ACMMathSoft, Volume = 3, Pages = "65--75" } @Article{ Kau79, Author = "L. Kaufman", Year = 1979, Title = "Application of Dense {H}ouseholder Transformations to a Sparse Matrix", Journal = ACMMathSoft, Volume = 5, Pages = "442--450" } @Article{ Kau83, Author = "L. Kaufman", Year = 1983, Title = "Matrix Methods for Queueing Problems", Journal = SIAMSciStat, Volume = 4, Pages = "525--552" } @Article{ Kau87, Author = "L. Kaufman", Year = 1987, Title = "The Generalized {H}ouseholder Transformation and Sparse Matrices", Journal = LinAlgApp, Volume = 90, Pages = "221--234" } @Article{ KauG83, Author = "J. Kautsky and G.H. Golub", Year = 1983, Title = "On the Calculation of {J}acobi Matrices", Journal = LinAlgApp, Volume = "52/53", Pages = "439--456" } @InCollection{ Ker82, Author = "D. Kershaw", Year = 1982, Title = "Solution of Single Tridiagonal Linear Systems and Vectorization of the {ICCG} Algorithm on the {C}ray-1", BookTitle = "Parallel Computation", Editor = "G. Roderigue", Publisher = Academic, Address = "New York" } @Article{ Kie87, Author = "A. Kielbasinski", Year = 1987, Title = "A Note on Rounding Error Analysis of {C}holesky Factorization", Journal = LinAlgApp, Volume = "88/89", Pages = "487--494" } @Book{ Knu81, Author = "D. Knuth", Year = 1981, Title = "Seminumerical-Algorithms", Edition = "second", Publisher = AddisonWesley, Address = "Reading, MA", Volume = 2, Series = "The Art of Computer Programming", } @Article{ Kog55, Author = "E.G. Kogbetliantz", Year = 1955, Title = "Solution of Linear Equations by Diagonalization of Coefficient Matrix", Journal = QuartApplMath, Volume = 13, Pages = "123--132" } @Article{ KouP81, Author = "S. Kourouklis and C.C. Paige", Year = 1981, Title = "A Constrained Least Squares Approach to the General {G}auss-{M}arkov Linear Model", Journal = AmerStatAssoc, Volume = 76, Pages = "620--625" } @Article{ KriM86a, Author = "A.S. Krishnakuma and M. Morf", Year = 1986, Title = "Eigenvalues of a Symmetric Tridiagonal Matrix: A Divide and Conquer Approach", Journal = NumerMath, Volume = 48, Pages = "349--368" } @Article{ Kub61, Author = "V.N. Kublanovskaya", Year = 1961, Title = "On Some Algorithms for the Solution of the Complete Eigenvalue Problem", Journal = USSRCompMathPhys, Volume = 3, Pages = "637--657" } @Article{ KubF64, Author = "V.N. Kublanovskaya and V.N. Fadeeva", Year = 1964, Title = "Computational Methods for the Solution of a Generalized Eigenvalue Problem", Journal = AMSTrans, Volume = 2, Pages = "271--290" } @Article{ KulM86b, Author = "U.W. Kulisch and W.L. Miranker", Year = 1986, Title = "The Arithmetic of the Digital Computer", Journal = SIAMReview, Volume = 28, Pages = "1--40" } @Article{ Kun82, Author = "H.T. Kung", Year = 1982, Title = "Why Systolic Architectures?", Journal = Computer, Volume = 15, Pages = "37--46" } @Article{ Bud64, Author = "C.D. La Budde", Year = 1964, Title = "Two Classes of Algorithms for Finding the Eigenvalues and Eigenvectors of Real Symmetric Matrices", Journal = JACM, Volume = 11, Pages = "53--58" } @Article{ LamV75, Author = "J. Lambiotte and R.G. Voigt", Year = 1975, Title = "The Solution of Tridiagonal Linear Systems on the {CDC-STAR 100} Computer", Journal = ACMMathSoft, Volume = 1, Pages = "308--329" } @Article{ Lan70, Author = "P. Lancaster", Year = 1970, Title = "Explicit Solution of Linear Matrix Equations", Journal = SIAMReview, Volume = 12, Pages = "544--566" } @Book{ LanT85, Author = "P. Lancaster and M. Tismenetsky", Year = 1985, Title = "The Theory of Matrices", Edition = "second", Publisher = Academic, Address = "New York" } @Article{ Lan50, Author = "C. Lanczos", Year = 1950, Title = "An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators", Journal = JResNatBurStand, Volume = 45, Pages = "255--282" } @Article{ LarS78, Author = "J. Larson and A. Sameh", Year = 1978, Title = "Efficient Calculation of the Effects of Roundoff Errors", Journal = ACMMathSoft, Volume = 4, Pages = "228--236" } @Article{ Lau81, Author = "A. Laub", Year = 1981, Title = "Efficient Multivariable Frequency Response Computations", Journal = IEEETransAC, Volume = "AC-26", Pages = "407--408" } @Article{ Lau85, Author = "A. Laub", Year = 1985, Title = "Numerical Linear Algebra Aspects of Control Design Computations", Journal = IEEETransAC, Volume = "AC-30", Pages = "97--108" } @Article{ LawH69, Author = "C.L. Lawson and R.J. Hanson", Year = 1969, Title = "Extensions and Applications of the {H}ouseholder Algorithm for Solving Linear Least Squares Problems", Journal = MathComp, Volume = 23, Pages = "787--812" } @Book{ LawH74, Author = "C.L. Lawson and R.J. Hanson", Year = 1974, Title = "Solving Least Squares Problems", Publisher = PrenticeHall, Address = "Englewood Cliffs, NJ" } @Article{ LawHKK79b, Author = "C.L. Lawson and R.J. Hanson and D.R. Kincaid and F.T. Krogh", Year = 1979, Title = "Basic Linear Algebra Subprograms for {F}ortran Usage", Journal = ACMMathSoft, Volume = 5, Pages = "308--323" } @Article{ LawHKK79a, Author = "C.L. Lawson and R.J. Hanson and D.R. Kincaid and F.T. Krogh", Year = 1979, Title = "Algorithm~539: Basic Linear Algebra Subprograms for {F}ortran Usage", Journal = ACMMathSoft, Volume = 5, Pages = "324--325" } @Article{ Leh63, Author = "N.J. Lehmann", Year = 1963, Title = "Optimale {E}igenwerteinschliessungen", Journal = NumerMath, Volume = 5, Pages = "246--272" } @Article{ Lem73, Author = "F. Lemeire", Year = 1973, Title = "Bounds for Condition Numbers of Triangular and Trapezoid Matrices", Journal = BIT, Volume = 15, Pages = "58--64" } @Book{ Leo80, Author = "S.J. Leon", Year = 1980, Title = "Linear Algebra with Applications.", Publisher = Macmillan, Address = "New York, NY" } @Article{ Lev47, Author = "N. Levinson", Year = 1947, Title = "The {W}einer {RMS} Error Criterion in Filter Design and Prediction", Journal = MathPhys, Volume = 25, Pages = "261--278" } @TechReport{ Lew77, Author = "J. Lewis", Year = 1977, Title = "Algorithms for Sparse Matrix Eigenvalue Problems", Number = "STAN-CS-77-595", Institution = "Department of Computer Science, Stanford University", Address = "Stanford, CA" } @Article{ LiC88, Author = "G. Li and T. Coleman", Year = 1988, Title = "A Parallel Triangular Solver for a Distributed-Memory Multiprocessor", Journal = SIAMSciStat, Volume = 9, Pages = "485--502" } @Book{ Lin61, Author = "I. Linnik", Year = 1961, Title = "Method of Least Squares and Principles of the Theory of Observation", Publisher = PergamonPress, Address = "New York, NY" } @Article{ LoPS87, Author = "S. Lo and B. Philippe and A. Sameh", Year = 1987, Title = "A Multiprocessor Algorithm for the Symmetric Tridiagonal Eigenvalue Problem", Journal = SIAMSciStat, Volume = 8, Pages = "s155--s165" } @Article{ Loi69, Author = "G. Loizou", Year = 1969, Title = "Nonnormality and {J}ordan Condition Numbers of Matrices", Journal = JACM, Volume = 16, Pages = "580--584" } @Article{ Loi72, Author = "G. Loizou", Year = 1972, Title = "On the Quadratic Convergence of the {J}acobi Method for Normal Matrices", Journal = CompJour, Volume = 15, Pages = "274--276" } @Article{ Lot56, Author = "M. Lotkin", Year = 1956, Title = "Characteristic Values of Arbitrary Matrices", Journal = QuartApplMath, Volume = 14, Pages = "267--275" } @Book{ Lue73, Author = "D. G. Luenberger", Year = 1973, Title = "Introduction to Linear and Nonlinear Programming", Publisher = AddisonWesley, Address = "New York" } @PhDThesis{ Luk78, Author = "F.T. Luk", Year = 1978, Title = "Sparse and Parallel Matrix Computations", Number = "STAN-CS-78-685", School = "Computer Science, Stanford University", Address = "Stanford, CA" } @Article{ Luk80, Author = "F.T. Luk", Year = 1980, Title = "Computing the Singular Value Decomposition on the {ILLIAC IV}", Journal = ACMMathSoft, Volume = 6, Pages = "524--539" } @Article{ Luk86a, Author = "F.T. Luk", Year = 1986, Title = "A Rotation Method for Computing the {QR} Factorization", Journal = SIAMSciStat, Volume = 7, Pages = "452--459" } @Article{ Luk86b, Author = "F.T. Luk", Year = 1986, Title = "A Triangular Processor Array for Computing Singular Values", Journal = LinAlgApp, Volume = 77, Pages = "259--274" } @TechReport{ LusO83, Author = "E. Lusk and R. Overbeek", Year = 1983, Title = "Implementation of Monitors with Macros: A Programming Aid for the {HEP} and other Parallel Processors", Number = "83-97", Institution = "Argonne National Laboratory", Address = "Argonne, ILL" } @Article{ McCS73a, Author = "C. McCarthy and G. Strang", Year = 1973, Title = "Optimal Conditioning of Matrices", Journal = SIAMNumAnal, Volume = 10, Pages = "370--388" } @Article{ McC72, Author = "S.F. McCormick", Year = 1972, Title = "A General Approach to One-Step Iterative Methods with Application to Eigenvalue Problems", Journal = CompSysSci, Volume = 6, Pages = "354--372" } @Article{ McK62, Author = "W.M. McKeeman", Year = 1962, Title = "Crout with Equilibration and Iteration", Journal = CACM, Volume = 5, Pages = "553--555" } @Article{ Mad59, Author = "A. Madansky", Year = 1959, Title = "The Fitting of Straight Lines When Both Variables Are Subject to Error", Journal = AmerStatAssoc, Volume = 54, Pages = "173--205" } @Article{ MadRK76, Author = "N. Madsen and G. Roderigue and J. Karush", Year = 1976, Title = "Matrix Multiplication by Diagonals of a Vector Parallel Processor", Journal = InfProcLet, Pages = "41--45" } @Article{ Mah79, Author = "K.N. Mahindar", Year = 1979, Title = "Linear Combinations of {H}ermitian and Real Symmetric Matrices", Journal = LinAlgApp, Volume = 25, Pages = "95--105" } @Article{ Mak75, Author = "J. Makhoul", Year = 1975, Title = "Linear Prediction: A Tutorial Review", Journal = ProcIEEE, Volume = "63(4)", Pages = "561--580" } @Article{ MalP74, Author = "M.A. Malcolm