%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nicholas John Higham", %%% version = "1.98", %%% date = "18 May 2024", %%% time = "14:03:08 MST", %%% filename = "higham-nicholas-john.bib", %%% address = "School of Mathematics %%% University of Manchester %%% Manchester M13 9PL %%% England", %%% telephone = "+44 (0)161 275 5800", %%% FAX = "+44 (0)161 275 5819", %%% checksum = "30278 9652 41852 426843", %%% email = "nick.higham at manchester.ac.uk (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography; BibTeX; Nicholas Higham", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a bibliography of publications of %%% Nicholas John Higham (25 December 1961--20 %%% January 2024). The companion LaTeX file %%% higham-nicholas-john.ltx can be used to %%% typeset this bibliography. %%% %%% At version 1.98, the year coverage looked %%% like this: %%% %%% 1983 ( 2) 1997 ( 13) 2011 ( 4) %%% 1984 ( 0) 1998 ( 14) 2012 ( 2) %%% 1985 ( 2) 1999 ( 11) 2013 ( 5) %%% 1986 ( 4) 2000 ( 10) 2014 ( 6) %%% 1987 ( 5) 2001 ( 12) 2015 ( 5) %%% 1988 ( 4) 2002 ( 9) 2016 ( 11) %%% 1989 ( 6) 2003 ( 7) 2017 ( 7) %%% 1990 ( 16) 2004 ( 3) 2018 ( 12) %%% 1991 ( 4) 2005 ( 9) 2019 ( 9) %%% 1992 ( 11) 2006 ( 5) 2020 ( 7) %%% 1993 ( 15) 2007 ( 10) 2021 ( 10) %%% 1994 ( 10) 2008 ( 10) 2022 ( 9) %%% 1995 ( 10) 2009 ( 8) 2023 ( 6) %%% 1996 ( 12) 2010 ( 7) 2024 ( 3) %%% %%% Article: 227 %%% Book: 15 %%% InCollection: 7 %%% InProceedings: 19 %%% MastersThesis: 1 %%% Misc: 7 %%% PhdThesis: 1 %%% Proceedings: 9 %%% TechReport: 39 %%% %%% Total entries: 325 %%% %%% This file is available as part of the BibNet %%% Project. The master copy is available for %%% public access on ftp.math.utah.edu in the %%% directory tree /pub/bibnet/authors. It is %%% mirrored to netlib.bell-labs.com in the directory %%% tree /netlib/bibnet/authors, from which it is %%% available via anonymous ftp and the Netlib %%% service. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ====================================================================

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%%% # "\input bibnames.sty " %%% # "\input path.sty " %%% old: PREAMBLE{ "\newcommand{\noopsort}[1]{}" } - causes warnings with chapterbib.

@String{ack-nhfb= "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|https://www.math.utah.edu/~beebe/|"} @String{ack-njh= "Nick Higham, e-mail: \path|nick.higham@manchester.ac.uk|"}

%%% ==================================================================== %%% Departments/Institutions and their addresses:

@String{inst-CS-U-MARYLAND= "Department of Computer Science, University of Maryland"} @String{inst-CS-U-MARYLAND:adr= "College Park, MD, USA"} @String{inst-CS-U-TENN= "Department of Computer Science, University of Tennessee"} @String{inst-CS-U-TENN:adr= "Knoxville, TN, USA"} @String{inst-CS-U-UMEA= "Institute of Information Processing, University of Ume{\aa}"} @String{inst-CS-U-UMEA:adr= "Sweden"} @String{inst-HARWELL= "{AERE} {Harwell} Laboratory"} @String{inst-HARWELL:adr= "Chilton, Oxon, England"} @String{inst-MCCM= "Manchester Centre for Computational Mathematics"} @String{inst-MCCM:adr= "Manchester, England"} @String{inst-MCS-ARGONNE= "Mathematics and Computer Science Division, Argonne National Laboratory"} @String{inst-MCS-ARGONNE:adr= "IL, USA"} @String{inst-MIMS= "Manchester Institute for Mathematical Sciences, The University of Manchester"} @String{inst-MIMS:adr= "Manchester, UK"} @String{inst-ORNL= "Oak Ridge National Laboratory"} @String{inst-ORNL:adr= "Oak Ridge, TN, USA"} @String{inst-RAL= "Atlas Centre, Rutherford Appleton Laboratory"} @String{inst-RAL:adr= "Didcot, Oxon, UK"} @String{inst-U-DUNDEE= "Department of Mathematics and Computer Science, University of Dundee"} @String{inst-U-DUNDEE:adr= "Dundee, Scotland"} @String{inst-U-MANCHESTER= "University of Manchester"} @String{inst-U-MANCHESTER:adr= "Manchester, England"} @String{inst-UNIV-WATERLOO= "University of Waterloo"} @String{inst-UNIV-WATERLOO:adr= "Waterloo, ON, Canada"} @String{inst-UTK-CS= "Department of Computer Science, University of Tennessee, Knoxville"} @String{inst-UTK-CS:adr= "Knoxville, TN 37996, USA"}

%%% ==================================================================== %%% Journal abbreviations:

@String{j-ACTA-NUMERICA= "Acta Numerica"} @String{j-AMER-MATH-MONTHLY= "American Mathematical Monthly"} @String{j-BIT= "BIT"} @String{j-BIT-NUM-MATH= "BIT Numerical Mathematics"} @String{j-BULL-AMS= "Bulletin of the American Mathematical Society"} @String{j-BULL-LOND-MATH-SOC= "Bulletin of the London Mathematical Society"} @String{j-CCPE= "Concurrency and Computation: Prac\-tice and Experience"} @String{j-COMPUT-SCI-ENG= "Computing in Science and Engineering"} @String{j-COMPUT-STAT-DATA-ANAL= "Computational Statistics \& Data Analysis"} @String{j-IEEE-COMPUT-SCI-ENG= "IEEE Computational Science \& Engineering"} @String{j-IJHPCA= "The International Journal of High Performance Computing Applications"} @String{j-IMA-BULL= "IMA Bulletin"} @String{j-IMA-J-NUMER-ANAL= "IMA Journal of Numerical Analysis"} @String{j-IMA-NUM-ANA-NEWSLETTER= "IMA Numerical Analysis Newsletter"} @String{j-INT-J-NUMER-METHODS-ENG= "International Journal for Numerical Methods in Engineering"} @String{j-J-COMPLEX-NETWORKS= "Journal of Complex Networks"} @String{j-J-FLUID-MECH= "Journal of Fluid Mechanics"} @String{j-LECT-NOTES-COMP-SCI= "Lecture Notes in Computer Science"} @String{j-LINEAR-ALGEBRA-APPL= "Linear Algebra and Appl."} @String{j-MATH-COMPUT= "Math. Comp."} @String{j-MATH-GAZ= "Mathematical Gazette"} @String{j-MATH-TODAY= "Mathematics Today"} @String{j-NA-DIGEST= "NA Digest"} @String{j-NUM-LIN-ALG-APPL= "Numerical Linear Algebra with Applications"} @String{j-NUM-MATH= "Numer. Math."} @String{j-NUMER-ALGORITHMS= "Numerical Algorithms"} @String{j-PARALLEL-COMPUTING= "Parallel Computing"} @String{j-PHILOS-TRANS-R-SOC-LOND-SER-A= "Philosophical transactions of the Royal Society of London Series A"} @String{j-PROC-R-SOC-LOND-SER-A= "Proceedings of the Royal Society of London. Series A"} @String{j-R-SOC-OPEN-SCI= "Royal Society Open Science"} @String{j-SIAM-J-MAT-ANA-APPL= "SIAM J. Matrix Anal. Appl."} @String{j-SIAM-J-NUMER-ANAL= "SIAM Journal on Numerical Analysis"} @String{j-SIAM-J-SCI-COMP= "SIAM Journal on Scientific Computing"} @String{j-SIAM-J-SCI-STAT-COMP= "SIAM Journal on Scientific and Statistical Computing"} @String{j-SIAM-NEWS= "SIAM News"} @String{j-SIAM-REVIEW= "SIAM Review"} @String{j-TOMS= "ACM Trans. Math. Software"}

%%% ==================================================================== %%% Publishers and their addresses:

@String{pub-ACM= "ACM Press"} @String{pub-ACM:adr= "New York, NY 10036, USA"} @String{pub-AMS= "American Mathematical Society"} @String{pub-AMS:adr= "Providence, RI, USA"} @String{pub-AP= "Academic Press"} @String{pub-AW-LONGMAN= "Ad{\-d}i{\-s}on-Wes{\-l}ey Longman"} @String{pub-AW-LONGMAN:adr= "Reading, MA, USA"} @String{pub-CH= "Chapman and Hall"} @String{pub-CH:adr-L= "London"} @String{pub-CHAPMAN-HALL-CRC= "Chapman and Hall/CRC"} @String{pub-CHAPMAN-HALL-CRC:adr= "Boca Raton, FL, USA"} @String{pub-ELS= "Elsevier Science Publishers B.V."} @String{pub-ELS:adr= "Amsterdam, The Netherlands"} @String{pub-IEEE= "IEEE Computer Society Press"} @String{pub-IEEE:adr= "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-LONGMAN-ST= "Longman Scientific and Technical"} @String{pub-LONGMAN-ST:adr= "Essex, UK"} @String{pub-KLUWER= "Kluwer Academic Publishers"} @String{pub-KLUWER:adr= "Norwell, MA, USA, and Dordrecht, The Netherlands"} @String{pub-OXFORD= "Oxford University Press"} @String{pub-OXFORD:adr= "Walton Street, Oxford OX2 6DP, UK"} @String{pub-PENGUIN= "Penguin"} @String{pub-PENGUIN:adr-H= "Harmondsworth, UK"} @String{pub-PENGUIN:adr-L= "London"} @String{pub-PENGUIN:adr-NY= "New York"} @String{pub-PRINCETON= "Princeton University Press"} @String{pub-PRINCETON:adr= "Princeton, NJ, USA"} @String{pub-SIAM= "Society for Industrial and Applied Mathematics"} @String{pub-SIAM:adr= "Philadelphia, PA, USA"} @String{pub-SPRINGER= "Spring{\-}er-Ver{\-}lag"} @String{pub-SPRINGER:adr-B= "Berlin"} @String{pub-SPRINGER:adr-NY= "New York"} @String{pub-SV= "Springer-Verlag"} @String{pub-SV:adr= "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-WORLD-SCI= "World Scientific Publishing Co."} @String{pub-WORLD-SCI:adr= "Singapore; Philadelphia, PA, USA; River Edge, NJ, USA"}

%%% ==================================================================== %%% Part 1 (of 2): Publications by Nicholas Higham.

@MastersThesis{Higham:1983:MCN, author = "N. J. Higham", title = "Matrix Condition Numbers", type = "{M.Sc. Thesis}", school = inst-U-MANCHESTER, address = inst-U-MANCHESTER:adr, pages = "iv + 86", month = oct, year = "1983", bibdate = "Tue Mar 21 16:29:28 GMT 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @TechReport{Higham:1983:UBC, author = "Nicholas J. Higham", title = "Upper bounds for the condition number of a triangular matrix", type = "Numerical Analysis Report", number = "86", institution = inst-U-MANCHESTER, address = inst-U-MANCHESTER:adr, month = may, year = "1983", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @TechReport{Higham:1985:MCB, author = "Nicholas J. Higham", title = "Matrix Computations in {Basic} on a Microcomputer", type = "Numerical Analysis Report", number = "101", institution = "Department of Mathematics, University of Manchester", address = "Manchester, M13 9PL, UK", pages = "62", month = jun, year = "1985", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "2013.10.02", subject-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", updated = "2013.10.02", } @PhdThesis{Higham:1985:NPN, author = "Nicholas J. Higham", title = "Nearness Problems in Numerical Linear Algebra", school = inst-U-MANCHESTER, address = inst-U-MANCHESTER:adr, pages = "173", month = jul, year = "1985", bibdate = "Tue Mar 21 16:29:32 GMT 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1986:CPD, author = "Nicholas J. Higham", title = "Computing the Polar Decomposition---with Applications", journal = j-SIAM-J-SCI-STAT-COMP, volume = "7", number = "4", pages = "1160--1174", month = oct, year = "1986", CODEN = "SIJCD4", ISSN = "0196-5204", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific and Statistical Computing", journal-URL = "http://epubs.siam.org/loi/sijcd4", mynote = "N.A. Report 94, November 1984. (Proof in Appendix is not in paper).", } @Article{Higham:1986:EAC, author = "Nicholas J. Higham", title = "Efficient Algorithms for Computing the Condition Number of a Tridiagonal Matrix", journal = j-SIAM-J-SCI-STAT-COMP, volume = "7", number = "1", pages = "150--165", year = "1986", CODEN = "SIJCD4", ISSN = "0196-5204", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific and Statistical Computing", journal-URL = "http://epubs.siam.org/loi/sijcd4", } @Article{Higham:1986:MCB, author = "Nicholas J. Higham", title = "Matrix Computations in {Basic} on a Microcomputer", journal = j-IMA-BULL, volume = "22", pages = "13--20", year = "1986", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "IMA Bulletin", } @Article{Higham:1986:NMM, author = "Nicholas J. Higham", title = "{Newton}'s Method for the Matrix Square Root", journal = j-MATH-COMPUT, volume = "46", number = "174", pages = "537--549", month = apr, year = "1986", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F30 (65H10)", MRnumber = "87d:65045", MRreviewer = "Lars Eld{\'e}n", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; JSTOR database; Theory/Matrix.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "Dept. of Math., Manchester Univ., UK", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "equation; iterative methods; mathematical convergence; matrix algebra; matrix square root; Newton iteration; Newton method; perturbation analysis; properties; quadratic matrix", kwds = "nla, matrix function, matrix square root, Newton's method", treatment = "T Theoretical or Mathematical", } @Article{Higham:1987:CRS, author = "Nicholas J. Higham", title = "Computing Real Square Roots of a Real Matrix", journal = j-LINEAR-ALGEBRA-APPL, volume = "88/89", pages = "405--430", year = "1987", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Higham:1987:EAB, author = "Nicholas J. Higham", title = "Error Analysis of the {Bj{\"o}rck--Pereyra} Algorithms for Solving {Vandermonde} Systems", journal = j-NUM-MATH, volume = "50", number = "5", pages = "613--632", year = "1987", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", } @InProceedings{Higham:1987:NLA, author = "N. J. Higham and G. W. Stewart", title = "Numerical Linear Algebra in Statistical Computing", crossref = "Iserles:1987:SAN", pages = "41--57", year = "1987", bibdate = "Thu May 29 17:14:49 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", xxpages = "41--58", } @Article{Higham:1987:SCN, author = "Nicholas J. Higham", title = "A Survey of Condition Number Estimation for Triangular Matrices", journal = j-SIAM-REVIEW, volume = "29", number = "4", pages = "575--596", month = dec, year = "1987", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1029112", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "65F35", MRnumber = "88j:65086", bibdate = "Sat Mar 29 09:54:19 MDT 2014", bibsource = "Compendex database; http://epubs.siam.org/toc/siread/29/4; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", abstract = "We survey and compare a wide variety of techniques for estimating the condition number of a triangular matrix, and make recommendations concerning the use of the estimates in applications. Each of the methods is shown to bound the condition number; the bounds can broadly be categorised as upper bounds from matrix theory and lower bounds from heuristic or probabilistic algorithms. For each bound we examine by how much, at worst, it can overestimate or underestimate the condition number. Numerical experiments are presented in order to illustrate and compare the practical performance of the condition estimators.", acknowledgement = ack-nhfb, affiliationaddress = "Univ of Manchester, Manchester, Engl", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", classification = "723; 921", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", journalabr = "SIAM Rev", keywords = "computer programming --- Algorithms; condition number estimation; mathematical techniques; Matrix Algebra; matrix condition number; qr decomposition; rank estimation; triangular matrices", onlinedate = "December 1987", } @Article{Higham:1988:AFC, author = "Nicholas J. Higham", title = "Algorithm 674: {FORTRAN} Codes for Estimating the One-Norm of a Real or Complex Matrix, with Applications to Condition Estimation", journal = j-TOMS, volume = "14", number = "4", pages = "381--396", month = dec, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65F35)", MRnumber = "1 062 484", bibdate = "Sat Aug 27 15:05:32 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "See also \cite{Higham:1989:CFC}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p381-higham/; http://www.acm.org/pubs/toc/Abstracts/0098-3500/214386.html", abstract = "FORTRAN 77 codes SONEST and CONEST are presented for estimating the 1-norm ( or the infinity-norm) of a real or complex matrix, respectively. The codes are of wide applicability in condition estimation since explicit access to the matrix, $A$, is not required; instead, matrix-vector products $ A x $ and $ A^T x $ are computed by the calling program via a reverse communication interface. The algorithms are based on a convex optimization method for estimating the 1-norm of a real matrix devised by Hager. We derive new results concerning the behavior of Hager's method, extend it to complex matrices, and make several algorithmic modifications in order to improve the reliability and efficiency.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://dl.acm.org/pub.cfm?id=J782", keywords = "algorithms; condition estimation; nla; software, nla, condition estimation, software", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Higham:1988:CNS, author = "Nicholas J. Higham", title = "Computing a Nearest Symmetric Positive Semidefinite Matrix", journal = j-LINEAR-ALGEBRA-APPL, volume = "103", pages = "103--118", year = "1988", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Higham:1988:FSV, author = "Nicholas J. Higham", title = "Fast Solution of {Vandermonde}-like Systems Involving Orthogonal Polynomials", journal = j-IMA-J-NUMER-ANAL, volume = "8", number = "4", pages = "473--486", month = oct, year = "1988", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/8.4.473", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65H10 (65F30)", MRnumber = "89k:65067", bibdate = "Thu Aug 25 10:58:30 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; MathSciNet database", abstract = "Consider the $ (n + 1) \times (n + 1) $ Vandermonde-like matrix $ P = [{pi - 1}(\alpha_{j - 1})] $, where the polynomials $ p_0 (x), \ldots {}, p_n(x) $ satisfy a three-term recurrence relation. We develop algorithms for solving the primal and dual systems, $ P x = b $ and $ P^T a = f $ respectively, in $ O(n^2) $ arithmetic operations and $ O(n) $ elements of storage. These algorithms generalize those of Bj{\"o}rck \& Pereyra which apply to the monomial case $ p_i(x) $. When the $ p_i(x) $ are the Chebyshev polynomials, the algorithms are shown to be numerically unstable. However, it is found empirically that the addition of just one step of iterative refinement is, in single precision, enough to make the algorithms numerically stable.", acknowledgement = ack-nhfb # " and " # ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", } @Article{Higham:1988:SPP, author = "Nicholas J. Higham", title = "The Symmetric {Procrustes} Problem", journal = j-BIT, volume = "28", number = "1", pages = "133--143", year = "1988", CODEN = "BITTEL, NBITAB", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", MRclass = "65F20 (41A29 73K05)", MRnumber = "89g:65047", MRreviewer = "N. Gass", bibdate = "Thu Nov 12 18:12:56 MST 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh # " and " # ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "BIT (Nordisk tidskrift for informationsbehandling)", journal-URL = "http://link.springer.com/journal/10543", } @Article{Higham:1989:AST, author = "Nicholas J. Higham", title = "The Accuracy of Solutions to Triangular Systems", journal = j-SIAM-J-NUMER-ANAL, volume = "26", number = "5", pages = "1252--1265", month = oct, year = "1989", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65F05 (65G05)", MRnumber = "90i:65053", MRreviewer = "James Weldon Demmel", bibdate = "Mon Jan 20 15:27:00 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", } @Article{Higham:1989:CFC, author = "Nicholas J. Higham", title = "Corrigendum: ``{Algorithm} 674: {FORTRAN} Codes for Estimating the One-Norm of a Real or Complex Matrix, with Applications to Condition Estimation''", journal = j-TOMS, volume = "15", number = "2", pages = "168--168", month = jun, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:18:49 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "See \cite{Higham:1988:AFC}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p168-higham/; http://www.acm.org/pubs/toc/Abstracts/0098-3500/214391.html", abstract = "We omitted giving this article an ACM algorithm number when it was first published in its entirety in the December 1988 issue of {\em TOMS}, Vol. 14, No. 4, pp. 381-396. To correct this, we do so here, and reprint the title as a pointer to the original article.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://dl.acm.org/pub.cfm?id=J782", keywords = "algorithms", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @TechReport{Higham:1989:CTM, author = "Nicholas J. Higham", title = "A Collection of Test Matrices in {MATLAB}", type = "Numerical Analysis Report", number = "172", institution = inst-U-MANCHESTER, address = inst-U-MANCHESTER:adr, month = jul, year = "1989", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", mynote = "Published version: \cite{Higham:1991:ACT}.", } @Article{Higham:1989:LGF, author = "Nicholas J. Higham and Desmond J. Higham", title = "Large Growth Factors in {Gaussian} Elimination with Pivoting", journal = j-SIAM-J-MAT-ANA-APPL, volume = "10", number = "2", pages = "155--164", month = apr, year = "1989", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:1989:MCP, author = "Nicholas J. Higham", title = "Matrix Computations on a {PC}", journal = j-SIAM-NEWS, volume = "22", pages = "16", month = jan, year = "1989", ISSN = "0036-1437", ISSN-L = "0036-1437", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", } @InProceedings{Higham:1989:MNP, author = "Nicholas J. Higham", editor = "M. J. C. Gover and S. Barnett", booktitle = "Applications of Matrix Theory", title = "Matrix Nearness Problems and Applications", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "1--27", year = "1989", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @TechReport{Demmel:1990:IEB, author = "J. Demmel and N. Higham", title = "Improved Error Bounds for Underdetermined System Solvers", type = "LAPACK Working Note", number = "23", institution = inst-UTK-CS, address = inst-UTK-CS:adr, month = aug, year = "1990", bibdate = "Fri Apr 22 17:06:37 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "UT-CS-90-113, August 1990.", URL = "http://www.netlib.org/lapack/lawns/lawn23.ps; http://www.netlib.org/lapack/lawnspdf/lawn23.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @TechReport{Demmel:1990:SBA, author = "J. Demmel and N. Higham", title = "Stability of Block Algorithms with Fast Level 3 {BLAS}", type = "LAPACK Working Note", number = "22", institution = inst-UTK-CS, address = inst-UTK-CS:adr, month = jul, year = "1990", bibdate = "Fri Apr 22 17:06:37 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "UT-CS-90-110, July 1990.", URL = "http://www.netlib.org/lapack/lawns/lawn22.ps; http://www.netlib.org/lapack/lawnspdf/lawn22.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @TechReport{DuCroz:1990:SMM, author = "J. {Du Croz} and N. Higham", title = "Stability of Methods for Matrix Inversion", type = "LAPACK Working Note", number = "27", institution = inst-UTK-CS, address = inst-UTK-CS:adr, month = oct, year = "1990", bibdate = "Fri Apr 22 17:06:37 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "UT-CS-90-119, October, 1990.", URL = "http://www.netlib.org/lapack/lawns/lawn27.ps; http://www.netlib.org/lapack/lawnspdf/lawn27.