and J. Palmer", Year = 1974, Title = "A Fast Method For Solving a Class of Tridiagonal Systems of Linear Equations", Journal = CACM, Volume = 17, Pages = "14--17" } @Article{ Man77, Author = "T.A. Manteuffel", Year = 1977, Title = "The {T}chebychev Iteration for Nonsymmetric Linear Systems", Journal = NumerMath, Volume = 28, Pages = "307--327" } @InProceedings{ Man79, Author = "T.A. Manteuffel", Year = 1979, Title = "Shifted Incomplete {C}holesky Factorization", BookTitle = "Sparse Matrix Proceedings 1978", Editor = "I.S. Duff and G.W. Stewart", Publisher = SIAMPub, Address = "Philadelphia, PA" } @Book{ MarM64, Author = "M. Marcus and H. Minc", Year = 1964, Title = "A Survey of Matrix Theory and Matrix Inequalities", Publisher = AllynBacon, Address = "Boston, MA" } @Book{ MarG76, Author = "J. Markel and A. Gray", Year = 1976, Title = "Linear Prediction of Speech", Publisher = Springer, Address = "Berlin and New York" } @Article{ MarPW65, Author = "R.S. Martin and G. Peters and J.H. Wilkinson", Year = 1965, Title = "Symmetric Decomposition of a Positive Definite Matrix", Journal = NumerMath, Volume = 7, Pages = "362--383", Note = "Also in \cite[pages 9--30]{WilR71}" } @Article{ MarPW66, Author = "R.S. Martin and G. Peters and J.H. Wilkinson", Year = 1966, Title = "Iterative Refinement of the Solution of a Positive Definite System of Equations", Journal = NumerMath, Volume = 8, Pages = "203--216", Note = "Also in \cite[pages 31--44]{WilR71}" } @Article{ MarPW70, Author = "R.S. Martin and G. Peters and J.H. Wilkinson", Year = 1970, Title = "The {QR} Algorithm for Real {H}essenberg Matrices", Journal = NumerMath, Volume = 14, Pages = "219--231", Note = "Also in \cite[pages 359--371]{WilR71}" } @Article{ MarRW70, Author = "R.S. Martin and C. Reinsch and J.H. Wilkinson", Year = 1970, Title = "The {QR} Algorithm for Band Symmetric Matrices", Journal = NumerMath, Volume = 16, Pages = "85--92", Note = "Also in \cite[pages 266--272]{WilR71}" } @Article{ MarW65, Author = "R.S. Martin and J.H. Wilkinson", Year = 1965, Title = "Symmetric Decomposition of Positive Definite Band Matrices", Journal = NumerMath, Volume = 7, Pages = "355--361", Note = "Also in \cite[pages 50--56]{WilR71}" } @Article{ MarW67, Author = "R.S. Martin and J.H. Wilkinson", Year = 1967, Title = "Solution of Symmetric and Unsymmetric Band Equations and the Calculation of Eigenvalues of Band Matrices", Journal = NumerMath, Volume = 9, Pages = "279--301", Note = "Also in \cite[pages 70--92]{WilR71}" } @Article{ MarW68a, Author = "R.S. Martin and J.H. Wilkinson", Year = 1968, Title = "{H}ouseholder's Tridiagonalization of a Symmetric Matrix", Journal = NumerMath, Volume = 11, Pages = "181--195", Note = "Also in \cite[pages 212--226]{WilR71}" } @Article{ MarW68b, Author = "R.S. Martin and J.H. Wilkinson", Year = 1968, Title = "The Modified {LR} Algorithm for Complex {H}essenberg Matrices", Journal = NumerMath, Volume = 12, Pages = "369--376", Note = "Also in \cite[pages 396--403]{WilR71}" } @Article{ MarW68c, Author = "R.S. Martin and J.H. Wilkinson", Year = 1968, Title = "Reduction of the Symmetric Eigenproblem {$Ax = \lambda Bx$} and Related Problems to Standard Form", Journal = NumerMath, Volume = 11, Pages = "99--110" } @Article{ MarW68d, Author = "R.S. Martin and J.H. Wilkinson", Year = 1968, Title = "Similarity Reduction of a General Matrix to {H}essenberg Form", Journal = NumerMath, Volume = 12, Pages = "349--368", Note = "Also in \cite[pages 339--358]{WilR71}" } @Article{ MvdV87, Author = "O. McBryan and van de Velde, E.F.", Year = 1987, Title = "Hypercube Algorithms and Implementations", Journal = SIAMSciStat, Volume = 8, Pages = "s227--s287" } @Article{ MdV77, Author = "J.A. Meijerink and Van der Vorst, H.A.", Year = 1977, Title = "An Iterative Solution Method for Linear Equations Systems of Which the Coefficient Matrix is a Symmetric {$M$}-Matrix", Journal = MathComp, Volume = 31, Pages = "148--162" } @Article{ Mei83, Author = "J. Meinguet", Year = 1983, Title = "Refined Error Analyses of {C}holesky Factorization", Journal = SIAMNumAnal, Volume = 20, Pages = "1243--1250" } @Article{ Mel87, Author = "R. Melhem", Year = 1987, Title = "Toward efficient Implementation of Preconditioned Conjugate Gradient Methods on Vector Supercomputers", Journal = IntSuper, Volume = 1, Pages = "70--98" } @Article{ Mer85, Author = "M.L. Merriam", Year = 1985, Title = "On the Factorization of Block Tridiagonals With Storage Constraints", Journal = SIAMSciStat, Volume = 6, Pages = "182--192" } @Article{ Meu84, Author = "G. Meurant", Year = 1984, Title = "The Block Preconditioned Conjugate Gradient Method on Vector Computers", Journal = BIT, Volume = 24, Pages = "623--633" } @Article{ Meu89, Author = "G. Meurant", Year = 1989, Title = "Domain Decomposition Methods for Partial Differential Equations on Parallel Computers", Journal = IntSuper, Note = "To appear" } @Article{ Mil75, Author = "W. Miller", Year = 1975, Title = "Computational Complexity and Numerical Stability", Journal = SIAMComp, Volume = 4, Pages = "97--107" } @Article{ MilS78, Author = "W. Miller and D. Spooner", Year = 1978, Title = "Software for Roundoff Analysis, {II}", Journal = ACMMathSoft, Volume = 4, Pages = "369--390" } @Article{ MimP82, Author = "G. Miminis and C.C. Paige", Year = 1982, Title = "An Algorithm for Pole Assignment of Time Invariant Linear Systems", Journal = IntControl, Volume = 35, Pages = "341--354" } @Book{ Mir55, Author = "L. Mirsky", Year = 1955, Title = "An Introduction to Linear Algebra", Publisher = OxfordPress, Address = "London, England" } @Article{ Mir60, Author = "L. Mirsky", Year = 1960, Title = "Symmetric Gauge Functions and Unitarily Invariant Norms", Journal = QuartMath, Volume = 11, Pages = "50--59" } @Book{ Mod88, Author = "J.J. Modi", Year = 1988, Title = "Parallel Algorithms and Matrix Computation", Publisher = OxfordPress, Address = "Oxford" } @Article{ ModC86, Author = "J.J. Modi and M.R.B. Clarke", Year = 1986, Title = "An Alternative {G}ivens Ordering", Journal = NumerMath, Volume = 43, Pages = "83--90" } @Article{ ModP85, Author = "J.J. Modi and J.D. Pryce", Year = 1985, Title = "Efficient Implementation of {J}acobi's Diagonalization Method on the {DAP}", Journal = NumerMath, Volume = 46, Pages = "443--454" } @Article{ Mol67, Author = "C.B. Moler", Year = 1967, Title = "Iterative Refinement in Floating Point", Journal = JACM, Volume = 14, Pages = "316--371" } @TechReport{ Mol80, Author = "C.B. Moler", Year = 1980, Title = "{MATLAB} User's Guide", Number = "CS81-1", Institution = "Computer Science, University of New New Mexico", Address = "Albuquerque, NM" } @InCollection{ Mol86, Author = "C.B. Moler", Year = 1986, Title = "Matrix Computations on Distributed Memory Multiprocessors", BookTitle = "Hypercube Multiprocessors", Editor = "M.T. Heath", Publisher = SIAMPub, Address = "Philadelphia, PA" } @Manual{ MolLB87, Author = "C.B. Moler and J.N. Little and S. Bangert", Year = 1987, Title = "{PC}-{M}atlab Users Guide", Publisher = MathWorks, Address = "20 N. Main St., Sherborn, MA", } @Article{ MolM83, Author = "C.B. Moler and D. Morrison", Year = 1983, Title = "Singular Value Analysis of Cryptograms", Journal = AmerMathMonthly, Volume = 90, Pages = "78--87" } @Article{ MolS73b, Author = "C.B. Moler and G.W. Stewart", Year = 1973, Title = "An Algorithm for Generalized Matrix Eigenvalue Problems", Journal = SIAMNumAnal, Volume = 10, Pages = "241--256" } @Article{ MolL78, Author = "C.B. Moler and Van Loan, C.F.", Year = 1978, Title = "Nineteen Dubious Ways to Compute the Exponential of a Matrix", Journal = SIAMReview, Volume = 20, Pages = "801--836" } @Article{ MonL82, Author = "R. Montoye and D. Laurie", Year = 1982, Title = "A Practical Algorithm for the Solution of Triangular Systems on a Parallel Processing System", Journal = IEEETransComp, Volume = "C-31", Pages = "1076--1082" } @Article{ Mue66, Author = "D. Mueller", Year = 1966, Title = "{H}ouseholder's Method for Complex Matrices and {H}ermitian Matrices", Journal = NumerMath, Volume = 8, Pages = "72--92" } @Article{ MurW31, Author = "F.D. Murnaghan and A. Wintner", Year = 1931, Title = "A Canonical Form for Real Matrices Under Orthogonal Transformations", Journal = ProcNAS, Volume = 17, Pages = "417--420" } @Article{ Nan85, Author = "T. Nanda", Year = 1985, Title = "Differential Equations and the {QR} Algorithm", Journal = SIAMNumAnal, Volume = 22, Pages = "310--321" } @Article{ Nas75, Author = "J.C. Nash", Year = 1975, Title = "A One-Sided Transformation Method for the Singular Value Decomposition and Algebraic Eigenproblem", Journal = CompJour, Volume = 18, Pages = "74--76" } @Book{ Nas76, Author = "M.Z. Nashed", Year = 1976, Title = "Generalized Inverses and Applications", Publisher = Academic, Address = "New York, NY" } @Article{ Nic74, Author = "R.A. Nicolaides", Year = 1974, Title = "On a Geometrical Aspect of {SOR} and the Theory of Consistent Ordering for Positive Definite Matrices", Journal = NumerMath, Volume = 23, Pages = "99--104" } @Article{ NieV83, Author = "W. Niethammer and R.S. Varga", Year = 1983, Title = "The Analysis of {$k$}-step Iterative Methods for Linear Systems from Summability Theory", Journal = NumerMath, Volume = 41, Pages = "177--206" } @Book{ NobD77, Author = "B. Noble and J.W. Daniel", Year = 1977, Title = "Applied Linear Algebra", Publisher = PrenticeHall, Address = "Englewood Cliffs, NJ" } @Article{ NooV75, Author = "A. Noor and R. Voigt", Year = 1975, Title = "Hypermatrix Scheme for the {STAR-100} Computer", Journal = CompStruct, Volume = 5, Pages = "287--296" } @Article{ OetP64, Author = "W. Oettli and W. Prager", Year = 1964, Title = "Compatibility of Approximate Solutions of Linear Equations with Given Error Bounds for Coefficients and Right Hand Sides", Journal = NumerMath, Volume = 6, Pages = "405--409" } @PhDThesis{ OLe76, Author = "D.P. O'Leary", Year = 1976, Title = "Hybrid Conjugate Gradient Algorithms", Number = "STAN-CS-76-548", School = "Computer Science, Stanford University", Address = "Stanford, CA" } @Article{ OLe80a, Author = "D.P. O'Leary", Year = 1980, Title = "The Block Conjugate Gradient Algorithm and Related Methods", Journal = LinAlgApp, Volume = 29, Pages = "293--322" } @Article{ OLe80b, Author = "D.P. O'Leary", Year = 1980, Title = "Estimating Matrix Condition Numbers", Journal = SIAMSciStat, Volume = 1, Pages = "205--209" } @Article{ OLeS81, Author = "D.P. O'Leary and J.A. Simmons", Year = 1981, Title = "A Bidiagonalization - Regularization Procedure for Large Scale Discretizations of Ill-Posed Problems", Journal = SIAMSciStat, Volume = 2, Pages = "474--489" } @Article{ OLeS85, Author = "D.P. O'Leary and G.W. Stewart", Year = 1985, Title = "Data Flow Algorithms for Parallel Matrix Computations", Journal = CACM, Volume = 28, Pages = "841--853" } @Article{ OLeS86, Author = "D.P. O'Leary and G.W. Stewart", Year = 1986, Title = "Assignment and Scheduling in Parallel Matrix Factorization", Journal = LinAlgApp, Volume = 77, Pages = "275--300" } @Book{ Opp78, Author = "A.V. Oppenheim", Year = 1978, Title = "Applications of Digital Signal Processing", Publisher = PrenticeHall, Address = "Englewood Cliffs, NJ" } @Book{ Ort72, Author = "J.M. Ortega", Year = 1972, Title = "Numerical Analysis: A Second Course", Publisher = Academic, Address = "New York, NY" } @Book{ Ort88, Author = "J.M. Ortega", Year = 1988, Title = "Matrix Theory: A Second Course", Publisher = PlenumPress, Address = "New York" } @Article{ OrtR88, Author = "J.M. Ortega and C.H. Romine", Year = 1988, Title = "The {$ijk$} Forms of Factorization Methods {II}: Parallel Systems", Journal = ParComputing, Volume = 7, Pages = "149--162" } @Article{ OrtV85, Author = "J.M. Ortega and R.G. Voigt", Year = 1985, Title = "Solution of Partial Differential Equations on Vector and Parallel Computers", Journal = SIAMReview, Volume = 27, Pages = "149--240" } @Article{ Osb60, Author = "E.E. Osborne", Year = 1960, Title = "On Preconditioning of Matrices", Journal = JACM, Volume = 7, Pages = "338--345" } @Article{ Paa71, Author = "M.H.C. Paardekooper", Year = 1971, Title = "An Eigenvalue Algorithm for Skew Symmetric Matrices", Journal = NumerMath, Volume = 17, Pages = "189--202" } @Article{ Pai70, Author = "C.C. Paige", Year = 1970, Title = "Practical Use of the Symmetric {L}anczos Process with Reorthogonalization", Journal = BIT, Volume = 10, Pages = "183--195" } @PhDThesis{ Pai71, Author = "C.C. Paige", Year = 1971, Title = "The Computation of Eigenvalues and Eigenvectors of Very Large Sparse Matrices", School = "London University", Address = "London, England" } @Article{ Pai73, Author = "C.C. Paige", Year = 1973, Title = "An Error Analysis of a Method for Solving Matrix Equations", Journal = MathComp, Volume = 27, Pages = "355--359" } @Article{ Pai74a, Author = "C.C. Paige", Year = 1974, Title = "Bidiagonalization of Matrices and Solution of Linear Equations", Journal = SIAMNumAnal, Volume = 11, Pages = "197--209" } @Article{ Pai74b, Author = "C.C. Paige", Year = 1974, Title = "Eigenvalues of Perturbed {H}ermitian Matrices", Journal = LinAlgApp, Volume = 8, Pages = "1--10" } @Article{ Pai76, Author = "C.C. Paige", Year = 1976, Title = "Error Analysis of the {L}anczos Algorithm for Tridiagonalizing a Symmetric Matrix", Journal = InstMathApp, Volume = 18, Pages = "341--349" } @Article{ Pai79a, Author = "C.C. Paige", Year = 1979, Title = "Computer Solution and Perturbation Analysis of Generalized Least Squares Problems", Journal = MathComp, Volume = 33, Pages = "171--184" } @Article{ Pai79b, Author = "C.C. Paige", Year = 1979, Title = "Fast Numerically Stable Computations for Generalized Linear Least Squares Problems", Journal = SIAMNumAnal, Volume = 16, Pages = "165--171" } @Article{ Pai80, Author = "C.C. Paige", Year = 1980, Title = "Accuracy and Effectiveness of the {L}anczos Algorithm for the Symmetric Eigenproblem", Journal = LinAlgApp, Volume = 34, Pages = "235--258" } @Article{ Pai81, Author = "C.C. Paige", Year = 1981, Title = "Properties of Numerical Algorithms Related to Computing Controllability", Journal = IEEETransAC, Volume = "AC-26", Pages = "130--138" } @Article{ Pai84, Author = "C.C. Paige", Year = 1984, Title = "A Note on a Result of {S}un {J}.-{G}uang: Sensitivity of the {CS} and {GSV} Decompositions", Journal = SIAMNumAnal, Volume = 21, Pages = "186--191" } @Article{ Pai85, Author = "C.C. Paige", Year = 1985, Title = "The General Linear Model and the Generalized Singular Value Decomposition", Journal = LinAlgApp, Volume = 70, Pages = "269--284" } @Article{ Pai86, Author = "C.C. Paige", Year = 1986, Title = "Computing the Generalized Singular Value Decomposition", Journal = SIAMSciStat, Volume = 7, Pages = "1126--1146" } @Article{ PaiD86, Author = "C.C. Paige and Van Dooren, P.", Year = 1986, Title = "On the Quadratic Convergence of {K}ogbetliantz's Algorithm for Computing the Singular Value Decomposition", Journal = LinAlgApp, Volume = 77, Pages = "301--313" } @Article{ PaiS75, Author = "C.C. Paige and M.A. Saunders", Year = 1975, Title = "Solution of Sparse Indefinite Systems of Linear Equations", Journal = SIAMNumAnal, Volume = 12, Pages = "617--629" } @TechReport{ PaiS78, Author = "C.C. Paige and M.A. Saunders", Year = 1978, Title = "A Bidiagonalization Algorithm for Sparse Linear Equations and Least Squares Problems", Number = "SOL 78-19", Institution = "Operations Research, Stanford University", Address = "Stanford, CA" } @Article{ PaiS81, Author = "C.C. Paige and M. Saunders", Year = 1981, Title = "Towards A Generalized Singular Value Decomposition", Journal = SIAMNumAnal, Volume = 18, Pages = "398--405" } @Article{ PaiS82b, Author = "C.C. Paige and M.A. Saunders", Year = 1982, Title = "{LSQR}: An Algorithm for Sparse Linear Equations and Sparse Least Squares", Journal = ACMMathSoft, Volume = 8, Pages = "43--71" } @Article{ PaiS82a, Author = "C.C. Paige and M.A. Saunders", Year = 1982, Title = "Algorithm~583~{LSQR}: Sparse Linear Equations and Least Squares Problems", Journal = ACMMathSoft, Volume = 8, Pages = "195--209" } @Article{ PaiL81, Author = "C.C. Paige and Van Loan, C.", Year = 1981, Title = "A {S}chur Decomposition for {H}amiltonian Matrices", Journal = LinAlgApp, Volume = 41, Pages = "11--32" } @Article{ Pan84, Author = "V. Pan", Year = 1984, Title = "How Can We Speed Up Matrix Multiplication?", Journal = SIAMReview, Volume = 26, Pages = "393--416" } @Article{ Par65, Author = "B.N. Parlett", Year = 1965, Title = "Convergence of the {QR} Algorithm", Journal = NumerMath, Volume = 7, Pages = "187--193", Note = "Correction in Numerische Mathematik 10, pp. 163--164" } @Article{ Par66, Author = "B.N. Parlett", Year = 1966, Title = "Singular and Invariant Matrices Under the {QR} Algorithm", Journal = MathComp, Volume = 20, Pages = "611--615" } @Article{ Par67, Author = "B.N. Parlett", Year = 1967, Title = "Canonical Decomposition of {H}essenberg Matrices", Journal = MathComp, Volume = 21, Pages = "223--227" } @Article{ Par68, Author = "B.N. Parlett", Year = 1968, Title = "Global Convergence of the Basic {QR} Algorithm on {H}essenberg Matrices", Journal = MathComp, Volume = 22, Pages = "803--817" } @Article{ Par71, Author = "B.N. Parlett", Year = 1971, Title = "Analysis of Algorithms for Reflections in Bisectors", Journal = SIAMReview, Volume = 13, Pages = "197--208" } @TechReport{ Par74a, Author = "B.N. Parlett", Year = 1974, Title = "Computation of Functions of Triangular Matrices", Type = "Memorandum", Number = "ERL-M481", Institution = "Electronics Research Laboratory, College of Engineering, University of California, Berkeley", Address = "Berkeley, CA" } @Article{ Par74b, Author = "B.N. Parlett", Year = 1974, Title = "The {R}ayleigh Quotient Iteration and Some Generalizations for Nonnormal Matrices", Journal = MathComp, Volume = 28, Pages = "679--693" } @Article{ Par76, Author = "B.N. Parlett", Year = 1976, Title = "A Recurrence Among the Elements of Functions of Triangular Matrices", Journal = LinAlgApp, Volume = 14, Pages = "117--121" } @Article{ Par80a, Author = "B.N. Parlett", Year = 1980, Title = "A New Look at the {L}anczos Algorithm for Solving Symmetric Systems and Linear Equations", Journal = LinAlgApp, Volume = 29, Pages = "323--346" } @Book{ Par80b, Author = "B.N. Parlett", Year = 1980, Title = "The Symmetric Eigenvalue Problem", Publisher = PrenticeHall, Address = "Englewood Cliffs, NJ" } @Article{ ParNO85, Author = "B.N. Parlett and B. Nour-Omid", Year = 1985, Title = "The Use of a Refined Error Bound When Updating Eigenvalues of Tridiagonals", Journal = LinAlgApp, Volume = 68, Pages = "179--220" } @Article{ ParP73, Author = "B.N. Parlett and W.G. Poole", Year = 1973, Title = "A Geometric Theory for the {QR}, {LU}, and Power Iterations", Journal = SIAMNumAnal, Volume = 10, Pages = "389--412" } @Article{ ParR70, Author = "B.N. Parlett and J.K. Reid", Year = 1970, Title = "On the Solution of a System of Linear Equations Whose Matrix is Symmetric But Not Definite", Journal = BIT, Volume = 10, Pages = "386--397" } @Article{ ParR81, Author = "B.N. Parlett and J.K. Reid", Year = 1981, Title = "Tracking the Progress of the {L}anczos Algorithm for Large Symmetric Eigenproblems", Journal = IMANumerAna, Volume = 1, Pages = "135--155" } @Article{ ParR69, Author = "B.N. Parlett and C. Reinsch", Year = 1969, Title = "Balancing a Matrix for Calculation of Eigenvalues and Eigenvectors", Journal = NumerMath, Volume = 13, Pages = "292-304", Note = "Also in \cite[pages 315--326]{WilR71}" } @Article{ ParS79, Author = "B.N. Parlett and D.S. Scott", Year = 1979, Title = "The {L}anczos Algorithm with Selective Orthogonalization", Journal = MathComp, Volume = 33, Pages = "217--238" } @Article{ ParSS82, Author = "B.N. Parlett and H. Simon and L.M. Stringer", Year = 1982, Title = "On Estimating the Largest Eigenvalue with the {L}anczos Algorithm", Journal = MathComp, Volume = 38, Pages = "153--166" } @Article{ PatJ84, Author = "N. Patel and H. Jordan", Year = 1984, Title = "A Parallelized Point Rowwise Successive Over-Relaxation Method on a Multiprocessor", Journal = ParComputing, Volume = 1, Pages = "207--222" } @Article{ PatS73, Author = "M.S. Paterson and L.J. Stockmeyer", Year = 1973, Title = "On the Number of Nonscalar Multiplications Necessary to Evaluate Polynomials", Journal = SIAMComp, Volume = 2, Pages = "60--66" } @Article{ Pea01, Author = "K. Pearson", Year = 1901, Title = "On Lines and Planes of Closest Fit to Points in Space", Journal = PhilMag, Volume = 2, Pages = "559--572" } @Article{ PetW69, Author = "G. Peters and J.H. Wilkinson", Year = 1969, Title = "Eigenvalue of {$Ax = \lambda Bx$} with Band Symmetric {$A$} and {$B$}", Journal = CompJour, Volume = 12, Pages = "398--404" } @Article{ PetW70a, Author = "G. Peters and J.H. Wilkinson", Year = 1970, Title = "{$Ax = \lambda Bx$} and the Generalized Eigenproblem", Journal = SIAMNumAnal, Volume = 7, Pages = "479--492" } @Article{ PetW70b, Author = "G. Peters and J.H. Wilkinson", Year = 1970, Title = "The Least Squares Problem and Pseudo-Inverses", Journal = CompJour, Volume = 13, Pages = "309--316" } @InCollection{ PetW71, Author = "G. Peters and J.H. Wilkinson", Year = 1971, Title = "The Calculation of Specified Eigenvectors by Inverse Iteration", BookTitle = "Handbook for Automatic Computation Vol. 2: Linear Algebra", Editor = "J.H. Wilkinson and C. Reinsch", Publisher = Springer, Address = "New York", Pages = "418--439" } @Article{ PetW79, Author = "G. Peters and J.H. Wilkinson", Year = 1979, Title = "Inverse Iteration, Ill-Conditioned Equations, and {N}ewton's Method", Journal = SIAMReview, Volume = 21, Pages = "339--360" } @Article{ Phi71, Author = "J.L. Phillips", Year = 1971, Title = "The Triangular Decomposition of {H}ankel Matrices", Journal = MathComp, Volume = 25, Pages = "599--602" } @Article{ Ple74, Author = "R.J. Plemmons", Year = 1974, Title = "Linear Least Squares by Elimination and {MGS}", Journal = JACM, Volume = 21, Pages = "581--585" } @Article{ Ple86, Author = "R.J. Plemmons", Year = 1986, Title = "A Parallel Block Iterative Scheme Applied to Computations in Structural Analysis", Journal = SIAMAlgMeth, Volume = 7, Pages = "337--347" } @Article{ PooO87, Author = "E.L. Poole and J.M. Ortega", Year = 1987, Title = "Multicolor {ICCG} Methods for Vector Computers", Journal = SIAMNumAnal, Volume = 24, Pages = "1394--1418" } @Article{ PopT57, Author = "D.A. Pope and C. Tompkins", Year = 1957, Title = "Maximizing Functions of Rotations: Experiments Concerning Speed of Diagonalization of Symmetric Matrices Using {J}acobi's Method", Journal = JACM, Volume = 4, Pages = "459--466" } @InCollection{ PotJV87, Author = "A. Pothen and S. Jha and U. Vemapulati", Year = 1987, Title = "Orthogonal Factorization on a Distributed Memory Multiprocessor", BookTitle = "Hypercube Multiprocessors", Editor = "M.T. Heath", Publisher = SIAMPub, Address = "Philadelphia, PA" } @InProceedings{ PowR68, Author = "M.J.D. Powell and J.K. Reid", Year = 1968, Title = "On Applying {H}ouseholder's Method to Linear Least Squares Problems", BookTitle = "Proceedings {IFIP} Congress", Pages = "122--126" } @Article{ Pry84, Author = "J.D. Pryce", Year = 1984, Title = "A New Measure of Relative Error for Vectors", Journal = SIAMNumAnal, Volume = 21, Pages = "202--221" } @Article{ Pry85, Author = "J.D. Pryce", Year = 1985, Title = "Multiplicative Error Analysis of Matrix Transformation Algorithms", Journal = IMANumerAna, Volume = 5, Pages = "437--445" } @Article{ Rat82, Author = "W. Rath", Year = 1982, Title = "Fast {G}ivens Rotations for Orthogonal Similarity", Journal = NumerMath, Volume = 40, Pages = "47--56" } @Article{ Rei67, Author = "J.K. Reid", Year = 1967, Title = "A Note on the Least Squares Solution of a Band System of Linear Equations by {H}ouseholder Reductions", Journal = CompJour, Volume = 10, Pages = "188--189" } @Article{ Rei71a, Author = "J.K. Reid", Year = 1971, Title = "A Note on the Stability of {G}aussian Elimination", Journal = InstMathApp, Volume = 8, Pages = "374--375" } @InCollection{ Rei71b, Author = "J.K. Reid", Year = 1971, Title = "On the Method of Conjugate Gradients for the Solution of Large Sparse Linear Equations", BookTitle = "Large Sparse Sets of Linear Equations", Editor = "J.K. Reid", Publisher = Academic, Address = "New York", Pages = "231--254" } @Article{ Rei72, Author = "J.K. Reid", Year = 1972, Title = "The Use of Conjugate Gradients for Systems of Linear Equations Possessing Property~{A}", Journal = SIAMNumAnal, Volume = 9, Pages = "325--332" } @Article{ ReiB68, Author = "C. Reinsch and F.L. Bauer", Year = 1968, Title = "Rational {QR} Transformations with {N}ewton's Shift for Symmetric Tridiagonal Matrices", Journal = NumerMath, Volume = 11, Pages = "264--272", Note = "Also in \cite[pages 257--265]{WilR71}" } @Article{ Ric66b, Author = "J.R. Rice", Year = 1966, Title = "Experiments on {G}ram-{S}chmidt Orthogonalization", Journal = MathComp, Volume = 20, Pages = "325--328" } @Article{ Ric66a, Author = "J. R. Rice", Year = 1966, Title = "A Theory of Condition", Journal = SIAMNumAnal, Volume = 3, Pages = "287--310" } @Book{ Ric81, Author = "J.R. Rice", Year = 1981, Title = "Matrix Computations and Mathematical Software", Publisher = Academic, Address = "New York" } @Article{ Rin55, Author = "R.F. Rinehart", Year = 1955, Title = "The Equivalence of Definitions of a Matrix Function", Journal = AmerMathMonthly, Volume = 62, Pages = "395--414" } @Article{ Ris73, Author = "J. Rissanen", Year = 1973, Title = "Algorithms for Triangular Decomposition of Block {H}ankel and {T}oeplitz Matrices with Application to Factoring Positive Matrix Polynomials", Journal = MathComp, Volume = 27, Pages = "147--154" } @Article{ Rob77, Author = "H.H. Robertson", Year = 1977, Title = "The Accuracy of Error Estimates for Systems of Linear Algebraic Equations", Journal = InstMathApp, Volume = 20, Pages = "409--414" } @Article{ Rod73, Author = "G. Rodrigue", Year = 1973, Title = "A Gradient Method for the Matrix Eigenvalue Problem {$Ax = \lambda Bx$}", Journal = NumerMath, Volume = 22, Pages = "1--16" } @Article{ RodW84a, Author = "G. Roderigue and D. Wolitzer", Year = 1984, Title = "Preconditioning by Incomplete Block Cyclic Reduction", Journal = MathComp, Volume = 42, Pages = "549--566" } @Book{ Rod82a, Editor = "G. Roderigue", Year = 1982, Title = "Parallel Computations", Publisher = Academic, Address = "New York" } @Article{ Ros69, Author = "D.J. Rose", Year = 1969, Title = "An Algorithm for Solving a Special Class of Tridiagonal Systems of Linear Equations", Journal = CACM, Volume = 12, Pages = "234--236" } @Book{ RosW72a, Editor = "D.J. Rose and R.A. Willoughby", Year = 1972, Title = "Sparse Matrices and Their Applications", Publisher = PlenumPress, Address = "New York, NY" } @Article{ RodW84b, Author = "G. Roderigue and D. Wolitzer", Year = 1984, Title = "Preconditioning by Incomplete Block Cyclic Reduction", Journal = MathComp, Volume = 42, Pages = "549--566" } @Book{ Rod82b, Editor = "G. Roderigue", Year = 1982, Title = "Parallel Computations", Publisher = Academic, Address = "New York, NY" } @Article{ RomO88, Author = "C.H. Romine and J.M. Ortega", Year = 1988, Title = "Parallel Solution of Triangular Systems of Equations", Journal = ParComputing, Volume = 6, Pages = "109--114" } @Article{ Ruh67, Author = "A. Ruhe", Year = 1967, Title = "On the Quadratic Convergence of the {J}acobi Method for Normal Matrices", Journal = BIT, Volume = 7, Pages = "305--313" } @Article{ Ruh68, Author = "A. Ruhe", Year = 1968, Title = "On the Quadratic Convergence of a Generalization of the {J}acobi Method to Arbitrary Matrices", Journal = BIT, Volume = 8, Pages = "210--231" } @Article{ Ruh69b, Author = "A. Ruhe", Year = 1969, Title = "The Norm of a Matrix after a Similarity Transformation", Journal = BIT, Volume = 9, Pages = "53--58" } @Article{ Ruh69a, Author = "A. Ruhe", Year = 1969, Title = "An Algorithm for Numerical Determination of the Structure of a General Matrix", Journal = BIT, Volume = 10, Pages = "196--216" } @Article{ Ruh70a, Author = "A. Ruhe", Year = 1970, Title = "Perturbation Bounds for Means of Eigenvalues and Invariant Subspaces", Journal = BIT, Volume = 10, Pages = "343--354" } @Article{ Ruh70b, Author = "A. Ruhe", Year = 1970, Title = "Properties of a Matrix with a Very Ill-Conditioned Eigenproblem", Journal = NumerMath, Volume = 15, Pages = "57--60" } @Article{ Ruh74, Author = "A. Ruhe", Year = 1974, Title = "{SOR} Methods for the Eigenvalue Problem with Large Sparse Matrices", Journal = MathComp, Volume = 28, Pages = "695--710" } @Article{ Ruh75, Author = "A. Ruhe", Year = 1975, Title = "On the Closeness of Eigenvalues and Singular Values for Almost Normal Matrices", Journal = LinAlgApp, Volume = 11, Pages = "87--94" } @Article{ Ruh78, Author = "A. Ruhe", Year = 1978, Title = "A Note on the Efficient Solution of Matrix Pencil Systems", Journal = BIT, Volume = 18, Pages = "276--281" } @Article{ Ruh79, Author = "A. Ruhe", Year = 1979, Title = "Implementation Aspects of Band {L}anczos Algorithms for Computation of Eigenvalues of Large Sparse Symmetric Matrices", Journal = MathComp, Volume = 33, Pages = "680--687" } @Article{ Ruh83, Author = "A. Ruhe", Year = 1983, Title = "Numerical Aspects of {G}ram-{S}chmidt Orthogonalization of Vectors", Journal = LinAlgApp, Volume = "52/53", Pages = "591--602" } @Article{ Ruh87, Author = "A. Ruhe", Year = 1987, Title = "Closest Normal Matrix Found!", Journal = BIT, Volume = 27, Pages = "585--598" } @Article{ RuhW72b, Author = "A. Ruhe and T. Wiberg", Year = 1972, Title = "The Method of Conjugate Gradients Used in Inverse Iteration", Journal = BIT, Volume = 12, Pages = "543--554" } @InCollection{ Rut58, Author = "H. Rutishauser", Year = 1958, Title = "Solution of Eigenvalue Problems with the {WR} Transformation", BookTitle = "Applied Mathematics Series", Publisher = NatBurStd, Volume = 49, Pages = "47--81" } @Article{ Rut66, Author = "H. Rutishauser", Year = 1966, Title = "The {J}acobi Method for Real Symmetric Matrices", Journal = NumerMath, Volume = 9, Pages = "1--10", Note = "Also in \cite[pages 202--211]{WilR71}" } @Article{ Rut69, Author = "H. Rutishauser", Year = 1969, Title = "Computation Aspects of {F}.