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @InProceedings{Higham:1990:ACD, author = "Nicholas J. Higham", editor = "M. G. Cox and S. J. Hammarling", booktitle = "Reliable Numerical Computation", title = "Analysis of the {Cholesky} Decomposition of a Semi-definite Matrix", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "161--185", year = "1990", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1990:BEG, author = "Nicholas J. Higham", title = "Bounding the Error in {Gaussian} Elimination for Tridiagonal Systems", journal = j-SIAM-J-MAT-ANA-APPL, volume = "11", number = "4", pages = "521--530", month = oct, year = "1990", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @InProceedings{Higham:1990:CEB, author = "Nicholas J. Higham", editor = "Philip J. Brown and Wayne A. Fuller", booktitle = "Statistical Analysis of Measurement Error Models and Applications, Contemporary Mathematics 112", title = "Computing Error Bounds for Regression Problems", publisher = pub-AMS, address = pub-AMS:adr, pages = "195--208", year = "1990", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1990:EFM, author = "Nicholas J. Higham", title = "Exploiting Fast Matrix Multiplication Within the Level 3 {BLAS}", journal = j-TOMS, volume = "16", number = "4", pages = "352--368", month = dec, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65F99)", MRnumber = "1 095 133", bibdate = "Sun Sep 04 23:21:57 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "Describes algorithms based on Strassen's method which are asymptotically faster than the standard $ {N}^3 $ algorithm, and in practice, faster for $ {N} \approx 100 $, and examines their numerical stability. See \cite{Dongarra:1990:ASL,Demmel:1992:SBA}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p352-higham/", abstract = "The Level 3 BLAS (BLAS3) are a set of specifications of FORTRAN 77 subprograms for carrying out matrix multiplications and the solution of triangular systems with multiple right-hand sides. They are intended to provide efficient and portable building blocks for linear algebra algorithms on high-performance computers. We describe algorithms for the BLAS3 operations that are asymptotically faster than the conventional ones. These algorithms are based on Strassen's method for fast matrix multiplication, which is now recognized to be a practically useful technique once matrix dimensions exceed about 100. We pay particular attention to the numerical stability of these ``fast BLAS3.'' Error bounds are given and their significance is explained and illustrated with the aid of numerical experiments. Our conclusion is that the fast BLAS3, although not as strongly stable as conventional implementations, are stable enough to merit careful consideration in many applications.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://dl.acm.org/pub.cfm?id=J782", keywords = "algorithms", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.", } @Article{Higham:1990:EMN, author = "Nicholas J. Higham", title = "Experience with a Matrix Norm Estimator", journal = j-SIAM-J-SCI-STAT-COMP, volume = "11", number = "4", pages = "804--809", month = jul, year = "1990", CODEN = "SIJCD4", ISSN = "0196-5204", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific and Statistical Computing", journal-URL = "http://epubs.siam.org/loi/sijcd4", mynote = "Timely Communication.", } @Article{Higham:1990:FMM, author = "Nicholas J. Higham", title = "Is Fast Matrix Multiplication of Practical Use?", journal = j-SIAM-NEWS, volume = "23", pages = "12--??", month = nov, year = "1990", ISSN = "0036-1437", ISSN-L = "0036-1437", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", } @Article{Higham:1990:FPD, author = "Nicholas J. Higham and Robert S. Schreiber", title = "Fast Polar Decomposition of an Arbitrary Matrix", journal = j-SIAM-J-SCI-STAT-COMP, volume = "11", number = "4", pages = "648--655", month = jul, year = "1990", CODEN = "SIJCD4", ISSN = "0196-5204", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, annote = "Prepublished as RIACS technical report 88.29 and NASA Contractor Report 185412.", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific and Statistical Computing", journal-URL = "http://epubs.siam.org/loi/sijcd4", } @InProceedings{Higham:1990:HAG, author = "Nicholas J. Higham", editor = "D. F. Griffiths and G. A. Watson", booktitle = "Numerical Analysis 1989, Proceedings of the 13th Dundee Conference", title = "How Accurate is {Gaussian} Elimination?", volume = "228", publisher = pub-LONGMAN-ST, address = pub-LONGMAN-ST:adr, pages = "137--154", year = "1990", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", series = "Pitman Research Notes in Mathematics", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @TechReport{Higham:1990:IRE, author = "Nicholas J. Higham", title = "Iterative Refinement Enhances the Stability of {$ Q R $} Factorization Methods for Solving Linear Equations", type = "Numerical Analysis Report", number = "182", institution = inst-U-MANCHESTER, address = inst-U-MANCHESTER:adr, month = apr, year = "1990", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", mynote = "Contains proofs in the appendix that are not in \cite{Higham:1991:IRE}.", } @Article{Higham:1990:RGH, author = "Nicholas J. Higham", title = "Review of {``G. H. Golub and C. F. Van Loan, Matrix Computations, Second Edition, Johns Hopkins University Press, Baltimore, Maryland, 1989''}", journal = j-LINEAR-ALGEBRA-APPL, volume = "141", pages = "289--292", year = "1990", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Higham:1990:RMJ, author = "Nicholas J. Higham", title = "Review of {``M. J. C. Gover and S. Barnett, eds., Applications of Matrix Theory, Oxford University Press, 1989''}", journal = j-MATH-GAZ, volume = "74", number = "468", pages = "202", year = "1990", CODEN = "MAGAAS", ISSN = "0025-5572 (print), 2056-6328 (electronic)", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Mathematical Gazette", journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620", } @Article{Higham:1990:SAA, author = "Nicholas J. Higham", title = "Stability Analysis of Algorithms for Solving Confluent {Vandermonde}-like Systems", journal = j-SIAM-J-MAT-ANA-APPL, volume = "11", number = "1", pages = "23--41", month = jan, year = "1990", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:1991:ACT, author = "Nicholas J. Higham", title = "Algorithm 694: {A} Collection of Test Matrices in {MATLAB}", journal = j-TOMS, volume = "17", number = "3", pages = "289--305", month = sep, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p289-higham/", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://dl.acm.org/pub.cfm?id=J782", keywords = "algorithms; experimentation; performance; theory", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Higham:1991:IRE, author = "Nicholas J. Higham", title = "Iterative Refinement Enhances the Stability of {$ Q R $} Factorization Methods for Solving Linear Equations", journal = j-BIT, volume = "31", number = "3", pages = "447--468", year = "1991", CODEN = "BITTEL, NBITAB", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", MRclass = "65F05 (65F10 65G05)", MRnumber = "92h:65043", MRreviewer = "James Weldon Demmel", bibdate = "Fri Nov 13 07:00:34 MST 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh # " and " # ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "BIT (Nordisk tidskrift for informationsbehandling)", journal-URL = "http://link.springer.com/journal/10543", } @InCollection{Higham:1991:SLE, author = "Nicholas J. Higham", editor = "Christine Bondi", booktitle = "New Applications of Mathematics", title = "Solving Linear Equations", publisher = pub-PENGUIN, address = pub-PENGUIN:adr-L, pages = "33--56", year = "1991", MRclass = "65-01", MRnumber = "1190077", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", mynote = "Chapter 2.", } @Article{Higham:1991:TMP, author = "Nicholas J. Higham", title = "Three Measures of Precision in Floating Point Arithmetic", journal = j-NA-DIGEST, volume = "91", number = "16", year = "1991", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "Electronic mail magazine: \path|na.help@na-net.ornl.gov|.", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "NA Digest", mynote = "Sunday, April 21, 1991.", } @TechReport{Demmel:1992:BLF, author = "James Demmel and Nick Higham and Rob Schreiber", title = "Block {LU} Factorization", type = "LAPACK Working Note", number = "40", institution = inst-UTK-CS, address = inst-UTK-CS:adr, month = feb, year = "1992", bibdate = "Fri Apr 22 17:06:37 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "UT-CS-92-149, February 1992.", URL = "http://www.netlib.org/lapack/lawns/lawn40.ps; http://www.netlib.org/lapack/lawnspdf/lawn40.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Demmel:1992:SBA, author = "James W. Demmel and Nicholas J. Higham", title = "Stability of Block Algorithms with Fast Level-3 {BLAS}", journal = j-TOMS, volume = "18", number = "3", pages = "274--291", month = sep, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:27:16 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "See \cite{Dongarra:1990:ASL,Higham:1990:EFM,Dayde:1994:PBI}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p274-demmel/", abstract = "Block algorithms are becoming increasingly popular in matrix computations. Since their basic unit of data is a submatrix rather than a scalar, they have a higher level of granularity than point algorithms, and this makes them well suited to high-performance computers. The numerical stability of the block algorithms in the new linear algebra program library LAPACK is investigated here. It is shown that these algorithms have backward error analyses in which the backward error bounds are commensurate with the error bounds for the underlying level-3 BLAS (BLAS3). One implication is that the block algorithms are as stable as the corresponding point algorithms when conventional BLAS3 are used. A second implication is that the use of BLAS3 based on fast matrix multiplication techniques affects the stability only insofar as it increases the constant terms in the normwise backward error bounds. For linear equation solvers employing {\em LU} factorization, it is shown that fixed precision iterative refinement helps to mitigate the effect of the larger error constants. Despite the positive results presented here, not all plausible block algorithms are stable; we illustrate this with the example of {\em LU} factorization with block triangular factors and describe how to check a block algorithm for stability without doing a full error analysis.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://dl.acm.org/pub.cfm?id=J782", keywords = "algorithms; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{DuCroz:1992:SMM, author = "Jeremy J. {Du Croz} and Nicholas J. Higham", title = "Stability of Methods for Matrix Inversion", journal = j-IMA-J-NUMER-ANAL, volume = "12", number = "1", pages = "1--19", year = "1992", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/12.1.1", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65F05", MRnumber = "92k:65047", bibdate = "Sat Dec 23 17:06:35 MST 2000", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; MathSciNet database", abstract = "Inversion of a triangular matrix can be accomplished in several ways. The standard methods are characterized by the loop ordering, whether matrix-vector multiplication, solution of a triangular system, or a rank-1 update is done inside the outer loop, and whether the method is blocked or unblocked. The numerical stability properties of these methods are investigated. It is shown that unblocked methods satisfy pleasing bounds on the left or right residual. However, for one of the block methods it is necessary to convert a matrix multiplication into the solution of a multiple right-hand side triangular system in order to have an acceptable residual bound. The inversion of a full matrix given a factorization PA=LU is also considered, including the special cases of symmetric indefinite and symmetric positive definite matrices. Three popular methods are shown to possess satisfactory residual bounds, subject to a certain requirement on the implementation, and an attractive new method is described. This work was motivated by the question of what inversion methods should be used in LAPACK.", acknowledgement = ack-nhfb # " and " # ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", } @Article{Higham:1992:BEC, author = "Desmond J. Higham and Nicholas J. Higham", title = "Backward Error and Condition of Structured Linear Systems", journal = j-SIAM-J-MAT-ANA-APPL, volume = "13", number = "1", pages = "162--175", month = jan, year = "1992", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:1992:CPT, author = "Desmond J. Higham and Nicholas J. Higham", title = "Componentwise Perturbation Theory for Linear Systems with Multiple Right-Hand Sides", journal = j-LINEAR-ALGEBRA-APPL, volume = "174", pages = "111--129", year = "1992", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Higham:1992:EMN, author = "Nicholas J. Higham", title = "Estimating the Matrix $p$-norm", journal = j-NUM-MATH, volume = "62", pages = "539--555", year = "1992", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", } @Article{Higham:1992:IWP, author = "Nicholas J. Higham", title = "{IMA} Workshop Participants {F}{\^e}te {Golub} on 60th Birthday", journal = j-SIAM-NEWS, volume = "25", pages = "3--??", month = may, year = "1992", ISSN = "0036-1437", ISSN-L = "0036-1437", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", } @Article{Higham:1992:JAF, author = "Nicholas J. Higham", title = "The Joy of Anonymous {FTP}", journal = j-IMA-NUM-ANA-NEWSLETTER, volume = "17", number = "1", pages = "61--64", month = oct, year = "1992", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "IMA Numerical Analysis Newsletter", } @Article{Higham:1992:LRM, author = "Nicholas J. Higham", title = "{LAPACK} Released in {March}", journal = j-SIAM-NEWS, volume = "25", pages = "20", month = may, year = "1992", ISSN = "0036-1437", ISSN-L = "0036-1437", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", } @TechReport{Higham:1992:PTB, author = "Nick Higham", title = "Perturbation Theory and Backward Error for {$ A X - X B = C $}", type = "LAPACK Working Note", number = "42", institution = inst-UTK-CS, address = inst-UTK-CS:adr, month = apr, year = "1992", bibdate = "Fri Apr 22 17:06:37 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "UT-CS-92-153, April, 1992.", URL = "http://www.netlib.org/lapack/lawns/lawn42.ps; http://www.netlib.org/lapack/lawnspdf/lawn42.