{L}. {B}auer's Simultaneous Iteration Method", Journal = NumerMath, Volume = 13, Pages = "4--13" } @Article{ Rut70, Author = "H. Rutishauser", Year = 1970, Title = "Simultaneous Iteration Method for Symmetric Matrices", Journal = NumerMath, Volume = 16, Pages = "205--223", Note = "Also in \cite[pages 284--302]{WilR71}" } @Article{ Saa80, Author = "Y. Saad", Year = 1980, Title = "On the Rates of Convergence of the {L}anczos and the Block {L}anczos Methods", Journal = SIAMNumAnal, Volume = 17, Pages = "687--706" } @Article{ Saa84, Author = "Y. Saad", Year = 1984, Title = "Practical Use of Some {K}rylov Subspace Methods for Solving Indefinite and Nonsymmetric Linear Systems", Journal = SIAMSciStat, Volume = 5, Pages = "203--228" } @Article{ Saa87, Author = "Y. Saad", Year = 1987, Title = "On the {L}anczos Method for Solving Symmetric Systems with Several Right Hand Sides", Journal = MathComp, Volume = 48, Pages = "651--662" } @Article{ Saa81, Author = "Y. Saad", Year = 1981, Title = "{K}rylov Subspace Methods for Solving Large Unsymmetric Linear Systems", Journal = MathComp, Volume = 37, Pages = "105--126" } @Article{ Saa82, Author = "Y. Saad", Year = 1982, Title = "The {L}anczos Biorthogonalization Algorithm and Other Oblique Projection Methods for Solving Large Unsymmetric Systems", Journal = SIAMNumAnal, Volume = 19, Pages = "485--506" } @Article{ Saa86, Author = "Y. Saad", Year = 1986, Title = "On the Condition Number of Some {G}ram Matrices Arising from Least Squares Approximation in the Complex Plane", Journal = NumerMath, Volume = 48, Pages = "337--348" } @TechReport{ SaaS85a, Author = " Y. Saad and M.H. Schultz", Year = 1985, Title = "Data Communication in Hypercubes", Number = "YALEU DCS RR-428", Institution = "Computer Science, Yale University", Address = "New Haven, CT" } @TechReport{ SaaS85b, Author = " Y. Saad and M.H. Schultz", Year = 1985, Title = "Topological Properties of Hypercubes", Number = "YALEU DCS RR-389", Institution = "Computer Science, Yale University", Address = "New Haven, CT" } @Article{ SaaS86, Author = "Y. Saad and M. Schultz", Year = 1986, Title = "{GMRES}: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems", Journal = SIAMSciStat, Volume = 7, Pages = "856--869" } @Article{ Sam71, Author = "A. Sameh", Year = 1971, Title = "On {J}acobi and {J}acobi-Like Algorithms for a Parallel Computer", Journal = MathComp, Volume = 25, Pages = "579--590" } @Article{ SamK78, Author = "A. Sameh and D. Kuck", Year = 1978, Title = "On Stable Parallel Linear System Solvers", Journal = JACM, Volume = 25, Pages = "81--91" } @Article{ SamLN75, Author = "A. Sameh and J. Lermit and K. Noh", Year = 1975, Title = "On the Intermediate Eigenvalues of Symmetric Sparse Matrices", Journal = BIT, Volume = 12, Pages = "543--554" } @Article{ SchS79, Author = "K. Schittkowski and J. Stoer", Year = 1979, Title = "A Factorization Method for the Solution of Constrained Linear Least Squares Problems Allowing for Subsequent Data Changes", Journal = NumerMath, Volume = 31, Pages = "431--463" } @Article{ Sch66, Author = "P. Schoenemann", Year = 1966, Title = "A Generalized Solution of the Orthogonal {P}rocrustes Problem", Journal = Psychometrika, Volume = 31, Pages = "1--10" } @Article{ Sch64, Author = "A. Schonage", Year = 1964, Title = "On the Quadratic Convergence of the {J}acobi Process", Journal = NumerMath, Volume = 6, Pages = "410--412" } @Article{ Sch79, Author = "A. Schonage", Year = 1979, Title = "Arbitrary Perturbations of {H}ermitian Matrices", Journal = LinAlgApp, Volume = 24, Pages = "143--149" } @Book{ Sch87, Author = "W. Sch{\"o}nauer", Year = 1987, Title = "Scientific Computing on Vector Computers", Publisher = NorthHolland, Address = "Amsterdam" } @Article{ Sch86, Author = "R. Schreiber", Year = 1986, Title = "Solving Eigenvalue and Singular Value Problems on an Undersized Systolic Array", Journal = SIAMSciStat, Volume = 7, Pages = "441--451" } @Article{ SchT86, Author = "R. Schreiber and W.P. Tang", Year = 1986, Title = "On Systolic Arrays for Updating the {C}holesky Factorization", Journal = BIT, Volume = 26, Pages = "451--466" } @Article{ SchP87, Author = "R. Schreiber and B.N. Parlett", Year = 1987, Title = "Block Reflectors: Theory and Computation", Journal = SIAMNumAnal, Volume = 25, Pages = "189--205" } @Article{ SchL89, Author = "R. Schreiber and Van Loan, C.", Year = 1989, Title = "A Storage Efficient {WY} Representation for Products of {H}ouseholder Transformations", Journal = SIAMSciStat, Volume = 10, Pages = "53--57" } @Article{ Sch09, Author = "I. Schur", Year = 1909, Title = "On the Characteristic Roots of a Linear Substitution with an Application to the Theory of Integral Equations", Journal = MathAnnalen, Volume = 66, Pages = "488--510", Note = "German" } @Article{ Sch68, Author = "H.R. Schwartz", Year = 1968, Title = "Tridiagonalization of a Symmetric Band Matrix", Journal = NumerMath, Volume = 12, Pages = "231--241", Note = "Also in \cite[pages 273--283]{WilR71}" } @Article{ Sch74, Author = "H.R. Schwartz", Year = 1974, Title = "The Method of Coordinate Relaxation for {$(A - \lambda B)x = 0$}", Journal = NumerMath, Volume = 23, Pages = "135--152" } @TechReport{ Sco78, Author = "D.S. Scott", Year = 1978, Title = "Analysis of the Symmetric {L}anczos Process", Number = "M78/40", Institution = "UCB-ERL, University of California, Berkeley", Address = "Berkeley, CA" } @TechReport{ Sco79a, Author = "D.S. Scott", Year = 1979, Title = "Block {L}anczos Software for Symmetric Eigenvalue Problems", Number = "ORNL/CSD-48", Institution = "Oak Ridge National Laboratory", Address = "Oak Ridge, TN" } @Article{ Sco79b, Author = "D.S. Scott", Year = 1979, Title = "How to Make the {L}anczos Algorithm Converge Slowly", Journal = MathComp, Volume = 33, Pages = "239--247" } @Article{ Sco84, Author = "D.S. Scott", Year = 1984, Title = "Computing a Few Eigenvalues and Eigenvectors of a Symmetric Band Matrix", Journal = SIAMSciStat, Volume = 5, Pages = "658--666" } @Article{ Sco85, Author = "D.S. Scott", Year = 1985, Title = "On the Accuracy of the {G}ershgorin Circle Theorem for Bounding the Spread of a Real Symmetric Matrix", Journal = LinAlgApp, Volume = 65, Pages = "147--155" } @Article{ ScoHW86, Author = "D.S. Scott and M.T. Heath and R.C. Ward", Year = 1986, Title = "Parallel Block {J}acobi Eigenvalue Algorithms Using Systolic Arrays", Journal = LinAlgApp, Volume = 77, Pages = "345--356" } @Article{ Sea86, Author = "M.K. Seager", Year = 1986, Title = "Parallelizing Conjugate Gradient for the {Cray X-MP}", Journal = ParComputing, Volume = 3, Pages = "35--47" } @Article{ Sea69, Author = "J.J. Seaton", Year = 1969, Title = "Diagonalization of Complex Symmetric Matrices Using a Modified {J}acobi Method", Journal = CompJour, Volume = 12, Pages = "156--157" } @Article{ Ser80, Author = "S. Serbin", Year = 1980, Title = "On Factoring a Class of Complex Symmetric Matrices Without Pivoting", Journal = MathComp, Volume = 35, Pages = "1231--1234" } @Article{ SerB79, Author = "S. Serbin and S. Blalock", Year = 1979, Title = "An Algorithm for Computing the Matrix Cosine", Journal = SIAMSciStat, Volume = 1, Pages = "198--204" } @Article{ She55, Author = "J.W. Sheldon", Year = 1955, Title = "On the Numerical Solution of Elliptic Difference Equations", Journal = TablesAidsComp, Volume = 9, Pages = "101--112" } @TechReport{ ShrS87, Author = "G. Shroff and R. Schreiber", Year = 1987, Title = "Convergence of Block {J}acobi Methods", Number = "87-25", Institution = "Computer Science, Rensselaer Polytechnic Institute", Address = "Troy, NY" } @Article{ Sim84, Author = "H. Simon", Year = 1984, Title = "Analysis of the Symmetric {L}anczos Algorithm with Reorthogonalization Methods", Journal = LinAlgApp, Volume = 61, Pages = "101--132" } @Article{ SinS76, Author = "B. Singer and S. Spilerman", Year = 1976, Title = "The Representation of Social Processes by {M}arkov Models", Journal = AmerSocio, Volume = 82, Pages = "1--54" } @Article{ Ske79, Author = "R.D. Skeel", Year = 1979, Title = "Scaling for Numerical Stability in {G}aussian Elimination", Journal = JACM, Volume = 26, Pages = "494--526" } @Article{ Ske80, Author = "R.D. Skeel", Year = 1980, Title = "Iterative Refinement Implies Numerical Stability for {G}aussian Elimination", Journal = MathComp, Volume = 35, Pages = "817--832" } @Article{ Ske81, Author = "R.D. Skeel", Year = 1981, Title = "Effect of Equilibration on Residual Size for Partial Pivoting", Journal = SIAMNumAnal, Volume = 18, Pages = "449--455" } @Book{ SmiBI+70, Author = "B.T. Smith and J.M. Boyle and Y. Ikebe and V.C. Klema and C.B. Moler", Year = 1970, Title = "Matrix Eigensystem Routines: {EISPACK} Guide", Edition = "second", Publisher = Springer, Address = "New York, NY", } @Article{ Smi67, Author = "R.A. Smith", Year = 1967, Title = "The Condition Numbers of the Matrix Eigenvalue Problem", Journal = NumerMath, Volume = 10, Pages = "232--240" } @Book{ Smi70, Author = "F. Smithies", Year = 1970, Title = "Integral Equations", Publisher = CambridgePress, Address = "Cambridge, England" } @Article{ Sor85, Author = "D. Sorensen", Year = 1985, Title = "Analysis of Pairwise Pivoting in {G}aussian Elimination", Journal = IEEETransComp, Volume = "C-34", Pages = "274--278" } @Article{ Ste81a, Author = "D. Stevenson", Year = 1981, Title = "A Proposed Standard for Binary Floating Point Arithmetic", Journal = Computer, Volume = 14, Month = mar, Pages = "51--62" } @Article{ Ste69, Author = "G.W. Stewart", Year = 1969, Title = "Accelerating the Orthogonal Iteration for the Eigenvectors of a {H}ermitian Matrix", Journal = NumerMath, Volume = 13, Pages = "362--376" } @Article{ Ste70, Author = "G.W. Stewart", Year = 1970, Title = "Incorporating Origin Shifts into the {QR} Algorithm for Symmetric Tridiagonal Matrices", Journal = CACM, Volume = 13, Pages = "365--367" } @Article{ Ste71, Author = "G.W. Stewart", Year = 1971, Title = "Error Bounds for Approximate Invariant Subspaces of Closed Linear Operators", Journal = SIAMNumAnal, Volume = 8, Pages = "796--808" } @Article{ Ste72, Author = "G.W. Stewart", Year = 1972, Title = "On the Sensitivity of the Eigenvalue Problem {$Ax = \lambda Bx$}", Journal = SIAMNumAnal, Volume = 9, Pages = "669--686" } @Article{ Ste73a, Author = "G.W. Stewart", Year = 1973, Title = "Conjugate Direction Methods for Solving Systems of Linear Equations", Journal = NumerMath, Volume = 21, Pages = "284--297" } @Article{ Ste73b, Author = "G.W. Stewart", Year = 1973, Title = "Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems", Journal = SIAMReview, Volume = 15, Pages = "727--764" } @Book{ Ste73c, Author = "G.W. Stewart", Year = 1973, Title = "Introduction to Matrix Computations", Publisher = Academic, Address = "New York, NY" } @InProceedings{ Ste74, Author = "G.W. Stewart", Year = 1974, Title = "The Numerical Treatment of Large Eigenvalue Problems", BookTitle = "Proceedings {IFIP} Congress 74", Publisher = NorthHolland, Pages = "666--672" } @Article{ Ste75a, Author = "G.W. Stewart", Year = 1975, Title = "The Convergence of the Method of Conjugate Gradients at Isolated Extreme Points in the Spectrum", Journal = NumerMath, Volume = 24, Pages = "85--93" } @Article{ Ste75b, Author = "G.W. Stewart", Year = 1975, Title = "{G}ershgorin Theory for the Generalized Eigenvalue Problem {$Ax = \lambda Bx$}", Journal = MathComp, Volume = 29, Pages = "600--606" } @InCollection{ Ste75c, Author = "G.W. Stewart", Year = 1975, Title = "Methods of Simultaneous Iteration for Calculating Eigenvectors of Matrices", BookTitle = "Topics in Numerical Analysis {II}", Editor = "J.H. Miller", Publisher = Academic, Address = "New York", Pages = "185--196" } @Article{ Ste76a, Author = "G.W. Stewart", Year = 1976, Title = "Algorithm~406 {HQR3 and~EXCHNG}: {F}ortran Subroutines for Calculating and Ordering and Eigenvalues of a Real Upper {H}essenberg Matrix", Journal = ACMMathSoft, Volume = 2, Pages = "275--280" } @InCollection{ Ste76b, Author = "G.W. Stewart", Year = 1976, Title = "A Bibliographical Tour of the Large Sparse Generalized Eigenvalue Problem", BookTitle = "Sparse Matrix Computations", Editor = "J.R. Bunch and D.J. Rose", Publisher = Academic, Address = "New York" } @Article{ Ste76c, Author = "G.W. Stewart", Year = 1976, Title = "The Economical Storage of Plane Rotations", Journal = NumerMath, Volume = 25, Pages = "137--138" } @Article{ Ste76d, Author = "G.W. Stewart", Year = 1976, Title = "Simultaneous Iteration for Computing Invariant Subspaces of Non-{H}ermitian Matrices", Journal = NumerMath, Volume = 25, Pages = "12--36" } @Article{ Ste77a, Author = "G.W. Stewart", Year = 1977, Title = "On the Perturbation of Pseudo-Inverses, Projections, and Linear Least Squares Problems", Journal = SIAMReview, Volume = 19, Pages = "634--662" } @Article{ Ste77b, Author = "G.W. Stewart", Year = 1977, Title = "Perturbation Bounds for the {QR} Factorization of a Matrix", Journal = SIAMNumAnal, Volume = 14, Pages = "509--518" } @TechReport{ Ste77c, Author = "G.W. Stewart", Year = 1977, Title = "Sensitivity Coefficients for the Effects of Errors in the Independent Variables in a Linear Regression", Number = "TR-571", Institution = "Computer Science, University of Maryland", Address = "College Park, MD" } @InCollection{ Ste78, Author = "G.W. Stewart", Year = 1978, Title = "Perturbation Theory for the Generalized Eigenvalue Problem", BookTitle = "Recent Advances in Numerical Analysis", Editor = "de Boor, C. and G.H. Golub", Publisher = Academic, Address = "New York" } @Article{ Ste79b, Author = "G.W. Stewart", Year = 1979, Title = "A Note on the Perturbation of Singular Values", Journal = LinAlgApp, Volume = 28, Pages = "213--216" } @Article{ Ste79c, Author = "G.W. Stewart", Year = 1979, Title = "Perturbation Bounds for the Definite Generalized Eigenvalue Problem", Journal = LinAlgApp, Volume = 23, Pages = "69--86" } @Article{ Ste79a, Author = "G.W. Stewart", Year = 1979, Title = "The Effects of Rounding Error on an Algorithm for Downdating a {C}holesky Factorization", Journal = InstMathApp, Volume = 23, Pages = "203--213" } @Article{ Ste80, Author = "G.W. Stewart", Year = 1980, Title = "The Efficient Generation of Random Orthogonal Matrices with an Application to Condition Estimators", Journal = SIAMNumAnal, Volume = 17, Pages = "403--409" } @Article{ Ste81b, Author = "G.W. Stewart", Year = 1981, Title = "On the Implicit Deflation of Nearly Singular Systems of Linear Equations", Journal = SIAMSciStat, Volume = 2, Pages = "136--140" } @InCollection{ Ste83, Author = "G.W. Stewart", Year = 1983, Title = "A Method for Computing the Generalized Singular Value Decomposition", BookTitle = "Matrix Pencils", Editor = "B. K{\aa}gstr{\"o}m and A. Ruhe", Publisher = Springer, Address = "New York", Pages = "207--220" } @Article{ Ste84c, Author = "G.W. Stewart", Year = 1984, Title = "Rank Degeneracy", Journal = SIAMSciStat, Volume = 5, Pages = "403--413" } @Article{ Ste84a, Author = "G.W. Stewart", Year = 1984, Title = "On the Asymptotic Behavior of Scaled Singular Value and {QR} Decompositions", Journal = MathComp, Volume = 43, Pages = "483--490" } @Article{ Ste84d, Author = "G.W. Stewart", Year = 1984, Title = "A Second Order Perturbation Expansion for Small Singular Values", Journal = LinAlgApp, Volume = 56, Pages = "231--236" } @Article{ Ste84b, Author = "G.W. Stewart", Year = 1984, Title = "On the Invariance of Perturbed Null Vectors Under Column Scaling", Journal = NumerMath, Volume = "33,34", Pages = "61--66" } @Article{ Ste85, Author = "G.W. Stewart", Year = 1985, Title = "A {J}acobi-Like Algorithm for Computing the {S}chur Decomposition of a Nonhermitian Matrix", Journal = SIAMSciStat, Volume = 6, Pages = "853--862" } @Article{ Ste87, Author = "G.W. Stewart", Year = 1987, Title = "Collinearity and Least Squares Regression", Journal = StatScience, Volume = 2, Pages = "68--100" } @Article{ Sto73, Author = "H.S. Stone", Year = 1973, Title = "An Efficient Parallel Algorithm for the Solution of a Tridiagonal Linear System of Equations", Journal = JACM, Volume = 20, Pages = "27--38" } @Article{ Sto75b, Author = "H.S. Stone", Year = 1975, Title = "Parallel Tridiagonal Equation Solvers", Journal = ACMMathSoft, Volume = 1, Pages = "289--307" } @Book{ Str88, Author = "G. Strang", Year = 1988, Title = "Linear Algebra and Its Applications", Edition = "third", Publisher = Academic, Address = "New York" } @Article{ Sto75a, Author = "H. Stone", Year = 1975, Title = "Parallel Tridiagonal Equation Solvers", Journal = ACMMathSoft, Volume = 1, Pages = "289--307" } @Article{ Str69, Author = "V. Strassen", Year = 1969, Title = "{G}aussian Elimination is Not Optimal", Journal = NumerMath, Volume = 13, Pages = "354--356" } @Article{ Sun82, Author = "Guang Sun, J.", Year = 1982, Title = "A Note on {S}tewart's Theorem for Definite Matrix Pairs", Journal = LinAlgApp, Volume = 48, Pages = "331--339" } @Article{ Sun83, Author = "Guang Sun, J.", Year = 1983, Title = "Perturbation Analysis for the Generalized Singular Value Problem", Journal = SIAMNumAnal, Volume = 20, Pages = "611--625" } @Article{ Swa79, Author = "P.N. Swarztrauber", Year = 1979, Title = "A Parallel Algorithm for Solving General Tridiagonal Equations", Journal = MathComp, Volume = 33, Pages = "185--199" } @Article{ SwaS73, Author = "P.N. Swarztrauber and R.A. Sweet", Year = 1973, Title = "The Direct Solution of the Discrete {P}oisson Equation on a Disk", Journal = SIAMNumAnal, Volume = 10, Pages = "900--907" } @Article{ Swe74, Author = "R.A. Sweet", Year = 1974, Title = "A Generalized Cyclic Reduction Algorithm", Journal = SIAMNumAnal, Volume = 11, Pages = "506--520" } @Article{ Swe77, Author = "R.A. Sweet", Year = 1977, Title = "A Cyclic Reduction Algorithm for Solving Block Tridiagonal Systems of Arbitrary Dimension", Journal = SIAMNumAnal, Volume = 14, Pages = "706--720" } @Article{ SymW80, Author = "H.J. Symm and J.H. Wilkinson", Year = 1980, Title = "Realistic Error Bounds for a Simple Eigenvalue and Its Associated Eigenvector", Journal = NumerMath, Volume = 35, Pages = "113--126" } @Article{ TanG81, Author = "W.P. Tang and G.H. Golub", Year = 1981, Title = "The Block Decomposition of a {V}andermonde Matrix and Its Applications", Journal = BIT, Volume = 21, Pages = "505--517" } @Article{ ThoW70, Author = "G.L. Thompson and R.L. Weil", Year = 1970, Title = "Reducing the Rank of {$A - \lambda B$}", Journal = ProcAMS, Volume = 26, Pages = "548--554" } @Article{ ThoW72, Author = "G.L. Thompson and R.L. Weil", Year = 1972, Title = "Roots of Matrix Pencils {$Ay = \lambda By$}: Existence, Calculations, and Relations to Game Theory", Journal = LinAlgApp, Volume = 5, Pages = "207--226" } @TechReport{ TreS87, Author = "L.N. Trefethen and R.S. Schreiber", Year = 1987, Title = "Average Case Stability of {G}aussian Elimination", Number = "88-3", Institution = "Numerical Analysis, Department of Mathematics, MIT", Address = "MA" } @Article{ Tre64, Author = "W.F. Trench", Year = 1964, Title = "An Algorithm for the Inversion of Finite {T}oeplitz Matrices", Journal = "J. SIAM", Volume = 12, Pages = "515--522" } @Article{ Tre74, Author = "W.F. Trench", Year = 1974, Title = "Inversion of {T}oeplitz Band Matrices", Journal = MathComp, Volume = 28, Pages = "1089--1095" } @Article{ Tsa75, Author = "N.K. Tsao", Year = 1975, Title = "A Note on Implementing the {H}ouseholder Transformation", Journal = SIAMNumAnal, Volume = 12, Pages = "53--58" } @Book{ TurA61, Author = "H.W. Turnbull and A.C. Aitken", Year = 1961, Title = "An Introduction to the Theory of Canonical Matrices", Publisher = DoverPub, Address = "New York" } @Article{ Uhl73, Author = "F. Uhlig", Year = 1973, Title = "Simultaneous Block Diagonalization of Two Real Symmetric Matrices", Journal = LinAlgApp, Volume = 7, Pages = "281--289" } @Article{ Uhl76, Author = "F. Uhlig", Year = 1976, Title = "A Canonical Form for a Pair of Real Symmetric Matrices that Generate a Nonsingular Pencil", Journal = LinAlgApp, Volume = 14, Pages = "189--210" } @TechReport{ Und75, Author = "R. Underwood", Year = 1975, Title = "An Iterative Block {L}anczos Method for the Solution of Large Sparse Symmetric Eigenproblems", Number = "STAN-CS-75-496", Institution = "Computer Science, Stanford University", Address = "Stanford, CA" } @Article{ Van71, Author = "J. Vandergraft", Year = 1971, Title = "Generalized {R}ayleigh Methods with Applications to Finding Eigenvalues of Large Matrices", Journal = LinAlgApp, Volume = 4, Pages = "353--368" } @Article{ vdS69, Author = "van der Sluis, A.", Year = 1969, Title = "Condition Numbers and Equilibration Matrices", Journal = NumerMath, Volume = 14, Pages = "14--23" } @Article{ vdS70, Author = "van der Sluis, A.", Year = 1970, Title = "Condition, Equilibration, and Pivoting in Linear Algebraic Systems", Journal = NumerMath, Volume = 15, Pages = "74--86" } @Article{ vdS75a, Author = "van der Sluis, A.", Year = 1975, Title = "Perturbations of Eigenvalues of Nonnormal Matrices", Journal = CACM, Volume = 18, Pages = "30--36" } @Article{ vdS75b, Author = "van der Sluis, A.", Year = 1975, Title = "Stability of the Solutions of Linear Least Squares Problem", Journal = NumerMath, Volume = 23, Pages = "241--254" } @Article{ vdSV79, Author = "van der Sluis, A. and G.W. Veltkamp", Year = 1979, Title = "Restoring Rank and Consistency by Orthogonal Projection", Journal = LinAlgApp, Volume = 28, Pages = "257--278" } @Article{ vdSV86, Author = "van der Sluis, A. and Van der Vorst, H.A.", Year = 1986, Title = "The Rate of Convergence of Conjugate Gradients", Journal = NumerMath, Volume = 48, Pages = "543--560" } @Article{ dV77, Author = "Van de Vel, H.", Year = 1977, Title = "Numerical Treatment of a Generalized {V}andermonde System of Equations", Journal = LinAlgApp, Volume = 17, Pages = "149--174" } @Article{ dV82b, Author = "Van der Vorst, H.A.", Year = 1982, Title = "A Vectorizable Variant of Some {ICCG} Methods", Journal = SIAMSciStat, Volume = 3, Pages = "350--356" } @Article{ dV82a, Author = "Van der Vorst, H.A.", Year = 1982, Title = "A Generalized {L}anczos Scheme", Journal = MathComp, Volume = 39, Pages = "559--562" } @Article{ Doo79, Author = "Van Dooren, P.", Year = 1979, Title = "The Computation of {K}ronecker's Canonical Form of a Singular Pencil", Journal = LinAlgApp, Volume = 27, Pages = "103--140" } @Article{ Doo81b, Author = "Van Dooren, P.", Year = 1981, Title = "A Generalized Eigenvalue Approach for Solving {R}iccati Equations", Journal = SIAMSciStat, Volume = 2, Pages = "121--135" } @Article{ Doo81a, Author = "Van Dooren, P.", Year = 1981, Title = "The Generalized Eigenstructure Problem in Linear System Theory", Journal = IEEETransAC, Volume = "AC-26", Pages = "111--128" } @InCollection{ Doo83, Author = "Van Dooren, P.", Year = 1983, Title = "Reducing Subspaces: definitions, properties and Algorithms", BookTitle = "Matrix Pencils", Editor = "B. K{\aa}gstr{\"o}m and A. Ruhe", Publisher = Springer, Address = "New York", Pages = "58--73" } @PhDThesis{ Huf87, Author = "Van Huffel, S.", Year = 1987, Title = "Analysis of the Total Least Squares Problem and Its Use in Parameter Estimation", School = "Electrical Engineering, Katholieke Universiteit Leuven", Address = "Leuven, Belgium" } @TechReport{ Huf88, Author = "Van Huffel, S.", Year = 1988, Title = "Comments on the Solution of the Nongeneric Total Least Squares Problem", Number = "ESAT-KUL-88/3", Institution = "Department of Electrical Engineering, Katholieke Universiteit Leuven", Address = "Leuven, Belgium" } @Article{ HufV88a, Author = "Van Huffel, S. and J. Vandewalle", Year = 1988, Title = "The Partial Total Least Squares Algorithm", Journal = CompApplMath, Volume = 21, Pages = "333--342" } @Article{ HufV87, Author = "Van Huffel, S. and J. Vandewalle", Year = 1987, Title = "Subset Selection Using the Total Least Squares Approach in Collinearity Problems with Errors in the Variables", Journal = LinAlgApp, Volume = "88/89", Pages = "695--714" } @Article{ HufVH87, Author = "Van Huffel, S. and J. Vandewalle and A. Haegemans", Year = 1987, Title = "An Efficient and Reliable Algorithm for Computing the Singular Subspace of a Matrix Associated with its Smallest Singular Values", Journal = CompApplMath, Volume = 19, Pages = "313--330" } @Article{ HufV88b, Author = "Van Huffel, S. and J. Vandewalle", Year = 1988, Title = "The Partial Total Least Squares Algorithm", Journal = CompApplMath, Volume = 21, Pages = "333--342" } @TechReport{ KatdV77, Author = "Van Kats, J.M. and Van der Vorst, H.A.", Year = 1977, Title = "Automatic Monitoring of {L}anczos Schemes for Symmetric or Skew-Symmetric Generalized Eigenvalue Problems", Number = "TR 7", Institution = "Academische Computer Centre", Address = "Utrecht, The Netherlands" } @Article{ vK66, Author = "van Kempen, H.P.M.", Year = 1966, Title = "On Quadratic Convergence of the Special Cyclic {J}acobi Method", Journal = NumerMath, Volume = 9, Pages = "19--22" } @PhDThesis{ Loa73, Author = "Van Loan, C.F.", Year = 1973, Title = "Generalized Singular Values with Algorithms and Applications", School = "University of Michigan", Address = "Ann Arbor, MI" } @Article{ Loa75a, Author = "Van Loan, C.F.", Year = 1975, Title = "A General Matrix Eigenvalue Algorithm", Journal = SIAMNumAnal, Volume = 12, Pages = "819--834" } @TechReport{ Loa75b, Author = "Van Loan, C.F.", Year = 1975, Title = "A Study of the Matrix Exponential", Number = "10", Institution = "Numerical Analysis, University of Manchester", Address = "England" } @Article{ Loa76, Author = "Van Loan, C.F.", Year = 1976, Title = "Generalizing the Singular Value Decomposition", Journal = SIAMNumAnal, Volume = 13, Pages = "76--83" } @InCollection{ Loa77a, Author = "Van Loan, C.F.", Year = 1977, Title = "On the Limitation and Application of the {P}ad{\'e} Approximation to the Matrix Exponential", BookTitle = "{P}ad{\'e} and Rational Approximation", Editor = "E.B. Saff and R.S. Varga", Publisher = Academic, Address = "New York" } @Article{ Loa77b, Author = "Van Loan, C.F.", Year = 1977, Title = "The Sensitivity of the Matrix Exponential", Journal = SIAMNumAnal, Volume = 14, Pages = "971--981" } @Article{ Loa78a, Author = "Van Loan, C.F.", Year = 1978, Title = "Computing Integrals Involving the Matrix Exponential", Journal = IEEETransAC, Volume = "AC-23", Pages = "395--404" } @Article{ Loa78b, Author = "Van Loan, C.F.", Year = 1978, Title = "A Note on the Evaluation of Matrix Polynomials", Journal = IEEETransAC, Volume = "AC-24", Pages = "320--321" } @InCollection{ Loa82, Author = "Van Loan, C.F.", Year = 1982, Title = "Using the {H}essenberg Decomposition in Control Theory", BookTitle = "Algorithms and Theory in Filtering and Control", Editor = "D.C. Sorensen and R.J. Wets", Series = "Mathematical Programming Study", Number = 18, Publisher = NorthHolland, Address = "Amsterdam", Pages = "102--111" } @InProceedings{ Loa83, Author = "Van Loan, C.F.", Year = 1983, Title = "A Generalized {SVD} Analysis of Some Weighting Methods for Equality-Constrained Least Squares", BookTitle = "Proceedings of the Conference on Matrix Pencils", Editor = "B. K{\aa}gstr{\"o}m and A. Ruhe", Publisher = Springer, Address = "New York" } @Article{ Loa84, Author = "Van Loan, C.F.", Year = 1984, Title = "A Symplectic Method for Approximating All the Eigenvalues of a {H}amiltonian Matrix", Journal = LinAlgApp, Volume = 61, Pages = "233--252" } @Article{ Loa85a, Author = "Van Loan, C.F.", Year = 1985, Title = "Computing the {CS} and Generalized Singular Value Decomposition", Journal = NumerMath, Volume = 46, Pages = "479--492" } @Article{ Loa85c, Author = "Van Loan, C.F.", Year = 1985, Title = "On the Method of Weighting for Equality Constrained Least Squares Problems", Journal = SIAMNumAnal, Volume = 22, Pages = "851--864" } @Article{ Loa85b, Author = "Van Loan, C.F.", Year = 1985, Title = "How Near is a Stable Matrix to an Unstable Matrix?", Journal = ContempMath, Volume = 47, Pages = "465--477" } @Article{ Loa87, Author = "Van Loan, C.F.", Year = 1987, Title = "On Estimating the Condition of Eigenvalues and Eigenvectors", Journal = LinAlgApp, Volume = "88/89", Pages = "715--732" } @Article{ Var68a, Author = "J.M. Varah", Year = 1968, Title = "The Calculation of the Eigenvectors of a General Complex Matrix by Inverse Iteration", Journal = MathComp, Volume = 22, Pages = "785--791" } @Article{ Var68b, Author = "J.M. Varah", Year = 1968, Title = "Rigorous Machine Bounds for the Eigensystem of a General Complex Matrix", Journal = MathComp, Volume = 22, Pages = "793--801" } @Article{ Var70a, Author = "J.M. Varah", Year = 1970, Title = "Computing Invariant Subspaces of a General Matrix when the Eigensystem is Poorly Determined", Journal = MathComp, Volume = 24, Pages = "137--149" } @Article{ Var79, Author = "J.M. Varah", Year = 1979, Title = "On the Separation of Two Matrices", Journal = SIAMNumAnal, Volume = 16, Pages = "216--222" } @Article{ Var72, Author = "J.M. Varah", Year = 1972, Title = "On the Solution of Block-Tridiagonal Systems Arising from Certain Finite-Difference Equations", Journal = MathComp, Volume = 26, Pages = "859--868" } @Article{ Var73, Author = "J.M. Varah", Year = 1973, Title = "On the Numerical Solution of Ill-Conditioned Linear Systems with Applications to Ill-Posed Problems", Journal = SIAMNumAnal, Volume = 10, Pages = "257--267" } @Article{ Var75, Author = "J.M. Varah", Year = 1975, Title = "A Lower Bound for the Smallest Singular Value of a Matrix", Journal = LinAlgApp, Volume = 11, Pages = "1--2" } @Article{ Var61, Author = "R.S. Varga", Year = 1961, Title = "On Higher-Order Stable Implicit Methods for Solving Parabolic Partial Differential Equations", Journal = MathPhys, Volume = 40, Pages = "220--231" } @Book{ Var62, Author = "R.S. Varga", Year = 1962, Title = "Matrix Iterative Analysis", Publisher = PrenticeHall, Address = "Englewood Cliffs, NJ" } @Article{ Var70b, Author = "R.S. Varga", Year = 1970, Title = "Minimal {G}ershgorin Sets for Partitioned Matrices", Journal = SIAMNumAnal, Volume = 7, Pages = "493--507" } @Article{ Var76, Author = "R.S. Varga", Year = 1976, Title = "On Diagonal Dominance Arguments for Bounding {$\|A^{-1}\|$}", Journal = LinAlgApp, Volume = 14, Pages = "211--217" } @Article{ Vet75, Author = "W.J. Vetter", Year = 1975, Title = "Vector Structures and Solutions of Linear Matrix Equations", Journal = LinAlgApp, Volume = 10, Pages = "181--188" } @Book{ Wac66, Author = "E.L. Wachpress", Year = 1966, Title = "Iterative Solution of Elliptic Systems", Publisher = PrenticeHall, Address = "Englewood Cliffs, NJ" } @InProceedings{ WalAC+88, Author = "D.W. Walker and T. Aldcroft and A. Cisneros and G. Fox and W. Furmanski", Year = 1988, Title = "{LU} Decomposition of Banded Matrices and the Solution of Linear Systems on Hypercubes", BookTitle = "The Third Conference on Hypercube Concurrent Computers and Applications, Vol. {II}, Applications", Editor = "G. Fox", Publisher = ACMPress, Address = "New York", Pages = "1635--1655" } @Article{ Wal88, Author = "H.F. Walker", Year = 1988, Title = "Implementation of the {GMRES} Method Using {H}ouseholder Transformations", Journal = SIAMSciStat, Volume = 9, Pages = "152--163" } @Article{ War75, Author = "R.C. Ward", Year = 1975, Title = "The Combination Shift {QZ} Algorithm", Journal = SIAMNumAnal, Volume = 12, Pages = "835--853" } @Article{ War77, Author = "R.C. Ward", Year = 1977, Title = "Numerical Computation of the Matrix Exponential with Accuracy Estimate", Journal = SIAMNumAnal, Volume = 14, Pages = "600--614" } @Article{ War81, Author = "R.C. Ward", Year = 1981, Title = "Balancing the Generalized Eigenvalue Problem", Journal = SIAMSciStat, Volume = 2, Pages = "141--152" } @Article{ WarG78, Author = "R.C. Ward and L.J. Gray", Year = 1978, Title = "Eigensystem Computation for Skew-Symmetric and a Class of Symmetric Matrices", Journal = ACMMathSoft, Volume = 4, Pages = "278--285" } @Article{ Wat82, Author = "D.S. Watkins", Year = 1982, Title = "Understanding the {QR} Algorithm", Journal = SIAMReview, Volume = 24, Pages = "427--440" } @Article{ Wat73, Author = "G.A. Watson", Year = 1973, Title = "An Algorithm for the Inversion of Block Matrices of {T}oeplitz Form", Journal = JACM, Volume = 20, Pages = "409--415" } @Article{ Wat88, Author = "G.A. Watson", Year = 1988, Title = "The Smallest Perturbation of a Submatrix which Lowers the Rank of the Matrix", Journal = IMANumerAna, Volume = 8, Pages = "295--304" } @Article{ Wed72, Author = "P.{\AA}. Wedin", Year = 1972, Title = "Perturbation Bounds in Connection with the Singular Value Decomposition", Journal = BIT, Volume = 12, Pages = "99--111" } @Article{ Wed73a, Author = "P.{\AA}. Wedin", Year = 1973, Title = "On the Almost Rank-Deficient Case of the Least Squares Problem", Journal = BIT, Volume = 13, Pages = "344--354" } @Article{ Wed73b, Author = "P.{\AA}. Wedin", Year = 1973, Title = "Perturbation Theory for Pseudo-Inverses", Journal = BIT, Volume = 13, Pages = "217--232" } @Article{ Wid78, Author = "O. Widlund", Year = 1978, Title = "A {L}anczos Method for a Class of Nonsymmetric Systems of Linear Equations", Journal = SIAMNumAnal, Volume = 15, Pages = "801--812" } @Article{ Wil61, Author = "J.H. Wilkinson", Year = 1961, Title = "Error Analysis of Direct Methods of Matrix Inversion", Journal = JACM, Volume = 10, Pages = "281--330" } @Book{ Wil63, Author = "J.H. Wilkinson", Year = 1963, Title = "Rounding Errors in Algebraic Processes", Publisher = PrenticeHall, Address = "Englewood Cliffs, NJ" } @Book{ Wil65a, Author = "J.H. Wilkinson", Year = 1965, Title = "The Algebraic Eigenvalue Problem", Publisher = ClaredonPress, Address = "Oxford, England" } @Article{ Wil65b, Author = "J.H. Wilkinson", Year = 1965, Title = "Convergence of the {LR}, {QR}, and Related Algorithms", Journal = CompJour, Volume = 8, Pages = "77--84" } @Article{ Wil68a, Author = "J.H. Wilkinson", Year = 1968, Title = "Almost Diagonal Matrices with Multiple or Close Eigenvalues", Journal = LinAlgApp, Volume = 1, Pages = "1--12" } @Article{ Wil68c, Author = "J.H. Wilkinson", Year = 1968, Title = "Global Convergence of Tridiagonal {QR} Algorithm with Origin Shifts", Journal = LinAlgApp, Volume = 1, Pages = "409--420" } @InProceedings{ Wil68b, Author = "J.H. Wilkinson", Year = 1968, Title = "A Priori Error Analysis of Algebraic Processes", BookTitle = "Proceedings International Congress Math. ({M}oscow: {I}zdat. {M}ir)", Pages = "629--639" } @Article{ Wil71, Author = "J.H. Wilkinson", Year = 1971, Title = "Modern Error Analysis", Journal = SIAMReview, Volume = 14, Pages = "548--568" } @Article{ Wil72, Author = "J.H. Wilkinson", Year = 1972, Title = "Note on Matrices with a Very Ill-Conditioned Eigenproblem", Journal = NumerMath, Volume = 19, Pages = "176--178" } @InCollection{ Wil77, Author = "J.H. Wilkinson", Year = 1977, Title = "Some Recent Advances in Numerical Linear Algebra", BookTitle = "The State of the Art in Numerical Analysis", Editor = "D.A. H. Jacobs", Publisher = Academic, Address = "New York", Pages = "1--53" } @InCollection{ Wil78, Author = "J.H. Wilkinson", Year = 1978, Title = "Linear Differential Equations and {K}ronecker's Canonical Form", BookTitle = "Recent Advances in Numerical Analysis", Editor = "de Boor, C. and G.H. Golub", Publisher = Academic, Address = "New York", Pages = "231--265" } @Article{ Wil79, Author = "J.H. Wilkinson", Year = 1979, Title = "{K}ronecker's Canonical Form and the {QZ} Algorithm", Journal = LinAlgApp, Volume = 28, Pages = "285--303" } @Book{ WilR71, Editor = "J.H. Wilkinson and C. Reinsch", Year = 1971, Title = "Linear Algebra", Volume = 2, Series = "Handbook for Automatic Computation", Publisher = Springer, Address = "New York, NY", } @Article{ Wil84, Author = "J.H. Wilkinson", Year = 1984, Title = "On Neighboring Matrices with Quadratic Elementary Divisors", Journal = NumerMath, Volume = 44, Pages = "1--21" } @Article{ WimZ72, Author = "H. Wimmer and A.D. Ziebur", Year = 1972, Title = "Solving the Matrix Equation {$\sum f_{p}(A)Xg_{p}(A)$}", Journal = SIAMReview, Volume = 14, Pages = "318--323" } @Article{ Win68, Author = "S. Winograd", Year = 1968, Title = "A New Algorithm for Inner Product", Journal = IEEETransComp, Volume = "C-17", Pages = "693--694" } @Article{ Woz80, Author = "H. Wozniakowski", Year = 1980, Title = "Roundoff Error Analysis of a New Class of Conjugate Gradient Algorithms", Journal = LinAlgApp, Volume = 29, Pages = "507--529" } @Article{ Wra73, Author = "A. Wragg", Year = 1973, Title = "Computation of the Exponential of a Matrix {I}: Theoretical Considerations", Journal = InstMathApp, Volume = 11, Pages = "369--375" } @Article{ Wra75, Author = "A. Wragg", Year = 1975, Title = "Computation of the Exponential of a Matrix {II}: Practical Considerations", Journal = InstMathApp, Volume = 15, Pages = "273--278" } @Article{ Yoh79, Author = "J.M. Yohe", Year = 1979, Title = "Software for Interval Arithmetic: A Reasonable Portable Package", Journal = ACMMathSoft, Volume = 5, Pages = "50--63" } @Article{ You70, Author = "D.M. Young", Year = 1970, Title = "Convergence Properties of the Symmetric and Unsymmetric Over-Relaxation Methods", Journal = MathComp, Volume = 24, Pages = "793--807" } @Book{ You71, Author = "D.M. Young", Year = 1971, Title = "Iterative Solution of Large Linear Systems", Publisher = Academic, Address = "New York" } @Article{ You72, Author = "D.M. Young", Year = 1972, Title = "Generalization of Property~{$A$} and Consistent Ordering", Journal = SIAMNumAnal, Volume = 9, Pages = "454--463" } @Article{ YouJ80, Author = "D.M. Young and K.C. Jea", Year = 1980, Title = "Generalized Conjugate Gradient Acceleration of Nonsymmetrizable Iterative Methods", Journal = LinAlgApp, Volume = 34, Pages = "159--194" } @Article{ Zoh69, Author = "S. Zohar", Year = 1969, Title = "{T}oeplitz Matrix Inversion: The Algorithm of {W}.{F}. {T}rench", Journal = {JACM}, Volume = 16, Pages = "592--601" }