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1992:SMM, author = "Nicholas J. Higham", title = "Stability of a Method for Multiplying Complex Matrices with Three Real Matrix Multiplications", journal = j-SIAM-J-MAT-ANA-APPL, volume = "13", number = "3", pages = "681--687", month = jul, year = "1992", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @TechReport{Balle:1993:STM, author = "Susanne M. Balle and Per Christian Hansen and Nicholas J. Higham", title = "A {Strassen}-Type Matrix Inversion Algorithm for the {Connection Machine}", number = "CNC/1993/028", institution = "Centre for Novel Computing, " # inst-U-MANCHESTER, address = inst-U-MANCHESTER:adr, type = "Technical Report", pages = "29", month = oct, year = "1993", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Demmel:1993:IEB, author = "James W. Demmel and Nicholas J. Higham", title = "Improved Error Bounds for Underdetermined System Solvers", journal = j-SIAM-J-MAT-ANA-APPL, volume = "14", number = "1", pages = "1--14", month = jan, year = "1993", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", mynote = "Also LAPACK Working Note \#23.", } @Article{Hammarling:1993:CHW, author = "Sven Hammarling and Nicholas J. Higham and Bo K{\aa}gstr{\"o}m", title = "{CERFACS} Hosts Workshop on Reliability of Computations", journal = j-SIAM-NEWS, volume = "26", pages = "4", month = jul, year = "1993", ISSN = "0036-1437", ISSN-L = "0036-1437", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", } @Article{Higham:1993:AFP, author = "Nicholas J. Higham", title = "The accuracy of floating point summation", journal = j-SIAM-J-SCI-COMP, volume = "14", number = "4", pages = "783--799", month = jul, year = "1993", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/0914050", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65G05 (65B10)", MRnumber = "94a:65025", bibdate = "Thu Aug 23 06:36:53 2001", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://citeseer.nj.nec.com/higham93accuracy.html; http://citeseer.nj.nec.com/rd/4651150%2C296147%2C1%2C0.25%2CDownload/http%253A%252F%252Fciteseer.nj.nec.com/cache/papers2/cs/14280/http%253AzSzzSzwww.maths.man.ac.ukzSz%257EnareportszSznarep198.pdf/higham93accuracy.pdf; http://citeseer.nj.nec.com/rd/4651150%2C296147%2C1%2C0.25%2CDownload/http%253A%252F%252Fwww.maths.man.ac.uk/%257Enareports/narep198.ps.gz", abstract = "The usual recursive summation technique is just one of several ways of computing the sum of $n$ floating point numbers. Five summation methods and their variations are analyzed. The accuracy of the methods is compared using rounding error analysis and numerical experiments. Four of the methods are shown to be special cases of a general class of methods, and an error analysis is given for this class. No one method is uniformly more accurate than the others, but some guidelines are given on the choice of method in particular cases.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Manchester Univ., UK", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", classification = "C4110 (Error analysis in numerical methods); C5230 (Digital arithmetic methods)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", keywords = "Floating point numbers; Floating point summation; Numerical experiments; Recursive summation technique; Rounding error analysis", pubcountry = "USA", thesaurus = "Digital arithmetic; Error analysis", } @InCollection{Higham:1993:CCL, author = "Nicholas J. Higham", editor = "M. Chu and others", booktitle = "The {Lanczos} Collected Papers with Commentaries", title = "{Commentary on C. Lanczos, ``Introduction'' to ``Tables of Chebyshev Polynomials $ S_n(x) $ and $ C_n(x) $'', Nat.\ Bur.\ Stand., Appl.\ Math.\ Series 9, 1952, v--xxvi}", publisher = "????", address = "????", year = "1993", bibdate = "Wed Nov 1 08:00:18 2000", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "To appear.", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @InProceedings{Higham:1993:CEA, author = "Nicholas J. Higham and Philip A. Knight", title = "Componentwise Error Analysis for Stationary Iterative Methods", crossref = "Meyer:1993:LAM", pages = "29--46", year = "1993", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", series = "IMA Volumes in Mathematics and its Applications", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1993:FPB, author = "Nicholas J. Higham and Philip A. Knight", title = "Finite Precision Behavior of Stationary Iteration for Solving Singular Systems", journal = j-LINEAR-ALGEBRA-APPL, volume = "192", pages = "165--186", year = "1993", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", mynote = "Special issue for Proceedings of Workshop on Computational Linear Algebra in Algebraic and Related Problems.", } @Book{Higham:1993:HWM, author = "Nicholas J. Higham", title = "Handbook of Writing for the Mathematical Sciences", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xii + 241", month = jun, year = "1993", ISBN = "0-89871-314-5", ISBN-13 = "978-0-89871-314-5", LCCN = "QA42.H54 1993", bibdate = "Tue Mar 1 12:03:19 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/texbook3.bib", price = "US\$21.50", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", note-1 = "[From the publisher]: Having trouble with your latest math paper? Giving a presentation that you just can't pull together? Struggling with your thesis or trying to get your first article published in a technical journal? Handbook of Writing for the Mathematical Sciences is the book for you! This handy volume provides information on virtually every issue you will face when writing a technical paper or talk, from choosing the right journal to handling your references. You'll also get an overview of the entire publication process--invaluable for anyone hoping to publish in a technical journal.", note-2 = "To write a truly impressive paper, you'll need to understand the anatomy of a research paper and the steps involved in revising a draft. This book offers discussions of these fundamental topics, along with illustrative and provocative examples. Also included are chapters on standard English usage, using computers for writing and research, and writing technical material when English is a foreign language. This handbook provides much-needed advice on handling the basic ingredients of a research paper, like definitions, theorems, examples, and equations. In addition, appendices provide essential reference material, including summaries of \LaTeX{} symbols and Emacs commands, addresses of mathematical societies, and a list of papers that have won expository writing prizes.", note-3 = "This book is ideal for graduate students and teachers. Among its special features: \begin{itemize} \item Detail and extensive use of examples make it an excellent teaching tool \item Discusses \TeX{} and other software tools for preparing publications \item Thorough treatment, with examples, of how to write slides (transparencies) for a mathematical talk. \item Comprehensive index and extensive bibliography make it an excellent reference \item Readable for everyone in the field--from undergraduates to seasoned professionals \end{itemize}", note-4 = "About the Author: Nicholas J. Higham is a Reader in Mathematics at the University of Manchester, UK. He is the author of more than 40 publications and is a member of the editorial board of the SIAM Journal on Matrix Analysis and Applications.", tableofcontents = "Preface \\ 1: General Principles \\ 2: Writer's Tools and Recommended Reading \\ 3: Mathematical Writing \\ 4: English Usage \\ 5: When English is a Foreign Language \\ 6: Writing a Paper \\ 7: Revising a Draft \\ 8: Publishing a Paper \\ 9: Writing a Talk \\ 10: Computer Aids for Writing and Research \\ Appendix A: The Greek Alphabet \\ Appendix B: Summary of \TeX{} and \LaTeX{} Symbols \\ Appendix C: GNU Emacs--The Sixty+ Most Useful Commands; \\ Appendix D: Mathematical Organizations in the UK and USA \\ Appendix E: Winners of Prizes for Expository Writing; \\ Appendix F: Glossary \\ Bibliography \\ Index", } @Article{Higham:1993:ODS, author = "Nicholas J. Higham", title = "Optimization by Direct Search in Matrix Computations", journal = j-SIAM-J-MAT-ANA-APPL, volume = "14", number = "2", pages = "317--333", month = apr, year = "1993", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @TechReport{Higham:1993:PSV, author = "Nicholas J. Higham and Pythagoras Papadimitriou", title = "Parallel Singular Value Decomposition via the Polar Decomposition", type = "Numerical Analysis Report", number = "239", institution = inst-MCCM, address = inst-MCCM:adr, month = oct, year = "1993", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", mynote = "Longer version of \cite{Higham:1994:PAC}.", } @InProceedings{Higham:1993:PTBa, author = "Nicholas J. Higham", title = "Perturbation theory and backward error for {$ A X - X B = C $}", crossref = "Moonen:1993:LAL", pages = "391--392", year = "1993", bibdate = "Thu May 29 18:39:54 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1993:PTBb, author = "Nicholas J. Higham", title = "Perturbation theory and backward error analysis for {$ A X - X B = C $}", journal = j-BIT, volume = "33", number = "1", pages = "124--136", year = "1993", CODEN = "BITTEL, NBITAB", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", MRclass = "65F05 (65G05)", MRnumber = "96a:65036", bibdate = "Fri Nov 13 07:00:34 MST 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://www.mai.liu.se/BIT/contents/bit33.html", acknowledgement = ack-njh # " and " # ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "BIT (Nordisk tidskrift for informationsbehandling)", journal-URL = "http://link.springer.com/journal/10543", } @TechReport{Higham:1993:TMT, author = "Nicholas J. Higham", title = "The {Test Matrix Toolbox} for {Matlab}", type = "Numerical Analysis Report", number = "237", institution = inst-MCCM, address = inst-MCCM:adr, pages = "76", month = dec, year = "1993", bibdate = "Tue Mar 30 17:06:37 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", abstract-1 = "We describe version 2.0 of the Test Matrix Toolbox for Matlab 4. The toolbox contains a collection of test matrices, routines for visualizing matrices, and miscellaneous routines that provide useful additions to Matlab's existing set of functions. There are 58 parametrized test matrices, which are mostly square, dense, nonrandom, and of arbitrary dimension. The test matrices include ones with known inverses or known eigenvalues; ill-conditioned or rank deficient matrices; and symmetric, positive definite, orthogonal, defective, involutary, and totally positive matrices.", abstract-2 = "We describe version 2.0 of the Test Matrix Toolbox for Matlab The visualization routines display surface plots of a matrix and its (pseudo-) inverse, the field of values, Gershgorin disks, and two- and three-dimensional views of pseudospectra. We explain the need for collections of test matrices and summarize the features of the collection in the toolbox. We give examples of the use of the toolbox and explain some of the interesting properties of the Frank and Pascal matrices, and of random, magic square and companion matrices. The leading comment lines from all the toolbox routines are listed.", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", keywords = "test matrix, Matlab, pseudospectrum, visualization, Frank matrix, Pascal matrix, companion matrix, magic square matrix, random matrix", } @Article{Higham:1994:BVT, author = "Nicholas J. Higham", title = "{\BibTeX}: {A} Versatile Tool for {\LaTeX} Users", journal = j-SIAM-NEWS, volume = "27", pages = "10, 11, 19", month = jan, year = "1994", ISSN = "0036-1437", ISSN-L = "0036-1437", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", } @Book{Higham:1994:HWM, author = "Nicholas J. Higham", title = "Handbook of Writing for the Mathematical Sciences", publisher = "Nippon Hyoron Sha", address = "Tokyo", pages = "x + 235", year = "1994", ISBN = "4-535-78211-3", ISBN-13 = "978-4-535-78211-2", bibdate = "Wed Sep 28 09:02:11 GMT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "Japanese edition of \cite{Higham:1993:HWM}, translated by Shoji Okumura and Takemitsu Hasegawa.", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1994:MSD, author = "Nicholas J. Higham", title = "The Matrix Sign Decomposition and Its Relation to the Polar Decomposition", journal = j-LINEAR-ALGEBRA-APPL, volume = "212/213", pages = "3--20", year = "1994", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Tue Jan 3 12:21:48 GMT 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @InProceedings{Higham:1994:NPA, author = "Nicholas J. Higham and Pythagoras Papadimitriou", editor = "John G. Lewis", booktitle = "Proceedings of the Fifth {SIAM} Conference on Applied Linear Algebra", title = "A New Parallel Algorithm for Computing the Singular Value Decomposition", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "80--84", year = "1994", ISBN = "0-89871-336-6", ISBN-13 = "978-0-89871-336-7", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1994:PAC, author = "Nicholas J. Higham and Pythagoras Papadimitriou", title = "A Parallel Algorithm for Computing the Polar Decomposition", journal = j-PARALLEL-COMPUTING, volume = "20", number = "8", pages = "1161--1173", month = aug, year = "1994", CODEN = "PACOEJ", ISSN = "0167-8191 (print), 1872-7336 (electronic)", ISSN-L = "0167-8191", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Parallel Computing", journal-URL = "http://www.sciencedirect.com/science/journal/01678191", } @TechReport{Higham:1994:SCPa, author = "Nicholas J. Higham", title = "A Survey of Componentwise Perturbation Theory in Numerical Linear Algebra", type = "Numerical Analysis Report", number = "241", institution = inst-U-MANCHESTER, address = inst-U-MANCHESTER:adr, month = feb, year = "1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "To appear in Mathematics of Computation 1943--1993, W. Gautschi, ed. Proceedings of Symposia in Applied Mathematics, American Mathematical Society.", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @InProceedings{Higham:1994:SCPb, author = "Nicholas J. Higham", editor = "Walter Gautschi", booktitle = "{Mathematics of Computation} 1943--1993: {A} Half Century of Computational Mathematics", title = "A Survey of Componentwise Perturbation Theory in Numerical Linear Algebra", volume = "48", publisher = pub-AMS, address = pub-AMS:adr, pages = "49--77", year = "1994", bibdate = "Fri Mar 24 08:51:18 GMT 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", series = "Proceedings of Symposia in Applied Mathematics", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1994:SPI, author = "Nicholas J. Higham and Alex Pothen", title = "Stability of the Partitioned Inverse Method for Parallel Solution of Sparse Triangular Systems", journal = j-SIAM-J-SCI-COMP, volume = "15", number = "1", pages = "139--148", month = jan, year = "1994", CODEN = "SJOCE3", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @Article{Higham:1994:WDM, author = "Nicholas J. Higham", title = "Which Dictionary for the Mathematical Scientist?", journal = j-IMA-BULL, volume = "30", number = "5/6", pages = "81--88", year = "1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "IMA Bulletin", } @TechReport{Braconnier:1995:CFV, author = "Thierry Braconnier and Nicholas J. Higham", title = "Computing the Field of Values and Pseudospectra Using the {Lanczos} Method with Continuation", type = "Numerical Analysis Report", number = "279", institution = inst-MCCM, address = inst-MCCM:adr, pages = "20", month = nov, year = "1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", note = "Submitted to " # j-BIT, bibdate = "Fri Jun 10 12:38:34 2011", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Demmel:1995:SBF, author = "James W. Demmel and Nicholas J. Higham and Robert S. Schreiber", title = "Stability of Block {$ L U $} Factorization", journal = j-NUM-LIN-ALG-APPL, volume = "2", number = "2", pages = "173--190", year = "1995", CODEN = "NLAAEM", ISSN = "1070-5325 (print), 1099-1506 (electronic)", ISSN-L = "1070-5325", bibdate = "Wed Apr 5 12:48:23 GMT 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "To appear.", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Numerical Linear Algebra with Applications", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506", } @TechReport{Higham:1995:DPS, author = "Nicholas J. Higham", title = "Diagonal Pivoting Stability \dots", type = "Numerical Analysis Report", number = "2xx", institution = inst-U-MANCHESTER, address = inst-U-MANCHESTER:adr, month = jun, year = "1995", bibdate = "Tue Mar 21 16:31:40 GMT 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "In preparation.", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @TechReport{Higham:1995:IRLa, author = "Nicholas J. Higham", title = "Iterative Refinement for Linear Systems and {LAPACK}", type = "Numerical Analysis Report", number = "277", institution = inst-MCCM, address = inst-MCCM:adr, pages = "17", month = sep, year = "1995", bibdate = "Mon Apr 21 19:26:38 GMT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "To appear in " # j-IMA-J-NUMER-ANAL # " (14) 1997.", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", mynote = "Also LAPACK Working Note 104.", } @TechReport{Higham:1995:IRLb, author = "N. J. Higham", title = "Iterative Refinement and {LAPACK}", type = "LAPACK Working Note", number = "104", institution = inst-UTK-CS, address = inst-UTK-CS:adr, month = oct, year = "1995", bibdate = "Fri Apr 22 17:06:37 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "UT-CS-95-308, October 1995.", URL = "http://www.netlib.org/lapack/lawns/lawn104.ps; http://www.netlib.org/lapack/lawnspdf/lawn104.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", mynote = "Also Manchester Numerical Analysis Report 277.", } @Article{Higham:1995:MPF, author = "Nicholas J. Higham and Philip A. Knight", title = "Matrix Powers in Finite Precision Arithmetic", journal = j-SIAM-J-MAT-ANA-APPL, volume = "16", number = "2", pages = "343--358", month = apr, year = "1995", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Tue Aug 29 09:11:08 GMT 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", mynote = "Page numbers from SIAM.", } @Article{Higham:1995:RHA, author = "Nicholas J. Higham", title = "Review of {``Howard Anton and Chris Rorres, Elementary Linear Algebra: Applications Version, Seventh edition, Wiley, New York, 1994.''}", journal = j-IMA-BULL, volume = "31", number = "7/8", pages = "122--123", year = "1995", bibdate = "Mon Aug 14 03:43:49 GMT 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "IMA Bulletin", } @TechReport{Higham:1995:SDP, author = "N. J. Higham", title = "Stability of the Diagonal Pivoting Method with Partial Pivoting", type = "LAPACK Working Note", number = "105", institution = inst-UTK-CS, address = inst-UTK-CS:adr, month = oct, year = "1995", bibdate = "Fri Apr 22 17:06:37 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "UT-CS-95-309, October 1995.", URL = "http://www.netlib.org/lapack/lawns/lawn105.ps; http://www.netlib.org/lapack/lawnspdf/lawn105.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1995:SPT, author = "Nicholas J. Higham", title = "Stability of Parallel Triangular System Solvers", journal = j-SIAM-J-SCI-COMP, volume = "16", number = "2", pages = "400--413", month = mar, year = "1995", CODEN = "SJOCE3", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", bibdate = "Wed Jul 5 10:32:41 GMT 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", mynote = "Page numbers from SIAM.", xxnote = "Check month: apr or mar??", } @TechReport{Higham:1995:TMT, author = "Nicholas J. Higham", title = "The {Test Matrix Toolbox} for {{\sc Matlab}}, Version 3.0", type = "Numerical Analysis Report", number = "276", institution = inst-MCCM, address = inst-MCCM:adr, pages = "70", month = sep, year = "1995", bibdate = "Thu Sep 28 10:50:20 GMT 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib", note = "Supersedes Numerical Analysis Report No. 237. In preparation.", URL = "http://p2chpd-cluster.univ-lyon1.fr/P2CHPD/matlab/pdf_doc/otherdocs/testmatrix.pdf", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Braconnier:1996:CFV, author = "Thierry Braconnier and Nicholas J. Higham", title = "Computing the Field of Values and Pseudospectra Using the {Lanczos} Method with Continuation", journal = j-BIT-NUM-MATH, volume = "36", number = "3", pages = "422--440", month = sep, year = "1996", CODEN = "BITTEL, NBITAB", ISSN = "0006-3835 (print), 1572-9125 (electronic)", MRclass = "65F15", MRnumber = "97d:65015", bibdate = "Fri Nov 13 07:00:34 MST 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "International Linear Algebra Year (Toulouse, 1995).", URL = "http://www.mai.liu.se/BIT/contents/bit36.html", acknowledgement = ack-njh # " and " # ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", journal-URL = "http://link.springer.com/journal/10543", } @Article{Carlisle:1996:LSY, author = "David P. Carlisle and Nicholas J. Higham", title = "{\LaTeXe}: {Should} You Upgrade To It?", journal = j-SIAM-NEWS, volume = "29", number = "1", pages = "12", month = jan # "\slash " # feb, year = "1996", ISSN = "0036-1437", ISSN-L = "0036-1437", bibdate = "Mon Feb 19 08:51:53 GMT 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", } @TechReport{Cheng:1996:MCA, author = "Sheung Hun Cheng and Nicholas J. Higham", title = "A Modified {Cholesky} Algorithm Based on a Symmetric Indefinite Factorization", type = "Numerical Analysis Report", number = "289", institution = inst-MCCM, address = inst-MCCM:adr, pages = "18", month = apr, year = "1996", bibdate = "Fri Feb 14 19:47:12 GMT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "To appear in " # j-SIAM-J-MAT-ANA-APPL # ".", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Hammarling:1996:HPP, author = "Sven Hammarling and Nicholas J. Higham", title = "How to Prepare a Poster", journal = j-SIAM-NEWS, volume = "29", number = "4", pages = "20, 19", month = may, year = "1996", ISSN = "0036-1437", ISSN-L = "0036-1437", bibdate = "Tue May 14 11:26:42 GMT 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", } @Book{Higham:1996:ASN, author = "Nicholas J. Higham", title = "Accuracy and Stability of Numerical Algorithms", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xxviii + 688", year = "1996", ISBN = "0-89871-355-2 (paperback)", ISBN-13 = "978-0-89871-355-8 (paperback)", LCCN = "QA297.H53 1996", MRclass = "65Fxx, 15-04, 65-02, 65G50", bibdate = "Tue Jan 30 11:01:35 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/texbook2.bib", price = "US\$39.00", URL = "http://www.ma.man.ac.uk/~higham/asna.html", acknowledgement = ack-njh # " and " # ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", remark = "Typeset with \LaTeX2e.", tableofcontents = "Principles of Finite Precision Computation \\ Relative Error and Significant Digits \\ Sources of Errors \\ Precision Versus Accuracy \\ Backward and Forward Errors \\ Conditioning \\ Cancellation \\ Solving a Quadratic Equation \\ Computing the Sample Variance \\ Solving Linear Equations \\ Accumulation of Rounding Errors \\ Instability Without Cancellation \\ Increasing the Precision \\ Cancellation of Rounding Errors \\ Rounding Errors Can Be Beneficial \\ Stability of an Algorithm Depends on the Problem \\ Rounding Errors Are Not Random \\ Designing Stable Algorithms \\ Misconceptions \\ Rounding Errors in Numerical Analysis \\ Floating Point Arithmetic \\ Floating Point Number System \\ Model of Arithmetic \\ IEEE Arithmetic \\ Aberrant Arithmetics \\ Exact Subtraction \\ Fused Multiply-Add Operation \\ Choice of Base and Distribution of Numbers \\ Statistical Distribution of Rounding Errors \\ Alternative Number Systems \\ Elementary Functions \\ Accuracy Tests \\ Inner and Outer Products \\ The Purpose of Rounding Error Analysis \\ Running Error Analysis \\ Notation for Error Analysis \\ Matrix Multiplication \\ Complex Arithmetic \\ Miscellany \\ Error Analysis Demystified \\ Other Approaches \\ Summation \\ Summation Methods \\ Error Analysis \\ Compensated Summation \\ Other Summation Methods \\ Statistical Estimates of Accuracy \\ Choice of Method \\ Polynomials \\ Horner's Method \\ Evaluating Derivatives \\ The Newton Form and Polynomial Interpolation \\ Matrix Polynomials \\ Norms \\ Vector Norms", } @InCollection{Higham:1996:CCL, author = "Nicholas J. Higham", editor = "M. Chu and others", booktitle = "The {Lanczos} Collected Papers with Commentaries", title = "{Commentary on C. Lanczos, ``Introduction'' to ``Tables of Chebyshev Polynomials $ S_n(x) $ and $ C_n(x) $'', Nat.\ Bur.\ Stand., Appl.\ Math.\ Series 9, 1952, v--xxvi}", publisher = "????", address = "????", pages = "??--??", year = "1996", bibdate = "Fri Jun 10 12:38:34 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", note = "To appear", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @TechReport{Higham:1996:FCS, author = "Nicholas J. Higham", title = "Factorizing Complex Symmetric Matrices with Positive Definite Real and Imaginary Parts", type = "Numerical Analysis Report", number = "298", institution = inst-MCCM, address = inst-MCCM:adr, pages = "12", month = nov, year = "1996", bibdate = "Mon May 19 12:01:10 GMT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "Published in \cite{Higham:1998:FCS}.", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @TechReport{Higham:1996:MIM, author = "Nicholas J. Higham and Sheung Hun Cheng", title = "Modifying the Inertia of Matrices Arising in Optimization", type = "Numerical Analysis Report", number = "295", institution = inst-MCCM, address = inst-MCCM:adr, pages = "17", month = sep, year = "1996", bibdate = "Mon Feb 24 12:42:49 GMT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "To appear in " # j-LINEAR-ALGEBRA-APPL # ".", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1996:RAN, author = "Nicholas J. Higham", title = "Review of {``Acta Numerica 1994 and Acta Numerica 1995, Cambridge University Press''}", journal = j-MATH-TODAY, volume = "32", number = "1/2", pages = "28--??", year = "1996", ISSN = "1361-2042", ISSN-L = "1361-2042", bibdate = "Sat Sep 24 08:44:10 2011", bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/Bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/actanumerica.bib", acknowledgement = ack-nhfb # " and " # ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Mathematics Today", journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html", } @Article{Higham:1996:RDB, author = "Nicholas J. Higham", title = "Review of {``Dario Bini and Victor Y. Pan. {\em Polynomial and Matrix Computations. Volume 1: Fundamental Algorithms}, Birkh{\"a}user, 1994''}", journal = j-MATH-COMPUT, volume = "65", number = "214", pages = "888--889", year = "1996", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Wed Jul 17 08:54:13 GMT 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{Higham:1996:RMB, author = "Nicholas J. Higham", title = "Review of {``Are Magnus Bruaset. A Survey of Preconditioned Iterative Methods, volume 328 of Pitman Research Notes in Mathematics. Longman Scientific and Technical, Essex, UK, 1995.''}", journal = j-IMA-BULL, volume = "32", number = "3/4", pages = "60", year = "1996", bibdate = "Wed Apr 17 16:22:01 GMT 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "IMA Bulletin", } @TechReport{Higham:1996:SBE, author = "Desmond J. Higham and Nicholas J. Higham", title = "Structured Backward Error and Condition of Generalized Eigenvalue Problems", type = "Numerical Analysis Report", number = "297", institution = inst-MCCM, address = inst-MCCM:adr, pages = "24", month = nov, year = "1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "Submitted to " # j-SIAM-J-MAT-ANA-APPL, bibdate = "Fri Nov 15 12:27:07 GMT 1996", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @TechReport{Cox:1997:ASN, author = "Anthony J. Cox and Nicholas J. Higham", title = "Accuracy and Stability of the Null Space Method for Solving the Equality Constrained Least Squares Problem", type = "Numerical Analysis Report", number = "306", institution = inst-MCCM, address = inst-MCCM:adr, pages = "20", month = aug, year = "1997", bibdate = "Sat Oct 31 10:24:09 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "To appear in " # j-BIT # ", 39(1): 1999", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @TechReport{Cox:1997:SHQ, author = "Anthony J. Cox and Nicholas J. Higham", title = "Stability of {Householder $ Q R $} Factorization for Weighted Least Squares Problems", type = "Numerical Analysis Report", number = "301", institution = inst-MCCM, address = inst-MCCM:adr, pages = "17", month = feb, year = "1997", bibdate = "Mon May 19 14:24:46 GMT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "To appear in Numerical Analysis 1997, Proceedings of the 17th Dundee Conference.", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @InCollection{Higham:1997:CCL, author = "Nicholas J. Higham", editor = "William R. Davis and others", booktitle = "Cornelius Lanczos Collected Published Papers with Commentaries", title = "{Commentary on C. Lanczos, ``Introduction'' to ``Tables of Chebyshev Polynomials $ S_n(x) $ and $ C_n(x) $'', Nat.\ Bur.\ Stand., Appl.\ Math.\ Series 9, 1952, v--xxvi}", volume = "VI(3)", publisher = "????", address = "????", pages = "557--559", year = "1997", bibdate = "Wed Aug 13 08:39:47 GMT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "To appear.", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", mynote = "Volume VI, Part 3, pp. 557--559.", } @Article{Higham:1997:IRL, author = "Nicholas J. Higham", title = "Iterative refinement for linear systems and {LAPACK}", journal = j-IMA-J-NUMER-ANAL, volume = "17", number = "4", pages = "495--509", month = oct, year = "1997", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/17.4.495", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65F30", MRnumber = "98e:65036", bibdate = "Sat Dec 23 17:06:35 MST 2000", bibsource = "http://www3.oup.co.uk/imanum/hdb/Volume_17/Issue_04/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; MathSciNet database", note = "Preprint published as Numerical Analysis Report 277, Manchester Centre for Computational Mathematics, Manchester, England, and as LAPACK Working Note 104.", URL = "http://www3.oup.co.uk/imanum/hdb/Volume_17/Issue_04/170495.sgm.abs.html", abstract = "The technique of iterative refinement for improving the computed solution to a linear system was used on desk calculators and computers in the 1940s and has remained popular. In the 1990s iterative refinement is well supported in software libraries, notably in LAPACK. Although the behaviour of iterative refinement in floating point arithmetic is reasonably well understood, the existing theory is not sufficient to justify the use of fixed precision iterative refinement in all the LAPACK routines in which it is implemented. We present analysis that provides the theoretical support needed for LAPACK. The analysis covers both mixed and fixed precision iterative refinement with an arbitrary number of iterations, makes only a general assumption on the underlying solver, and is relatively short. We identify some remaining open problems.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", } @Article{Higham:1997:MHI, author = "Nicholas J. Higham", title = "{Manchester} Hosts Inaugural Meeting of {UK} and {Irish SIAM Section}", journal = j-SIAM-NEWS, volume = "30", number = "3", pages = "3", month = apr, year = "1997", ISSN = "0036-1437", ISSN-L = "0036-1437", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", } @InProceedings{Higham:1997:RDD, author = "Nicholas J. Higham", title = "Recent Developments in Dense Numerical Linear Algebra", crossref = "Duff:1997:SAN", pages = "1--26", year = "1997", bibdate = "Fri Jul 11 16:11:28 GMT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1997:RJR, author = "Nicholas J. Higham", title = "Review of {``James R. Schott, Matrix Analysis for Statistics, Wiley, 1997''}", journal = j-MATH-TODAY, volume = "33", number = "5", pages = "161--162", year = "1997", ISSN = "1361-2042", ISSN-L = "1361-2042", bibdate = "Sun Oct 12 15:29:25 GMT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Mathematics Today", journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html", oldlabel = "high97:scho97", } @TechReport{Higham:1997:SBF, author = "Nicholas J. Higham", title = "Stability of Block $ \mathrm {LDL^T} $ Factorization of a Symmetric Tridiagonal Matrix", institution = inst-MCCM, address = inst-MCCM:adr, year = "1997", bibdate = "Wed Aug 20 15:29:39 GMT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "In preparation.", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1997:SDP, author = "Nicholas J. Higham", title = "Stability of the Diagonal Pivoting Method with Partial Pivoting", journal = j-SIAM-J-MAT-ANA-APPL, volume = "18", number = "1", pages = "52--65", month = jan, year = "1997", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Sun Mar 2 11:16:54 GMT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @TechReport{Higham:1997:SIMa, author = "Nicholas J. Higham", title = "Stable Iterations for the Matrix Square Root", type = "Numerical Analysis Report", number = "305", institution = inst-MCCM, address = inst-MCCM:adr, pages = "20", month = apr, year = "1997", bibdate = "Mon Jun 16 12:13:21 GMT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "Published in \cite{Higham:1997:SIMb}.", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1997:SIMb, author = "Nicholas J. Higham", title = "Stable iterations for the matrix square root", journal = j-NUMER-ALGORITHMS, volume = "15", number = "2", pages = "227--242", month = "????", year = "1997", CODEN = "NUALEG", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", MRclass = "65F30 (65F05)", MRnumber = "98d:65055", bibdate = "Mon Sep 29 08:36:51 MDT 2003", bibsource = "http://www.kluweronline.com/issn/1017-1398; http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/7/6/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/7/6/fulltext.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", } @InProceedings{Higham:1997:TLA, author = "Nicholas J. Higham", editor = "Ronald F. Boisvert", booktitle = "Quality of Numerical Software: {Assessment} and Enhancement", title = "Testing Linear Algebra Software", publisher = pub-CH, address = pub-CH:adr-L, pages = "109--122", year = "1997", bibdate = "Mon Feb 3 09:14:23 GMT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Cheng:1998:MCA, author = "Sheung Hun Cheng and Nicholas J. Higham", title = "A Modified {Cholesky} Algorithm Based on a Symmetric Indefinite Factorization", journal = j-SIAM-J-MAT-ANA-APPL, volume = "19", number = "4", pages = "1097--1110", month = oct, year = "1998", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Fri Dec 4 12:14:09 MST 1998", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/19/4; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/30289", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @TechReport{Cheng:1998:NDP, author = "Sheung Hun Cheng and Nicholas J. Higham", title = "The Nearest Definite Pair for the {Hermitian} Generalized Eigenvalue Problem", type = "Numerical Analysis Report", number = "325", institution = inst-MCCM, address = inst-MCCM:adr, pages = "15", month = may, year = "1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "Submitted to " # j-LINEAR-ALGEBRA-APPL, bibdate = "Mon May 11 14:55:05 GMT 1998", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", oldlabel = "chhi98", } @TechReport{Cox:1998:BEB, author = "Anthony J. Cox and Nicholas J. Higham", title = "Backward Error Bounds for Constrained Least Squares Problems", type = "Numerical Analysis Report", number = "321", institution = inst-MCCM, address = inst-MCCM:adr, pages = "20", month = apr, year = "1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "Submitted to " # j-BIT, bibdate = "Fri Apr 17 12:13:36 GMT 1998", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", oldlabel = "cohi98c", } @TechReport{Cox:1998:RWB, author = "Anthony J. Cox and Nicholas J. Higham", title = "Row-Wise Backward Stable Elimination Methods for the Equality Constrained Least Squares Problem", type = "Numerical Analysis Report", number = "319", institution = inst-MCCM, address = inst-MCCM:adr, pages = "18", month = mar, year = "1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "To appear in " # j-SIAM-J-MAT-ANA-APPL, bibdate = "Fri Aug 14 18:34:14 GMT 1998", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", oldlabel = "cohi98r", } @InProceedings{Cox:1998:SHQ, author = "Anthony J. Cox and Nicholas J. Higham", title = "Stability of {Householder QR} Factorization for Weighted Least Squares Problems", crossref = "Higham:1998:NAP", pages = "57--73", year = "1998", bibdate = "Mon Aug 29 22:30:58 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", series = "Pitman Research Notes in Mathematics", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1998:BNR, author = "Nicholas J. Higham", title = "Book News \& Reviews: Review of {``Christoph W. Ueberhuber, Numerical Computation: Methods, Software and Analysis, Springer-Verlag, 1997''}", journal = j-IEEE-COMPUT-SCI-ENG, volume = "5", number = "1", pages = "79--79", month = jan # "\slash " # mar, year = "1998", CODEN = "ISCEE4", ISSN = "1070-9924 (print), 1558-190X (electronic)", ISSN-L = "1070-9924", bibdate = "Sat Jan 9 08:57:23 MST 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://dlib.computer.org/cs/books/cs1998/pdf/c1079.pdf", acknowledgement = ack-njh # " and " # ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "IEEE Computational Science \& Engineering", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=99", mynote = "Jan-Mar", oldlabel = "high98:uebe97", } @TechReport{Higham:1998:FCP, author = "Nicholas J. Higham", title = "{$ Q R $} Factorization with Complete Pivoting and Accurate Computation of the {SVD}", type = "Numerical Analysis Report", number = "324", institution = inst-MCCM, address = inst-MCCM:adr, pages = "26", month = sep, year = "1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "Submitted to " # j-LINEAR-ALGEBRA-APPL, bibdate = "Mon Sep 14 14:06:12 GMT 1998", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", oldlabel = "high98q", } @Article{Higham:1998:FCS, author = "Nicholas J. Higham", title = "Factorizing complex symmetric matrices with positive definite real and imaginary parts", journal = j-MATH-COMPUT, volume = "67", number = "224", pages = "1591--1599", year = "1998", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F15 (15A23 65F10 65G05)", MRnumber = "1 474 652", bibdate = "Thu Oct 15 16:27:48 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Book{Higham:1998:HWM, author = "Nicholas J. Higham", title = "Handbook of Writing for the Mathematical Sciences", publisher = pub-SIAM, address = pub-SIAM:adr, edition = "Second", pages = "xvi + 302", year = "1998", ISBN = "0-89871-420-6 (paperback), 0-89871-955-0 (e-book)", ISBN-13 = "978-0-89871-420-3 (paperback), 978-0-89871-955-0 (e-book)", LCCN = "QA42 .H54 1998", bibdate = "Wed Oct 30 14:21:33 2002", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/texbook3.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", tableofcontents = "Preface to the second edition \\ Preface to the first edition \\ 1. General principles \\ 2. Writer's tools and recommended reading \\ 3. Mathematical writing \\ 4. English usage \\ 5. When English is a foreign language \\ 6. Writing a paper \\ 7. Revising a draft \\ 8. Publishing a paper \\ 9. Writing and defending a thesis \\ 10. Writing a talk \\ 11. Giving a talk \\ 12. Preparing a poster \\ 13. TeX and LaTeX \\ 14. Aids and resources for writing and research \\ Appendix A. The Greek alphabet \\ Appendix B. Summary of TeX and LaTeX symbols \\ Appendix C. GNU Emacs commands \\ Appendix D. Mathematical and other organizations \\ Appendix E. Prizes for expository writing \\ Glossary \\ Bibliography \\ Name index \\ Subject index", } @Article{Higham:1998:MIM, author = "Nicholas J. Higham and Sheung Hun Cheng", title = "Modifying the Inertia of Matrices Arising in Optimization", journal = j-LINEAR-ALGEBRA-APPL, volume = "275-276", pages = "261--279", year = "1998", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Mon Jul 27 12:37:04 GMT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", oldlabel = "hich98", } @TechReport{Higham:1998:NAS, author = "Nicholas J. Higham", title = "Notes on Accuracy and Stability of Algorithms in Numerical Linear Algebra", type = "Numerical Analysis Report", number = "333", institution = inst-MCCM, address = inst-MCCM:adr, pages = "42", month = aug, year = "1998", bibdate = "Mon Sep 7 09:59:00 GMT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "To appear in proceedings of EPSRC Numerical Analysis Summer School, Leicester University, July 1998.", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", oldlabel = "high98a", } @Article{Higham:1998:NWE, author = "Nicholas J. Higham and David J. Silvester", title = "``{Nothing was Ever the Same Again}''", journal = j-SIAM-NEWS, volume = "31", number = "7", pages = "1, 8", month = sep, year = "1998", ISSN = "0036-1437", ISSN-L = "0036-1437", bibdate = "Wed Sep 16 11:49:30 GMT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "https://www.siam.org/news/news.php?id=868", abstract = "In 1948, the world's first stored-program computer performed its first (dramatic) computation at the University of Manchester; this spring, researchers gathered at Manchester to celebrate 50 years of progress in computers and numerical analysis.", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", keywords = "Manchester ``Baby'' computer", } @Article{Higham:1998:SBE, author = "Desmond J. Higham and Nicholas J. Higham", title = "Structured Backward Error and Condition of Generalized Eigenvalue Problems", journal = j-SIAM-J-MAT-ANA-APPL, volume = "20", number = "2", pages = "493--512", year = "1998", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479896313188", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Fri Dec 4 12:14:09 MST 1998", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/20/2; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/31318", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Cheng:1999:NDP, author = "Sheung Hun Cheng and Nicholas J. Higham", title = "The nearest definite pair for the {Hermitian} generalized eigenvalue problem", journal = j-LINEAR-ALGEBRA-APPL, volume = "302-303", number = "1--3", pages = "63--76", day = "1", month = dec, year = "1999", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Mon Oct 9 10:54:40 MDT 2000", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://www.elsevier.nl/gej-ng/10/30/19/117/25/30/abstract.html; http://www.elsevier.nl/gej-ng/10/30/19/117/25/30/article.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Cox:1999:ASN, author = "Anthony J. Cox and Nicholas J. Higham", title = "Accuracy and Stability of the Null Space Method for Solving the Equality Constrained Least Squares Problem", journal = j-BIT-NUM-MATH, volume = "39", number = "1", pages = "34--49", month = "????", year = "1999", CODEN = "BITTEL, NBITAB", ISSN = "0006-3835 (print), 1572-9125 (electronic)", bibdate = "Thu Oct 16 08:15:34 2003", bibsource = "http://www.mai.liu.se/BIT/contents/bit39.html; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; OCLC Article1st database", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", journal-URL = "http://link.springer.com/journal/10543", } @Article{Cox:1999:BEB, author = "A. J. Cox and N. J. Higham", title = "Backward error bounds for constrained least squares problems", journal = j-BIT-NUM-MATH, volume = "39", number = "2", pages = "210--227", month = "????", year = "1999", CODEN = "BITTEL, NBITAB", ISSN = "0006-3835 (print), 1572-9125 (electronic)", bibdate = "Thu Oct 16 08:15:34 2003", bibsource = "http://www.mai.liu.se/BIT/contents/bit39.html; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; OCLC Article1st database", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", journal-URL = "http://link.springer.com/journal/10543", } @Article{Higham:1999:BRL, author = "Nicholas J. Higham", title = "Book Review: {{\em Linear Algebra (Pure and Applied Mathematics)}, by Peter D. Lax: 250 pp., \pounds 55.00, ISBN 0-471-11111-2 (John Wiley \& Sons, 1996)}", journal = j-BULL-LOND-MATH-SOC, volume = "31", number = "3", pages = "374--375", month = may, year = "1999", CODEN = "LMSBBT", DOI = "https://doi.org/10.1112/S0024609397264167", ISSN = "0024-6093 (print), 1469-2120 (electronic)", ISSN-L = "0024-6093", bibdate = "Thu Aug 25 10:49:37 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://blms.oxfordjournals.org/content/31/3/374.full.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Bulletin of the London Mathematical Society", journal-URL = "http://blms.oxfordjournals.org/content/by/year", } @Article{Higham:1999:FBR, author = "Nicholas J. Higham", title = "Featured Book Review: {Selected} Books on Numerical Linear Algebra", journal = j-SIAM-REVIEW, volume = "41", number = "3", pages = "607--610", month = sep, year = "1999", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/SIREAD000041000003000605000001", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "1999.05.20", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", updated = "2014.07.26", } @Article{Higham:1999:FTP, author = "Nicholas J. Higham", title = "A Fitting Tribute to a Pioneering Numerical Analyst [{Cleve Moler}]", journal = j-SIAM-NEWS, volume = "32", number = "10", pages = "3", month = dec, year = "1999", ISSN = "0036-1437", ISSN-L = "0036-1437", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib", note = "Celebrating Cleve Moler's 60th birthday!", URL = "https://www.siam.org/news/news.php?id=796", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "2000.01.05", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", updated = "2000.01.05", } @InCollection{Higham:1999:NAS, author = "Nicholas J. Higham", title = "Notes on Accuracy and Stability of Algorithms in Numerical Analysis", crossref = "Ainsworth:1999:GSG", pages = "48--82", year = "1999", bibdate = "Wed Jul 14 14:57:11 2004", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:1999:RPD, author = "Nicholas J. Higham", title = "Review of {``Peter D. Lax, \booktitle{Linear Algebra}, Wiley, 1997''}", journal = j-BULL-LOND-MATH-SOC, volume = "31", pages = "374--375", year = "1999", CODEN = "LMSBBT", ISSN = "0024-6093 (print), 1469-2120 (electronic)", ISSN-L = "0024-6093", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "1999.05.27", fjournal = "Bulletin of the London Mathematical Society", journal-URL = "http://blms.oxfordjournals.org/content/by/year", updated = "1999.05.27", } @Article{Higham:1999:SBE, author = "Desmond J. Higham and Nicholas J. Higham", title = "Structured Backward Error and Condition of Generalized Eigenvalue Problems", journal = j-SIAM-J-MAT-ANA-APPL, volume = "20", number = "2", pages = "493--512", month = apr, year = "1999", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Fri Dec 4 12:14:09 MST 1998", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/20/2; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/31318", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:1999:SBL, author = "Nicholas J. Higham", title = "Stability of block {LDL$^T$} factorization of a symmetric tridiagonal matrix", journal = j-LINEAR-ALGEBRA-APPL, volume = "287", number = "1--3", pages = "181--189", day = "15", month = jan, year = "1999", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Fri May 28 08:42:54 MDT 1999", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://www.elsevier.com/cas/tree/store/laa/sub/1999/287/1-3/6193.pdf; http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1999&volume=287&issue=1-3&aid=6193", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @InProceedings{Cheng:2000:ALM, author = "Sheung Hun Cheng and Nicholas J. Higham", title = "Approximating the logarithm of a matrix with variable accuracy", crossref = "Watson:2000:NAD", pages = "??--??", year = "2000", bibdate = "Tue Nov 28 11:45:46 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Cox:2000:RWB, author = "Anthony J. Cox and Nicholas J. Higham", title = "Row-Wise Backward Stable Elimination Methods for the Equality Constrained Least Squares Problem", journal = j-SIAM-J-MAT-ANA-APPL, volume = "21", number = "1", pages = "313--326", month = jan, year = "2000", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Sat Jan 22 14:39:17 MST 2000", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/21/1; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/33595", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Davies:2000:NSG, author = "Philip I. Davies and Nicholas J. Higham", title = "Numerically Stable Generation of Correlation Matrices and Their Factors", journal = j-BIT-NUM-MATH, volume = "40", number = "4", pages = "640--651", month = dec, year = "2000", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1023/A:1022384216930", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", MRclass = "65F18", MRnumber = "MR1799307 (2002g:65045)", MRreviewer = "Ram Shanmugam", bibdate = "Wed Jan 4 15:06:04 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=40&issue=4; http://www.mai.liu.se/BIT/contents/bit40.html; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=40&issue=4&spage=640", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "BIT. Numerical Mathematics", journal-URL = "http://link.springer.com/journal/10543", } @Article{Higham:2000:BAM, author = "Nicholas J. Higham and Fran{\c{c}}oise Tisseur", title = "A Block Algorithm for Matrix $1$-Norm Estimation, with an Application to $1$-Norm Pseudospectra", journal = j-SIAM-J-MAT-ANA-APPL, volume = "21", number = "4", pages = "1185--1201", month = oct, year = "2000", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479899356080", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F20 (65F15)", MRnumber = "MR1780268 (2001d:65051)", bibdate = "Fri Oct 27 07:23:32 MDT 2000", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/21/4; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/35608", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:2000:FCP, author = "Nicholas J. Higham", title = "{$ Q R $} factorization with complete pivoting and accurate computation of the {SVD}", journal = j-LINEAR-ALGEBRA-APPL, volume = "309", number = "1--3", pages = "153--174", year = "2000", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/S0024-3795(99)00230-X", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65F20 (15A23)", MRnumber = "MR1758366 (2001c:65049)", MRreviewer = "Jesse L. Barlow", bibdate = "Sat Apr 16 17:54:53 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", remark = "Proceedings of the International Workshop on Accurate Solution of Eigenvalue Problems (University Park, PA, 1998)", } @Book{Higham:2000:MG, author = "Desmond J. Higham and Nicholas J. Higham", title = "{MATLAB} Guide", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xxii + 283", year = "2000", ISBN = "0-89871-469-9", ISBN-13 = "978-0-89871-469-2", LCCN = "QA297 .H5217 2000", MRclass = "65-04 (00A20)", MRnumber = "MR1787308 (2001e:65003)", bibdate = "Tue Jan 23 09:04:18 2001", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", keywords = "Matlab; numerical analysis -- data processing", } @Article{Higham:2000:NAQ, author = "Nicholas J. Higham and Hyun-Min Kim", title = "Numerical analysis of a quadratic matrix equation", journal = j-IMA-J-NUMER-ANAL, volume = "20", number = "4", pages = "499--519", month = oct, year = "2000", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/20.4.499", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65F30 (15A24)", MRnumber = "MR1795295 (2001i:65054)", bibdate = "Mon Feb 12 16:52:03 2001", bibsource = "http://www3.oup.co.uk/imanum/hdb/Volume_20/Issue_04/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://www3.oup.co.uk/imanum/hdb/Volume_20/Issue_04/200499abs.pdf; http://www3.oup.co.uk/imanum/hdb/Volume_20/Issue_04/pdf/200499.pdf", abstract = "The quadratic matrix equation $ A X^2 + B X + C = 0 $ in $ n \times n $ matrices arises in applications and is of intrinsic interest as one of the simplest nonlinear matrix equations. We give a complete characterization of solutions in terms of the generalized Schur decomposition and describe and compare various numerical solution techniques. In particular, we give a thorough treatment of functional iteration methods based on Bernoulli's method. Other methods considered include Newton's method with exact line searches, symbolic solution and continued fractions. We show that functional iteration applied to the quadratic matrix equation can provide an efficient way to solve the associated quadratic eigenvalue problem $ (\lambda^2 A + \lambda B + C) x = 0 $.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", } @Article{Higham:2000:QFC, author = "Nicholas J. Higham", title = "{QR} factorization with complete pivoting and accurate computation of the {SVD}", journal = j-LINEAR-ALGEBRA-APPL, volume = "309", number = "1--3", pages = "153--174", day = "15", month = apr, year = "2000", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Mon Oct 9 10:54:41 MDT 2000", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://www.elsevier.nl/gej-ng/10/30/19/126/25/34/abstract.html; http://www.elsevier.nl/gej-ng/10/30/19/126/25/34/article.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Higham:2000:RJJ, author = "Nicholas J. Higham", title = "Review of {``Jack J. Dongarra, Iain S. Duff, Danny C. Sorensen, and Henk A. van der Vorst, \booktitle{Numerical Linear Algebra for High-Performance Computers}, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1998''}", journal = j-SIAM-REVIEW, volume = "42", number = "3", pages = "529", month = sep, year = "2000", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/SIREAD000042000003000513000001", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Fri Oct 6 15:10:21 GMT 2000", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "2000.10.06", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", updated = "2014.07.26", } @TechReport{Anjos:2001:SPA, author = "M. F. Anjos and N. Higham and M. Takouda and H. Wolkowicz", title = "A semidefinite programming approach for the closest correlation matrix problem", number = "CORR 2001-in progress", institution = inst-UNIV-WATERLOO, address = inst-UNIV-WATERLOO:adr, year = "2001", bibdate = "Wed Sep 9 06:36:42 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Cheng:2001:ALM, author = "Sheung Hun Cheng and Nicholas J. Higham and Charles S. Kenney and Alan J. Laub", title = "Approximating the logarithm of a matrix to specified accuracy", journal = j-SIAM-J-MAT-ANA-APPL, volume = "22", number = "4", pages = "1112--1125", year = "2001", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479899364015", ISSN = "1095-7162", ISSN-L = "0895-4798", MRclass = "65F30", MRnumber = "MR1825853 (2002a:65069)", MRreviewer = "Jin Yun Yuan", bibdate = "Sat Apr 16 17:54:57 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @TechReport{Cheng:2001:ILB, author = "S. Cheng and N. Higham", title = "Implementation for {LAPACK} of a Block Algorithm for Matrix $1$-Norm Estimation", type = "LAPACK Working Note", number = "152", institution = inst-UTK-CS, address = inst-UTK-CS:adr, month = aug, year = "2001", bibdate = "Fri Apr 22 17:06:37 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "UT-CS-01-470, August 2001.", URL = "http://www.netlib.org/lapack/lawns/lawn152.ps; http://www.netlib.org/lapack/lawnspdf/lawn152.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Cheng:2001:PIB, author = "Sheung Hun Cheng and Nicholas J. Higham", title = "Parallel Implementation of a Block Algorithm for Matrix $1$-Norm Estimation", journal = j-LECT-NOTES-COMP-SCI, volume = "2150", pages = "568--??", year = "2001", CODEN = "LNCSD9", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Sat Feb 2 13:05:53 MST 2002", bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2150.htm; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2150/21500568.htm; http://link.springer-ny.com/link/service/series/0558/papers/2150/21500568.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Lecture Notes in Computer Science", journal-URL = "http://link.springer.com/bookseries/558", } @Article{Davies:2001:ACM, author = "Philip I. Davies and Nicholas J. Higham and Fran{\c{c}}oise Tisseur", title = "Analysis of the {Cholesky} Method with Iterative Refinement for Solving the Symmetric Definite Generalized Eigenproblem", journal = j-SIAM-J-MAT-ANA-APPL, volume = "23", number = "2", pages = "472--493", year = "2001", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479800373498", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F15", MRnumber = "MR1871323 (2002i:65039)", MRreviewer = "David Scott Watkins", bibdate = "Fri Feb 22 09:58:16 MST 2002", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/23/2; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/37349", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @TechReport{Higham:2001:BEM, author = "Nicholas J. Higham and Fran{\c{c}}oise Tisseur", title = "Bounds for Eigenvalues of Matrix Polynomials", type = "Numerical Analysis Report", number = "371", institution = inst-MCCM, address = inst-MCCM:adr, pages = "16", month = jan, year = "2001", bibdate = "Wed Sep 9 06:38:11 2015", note = "To appear in " # j-LINEAR-ALGEBRA-APPL, bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:2001:EPA, author = "Nicholas J. Higham", title = "Evaluating {Pad{\'e}} approximants of the matrix logarithm", journal = j-SIAM-J-MAT-ANA-APPL, volume = "22", number = "4", pages = "1126--1135", year = "2001", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479800368688", ISSN = "1095-7162", ISSN-L = "0895-4798", MRclass = "65F30 (65D15)", MRnumber = "MR1824061 (2002d:65039)", MRreviewer = "Assem Deif", bibdate = "Sat Apr 16 17:55:00 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:2001:P, author = "Nicholas Higham and Roger Horn and Thomas J. Laffey and Ferran Puerta", title = "Preface", journal = j-LINEAR-ALGEBRA-APPL, volume = "332--334", number = "1", pages = "1--1", day = "1", month = aug, year = "2001", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Jul 25 17:54:46 MDT 2001", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://www.elsevier.nl/gej-ng/10/30/19/157/25/25/abstract.html; http://www.elsevier.nl/gej-ng/10/30/19/157/25/25/article.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Higham:2001:RMA, author = "Nicholas J. Higham", title = "Review of {``Michael Alley, \booktitle{The Craft of Editing: A Guide for Managers, Scientists and Engineers}. Springer-Verlag, 2000''}", journal = j-SIAM-REVIEW, volume = "43", number = "1", pages = "202", month = mar, year = "2001", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/SIREAD000043000001000179000001", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "2001.04.19", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", updated = "2014.07.26", } @Article{Higham:2001:SQM, author = "Nicholas J. Higham and Hyun-Min Kim", title = "Solving a quadratric matrix equation by {Newton}'s method with exact line searches", journal = j-SIAM-J-MAT-ANA-APPL, volume = "23", number = "2", pages = "303--316", year = "2001", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479899350976", ISSN = "1095-7162", ISSN-L = "0895-4798", MRclass = "65H10 (65F30)", MRnumber = "MR1871314 (2002j:65055)", bibdate = "Sat Apr 16 17:55:00 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Tisseur:2001:SPP, author = "Fran{\c{c}}oise Tisseur and Nicholas J. Higham", title = "Structured pseudospectra for polynomial eigenvalue problems, with applications", journal = j-SIAM-J-MAT-ANA-APPL, volume = "23", number = "1", pages = "187--208", year = "2001", CODEN = "SJMAEL", ISSN = "1095-7162", ISSN-L = "0895-4798", MRclass = "15A18 (15A22 65F15)", MRnumber = "MR1856605 (2002k:15024)", MRreviewer = "Jesse L. Barlow", bibdate = "Sat Apr 16 17:55:00 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Book{Higham:2002:ASN, author = "Nicholas J. Higham", title = "Accuracy and Stability of Numerical Algorithms", publisher = pub-SIAM, address = pub-SIAM:adr, edition = "Second", pages = "xxx + 680", year = "2002", DOI = "https://doi.org/10.1137/1.9780898718027", ISBN = "0-89871-521-0 (hardcover), 0-89871-802-3 (e-book)", ISBN-13 = "978-0-89871-521-7 (hardcover), 978-0-89871-802-7 (e-book)", LCCN = "QA297 .H53 2002", MRclass = "65G50 (65-02)", MRnumber = "MR1927606 (2003g:65064)", bibdate = "Wed Oct 30 14:20:02 2002", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib", abstract = "\booktitle{Accuracy and Stability of Numerical Algorithms} gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing $ L U $ factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", keywords = "accurate floating-point summation", tableofcontents = "List of Figures \\ List of Tables \\ Preface to Second Edition \\ Preface to First Edition \\ About the Dedication \\ 1: Principles of Finite Precision Computation \\ 2: Floating Point Arithmetic \\ 3: Basics \\ 4: Summation \\ 5: Polynomials \\ 6: Norms \\ 7: Perturbation Theory for Linear Systems \\ 8: Triangular Systems \\ 9: $ L U $ Factorization and Linear Equations \\ 10: Cholesky Factorization \\ 11: Symmetric Indefinite and Skew-Symmetric Systems \\ 12: Iterative Refinement \\ 13: Block LU Factorization \\ 14: Matrix Inversion \\ 15: Condition Number Estimation \\ 16: The Sylvester Equation \\ 17: Stationary Iterative Methods \\ 18: Matrix Powers \\ 19: QR Factorization \\ 20: The Least Squares Problem \\ 21: Underdetermined Systems \\ 22: Vandermonde Systems \\ 23: Fast Matrix Multiplication \\ 24: The Fast Fourier Transform and Applications \\ 25: Nonlinear Systems and Newton's Method \\ 26: Automatic Error Analysis \\ 27: Software Issues in Floating Point Arithmetic \\ 28: A Gallery of Test Matrices \\ Appendix A: Solutions to Problems \\ Appendix B: Acquiring Software \\ Appendix C: Program Libraries \\ Appendix D: The Matrix Computation Toolbox \\ Bibliography \\ Name Index \\ Subject Index", } @Article{Higham:2002:CNC, author = "Nicholas J. Higham", title = "Computing the nearest correlation matrix---a problem from finance", journal = j-IMA-J-NUMER-ANAL, volume = "22", number = "3", pages = "329--343", month = jul, year = "2002", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/22.3.329", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65F30 (91B02)", MRnumber = "MR1918653 (2003d:65037)", bibdate = "Fri Oct 18 09:49:23 MDT 2002", bibsource = "http://www3.oup.co.uk/imanum/hdb/Volume_22/Issue_03/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://www3.oup.co.uk/imanum/hdb/Volume_22/Issue_03/220329.sgm.abs.html; http://www3.oup.co.uk/imanum/hdb/Volume_22/Issue_03/pdf/220329.pdf", abstract = "Given a symmetric matrix, what is the nearest correlation matrix that is, the nearest symmetric positive semidefinite matrix with unit diagonal? This problem arises in the finance industry, where the correlations are between stocks. For distance measured in two weighted Frobenius norms we characterize the solution using convex analysis. We show how the modified alternating projections method can be used to compute the solution for the more commonly used of the weighted Frobenius norms. In the finance application the original matrix has many zero or negative eigenvalues; we show that for a certain class of weights the nearest correlation matrix has correspondingly many zero eigenvalues and that this fact can be exploited in the computation.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", keywords = "convex analysis; correlation matrix; nearness problem; positive semidefinite matrix; weighted", } @Article{Higham:2002:DDH, author = "Nicholas J. Higham and Fran{\c{c}}oise Tisseur and Paul M. {Van Dooren}", title = "Detecting a definite {Hermitian} pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems", journal = j-LINEAR-ALGEBRA-APPL, volume = "351--352", pages = "455--474", day = "15", month = aug, year = "2002", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/S0024-3795(02)00281-1", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "93B60 (15A18 93B40 93C05)", MRnumber = "MR1917487 (2003f:93047)", MRreviewer = "A. Barraud", bibdate = "Fri Aug 9 09:25:01 MDT 2002", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "Fourth special issue on linear systems and control", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @TechReport{Higham:2002:MCT, author = "Nicholas J. Higham", title = "The {Matrix Computation Toolbox} for {MATLAB} (Version 1.0)", type = "Numerical Analysis Report", number = "410", institution = inst-MCCM, address = inst-MCCM:adr, pages = "19", month = aug, year = "2002", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "2002.08.23", updated = "2002.08.23", } @Article{Higham:2002:MPP, author = "Nicholas J. Higham and Fran{\c{c}}oise Tisseur", title = "More on pseudospectra for polynomial eigenvalue problems and applications in control theory", journal = j-LINEAR-ALGEBRA-APPL, volume = "351--352", pages = "435--453", day = "15", month = aug, year = "2002", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/S0024-3795(01)00542-0", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "93B60 (15A18 65F15)", MRnumber = "MR1917486 (2003e:93035)", MRreviewer = "Pablo A. Iglesias", bibdate = "Fri Aug 9 09:25:01 MDT 2002", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "Fourth special issue on linear systems and control", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Higham:2002:RAN, author = "Nicholas J. Higham", title = "Review of {``Arnold Neumaier. \booktitle{Introduction to Numerical Analysis}. Cambridge University Press, 2001''}", journal = j-SIAM-REVIEW, volume = "44", number = "3", pages = "492--493", month = sep, year = "2002", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/SIREAD000044000003000477000001", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "2002.09.25", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", updated = "2014.07.26", } @Article{Higham:2002:RMO, author = "Nicholas J. Higham", title = "Review of {``Michael Overton, \booktitle{Numerical Computing with IEEE Floating Point Arithmetic: Including One Theorem, One Rule of Thumb, and One Hundred and One Exercises}. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2001''}", journal = j-SIAM-REVIEW, volume = "44", number = "2", pages = "287--288", month = jun, year = "2002", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/SIREAD000044000002000279000001", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "2002.07.16", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", updated = "2014.10.13", } @Article{Higham:2002:SQM, author = "Nicholas J. Higham and Hyun-Min Kim", title = "Solving a Quadratic Matrix Equation by {Newton}'s Method with Exact Line Searches", journal = j-SIAM-J-MAT-ANA-APPL, volume = "23", number = "2", pages = "303--316", month = apr, year = "2002", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Fri Feb 22 09:58:16 MST 2002", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/23/2; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/35097", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Tisseur:2002:SPP, author = "Fran{\c{c}}oise Tisseur and Nicholas J. Higham", title = "Structured Pseudospectra for Polynomial Eigenvalue Problems, with Applications", journal = j-SIAM-J-MAT-ANA-APPL, volume = "23", number = "1", pages = "187--208", month = jan, year = "2002", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Wed Oct 23 08:36:32 MDT 2002", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/23/1; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/37145", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Bojanczyk:2003:ECI, author = "Adam Bojanczyk and Nicholas J. Higham and Harikrishna Patel", title = "The equality constrained indefinite least squares problem: theory and algorithms", journal = j-BIT, volume = "43", number = "3", pages = "505--517", year = "2003", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1023/B:BITN.0000007020.58972.07", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", MRclass = "65F20", MRnumber = "MR2026712 (2004m:65049)", bibdate = "Sat Apr 16 17:55:00 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "BIT. Numerical Mathematics", journal-URL = "http://link.springer.com/journal/10543", } @Article{Bojanczyk:2003:SIL, author = "Adam Bojanczyk and Nicholas J. Higham and Harikrishna Patel", title = "Solving the Indefinite Least Squares Problem by Hyperbolic {QR} Factorization", journal = j-SIAM-J-MAT-ANA-APPL, volume = "24", number = "4", pages = "914--931", month = oct, year = "2003", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479802401497", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F30 (90C20)", MRnumber = "MR2003312 (2004f:65054)", MRreviewer = "David Scott Watkins", bibdate = "Fri Aug 15 05:16:20 MDT 2003", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/24/4; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/40149", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Davies:2003:SPA, author = "Philip I. Davies and Nicholas J. Higham", title = "A {Schur--Parlett} Algorithm for Computing Matrix Functions", journal = j-SIAM-J-MAT-ANA-APPL, volume = "25", number = "2", pages = "464--485", month = apr, year = "2003", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479802410815", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F30", MRnumber = "MR2047429 (2004m:65056)", bibdate = "Tue Sep 30 10:28:35 MDT 2003", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/25/2; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/41081", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:2003:BEM, author = "Nicholas J. Higham and Fran{\c{c}}oise Tisseur", title = "Bounds for eigenvalues of matrix polynomials", journal = j-LINEAR-ALGEBRA-APPL, volume = "358", number = "1--3", pages = "5--22", day = "1", month = jan, year = "2003", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/S0024-3795(01)00316-0", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A42 (15A18 65F15)", MRnumber = "MR1942721 (2003k:15020)", MRreviewer = "Ilse C. F. Ipsen", bibdate = "Mon Apr 28 07:27:21 MDT 2003", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "Special issue on accurate solution of eigenvalue problems (Hagen, 2000)", URL = "http://www.elsevier.nl/gej-ng/10/30/19/207/25/27/abstract.html; http://www.sciencedirect.com/science?_ob=GatewayURL&_origin=SOCJLA&_urlversion=4&_method=citationSearch&_version=1&_piikey=S0024379501003160&_volkey=00243795%23358%235&_refkey=Higham%232003%235%2322&md5=51223bc8229cca92374c1fcdbfa6b770", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Higham:2003:CMC, author = "Nicholas J. Higham and Matthew I. Smith", title = "Computing the Matrix Cosine", journal = j-NUMER-ALGORITHMS, volume = "34", number = "1", pages = "13--26", month = sep, year = "2003", CODEN = "NUALEG", DOI = "https://doi.org/10.1023/A:1026152731904", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", MRclass = "65F30", MRnumber = "MR2015575 (2004j:65053)", bibdate = "Fri Oct 24 09:37:49 MDT 2003", bibsource = "http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://ipsapp008.kluweronline.com/content/getfile/5058/47/2/abstract.htm; http://ipsapp008.kluweronline.com/content/getfile/5058/47/2/fulltext.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", } @Article{Higham:2003:OMP, author = "Nicholas J. Higham", title = "{$J$}-Orthogonal Matrices: Properties and Generation", journal = j-SIAM-REVIEW, volume = "45", number = "3", pages = "504--519", month = sep, year = "2003", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/S0036144502414930", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "65F25 (15A23 15A57)", MRnumber = "MR2046506 (2004m:65054)", MRreviewer = "Ilse C. F. Ipsen", bibdate = "Sat Mar 29 09:56:44 MDT 2014", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/45/3; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/41493", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @Article{Higham:2003:SPS, author = "Nicholas J. Higham", title = "{SIAG/LA} Prizewinners Speed Up the {$ Q R $} Algorithm", journal = j-SIAM-NEWS, volume = "36", number = "9", pages = "3", month = nov, year = "2003", ISSN = "0036-1437", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "1994.01.01", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", updated = "1994.01.01", } @Article{Graham:2004:UAC, author = "Ivan Graham and Nicholas J. Higham", title = "{UKIE} Applied\slash Computational Mathematicians Greet the Year in {Sheffield}, {Manchester}", journal = j-SIAM-NEWS, volume = "37", number = "4", pages = "12", month = may, year = "2004", ISSN = "0036-1437", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "1994.01.01", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", updated = "1994.01.01", } @Article{Higham:2004:CPD, author = "Nicholas J. Higham and D. Steven Mackey and Niloufer Mackey and Fran{\c{c}}oise Tisseur", title = "Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups", journal = j-SIAM-J-MAT-ANA-APPL, volume = "25", number = "4", pages = "1178--1192", month = oct, year = "2004", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479803426644", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A23", MRnumber = "MR2081137", bibdate = "Sat Apr 16 10:32:34 MDT 2005", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/25/4; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/42664", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:2004:NSB, author = "Nicholas J. Higham", title = "The numerical stability of barycentric {Lagrange} interpolation", journal = j-IMA-J-NUMER-ANAL, volume = "24", number = "4", pages = "547--556", month = oct, year = "2004", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/24.4.547", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65D05", MRnumber = "MR2094569 (2005e:65007)", bibdate = "Fri Jul 8 07:42:09 MDT 2005", bibsource = "http://imanum.oxfordjournals.org/content/vol24/issue4/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://imanum.oupjournals.org/cgi/content/abstract/24/4/547; http://imanum.oupjournals.org/cgi/reprint/24/4/547", abstract = "The Lagrange representation of the interpolating polynomial can be rewritten in two more computationally attractive forms: a modified Lagrange form and a barycentric form. We give an error analysis of the evaluation of the interpolating polynomial using these two forms. The modified Lagrange formula is shown to be backward stable. The barycentric formula has a less favourable error analysis, but is forward stable for any set of interpolating points with a small Lebesgue constant. Therefore the barycentric formula can be significantly less accurate than the modified Lagrange formula only for a poor choice of interpolating points. This analysis provides further weight to the argument of Berrut and Trefethen that barycentric Lagrange interpolation should be the polynomial interpolation method of choice.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", } @Article{Bini:2005:AMR, author = "Dario A. Bini and Nicholas J. Higham and Beatrice Meini", title = "Algorithms for the matrix $p$ th root", journal = j-NUMER-ALGORITHMS, volume = "39", number = "4", pages = "349--378", month = aug, year = "2005", CODEN = "NUALEG", DOI = "https://doi.org/10.1007/s11075-004-6709-8", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", MRclass = "65F30", MRnumber = "MR2134331 (2005m:65094)", MRreviewer = "Jin Yun Yuan", bibdate = "Sat May 14 09:10:05 MDT 2005", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=1017-1398; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", } @InProceedings{Davies:2005:CMF, author = "Philip I. Davies and Nicholas J. Higham", editor = "Artan Bori{\c{c}i} and others", booktitle = "{QCD and numerical analysis III. Proceedings of the third international workshop on numerical analysis and lattice QCD, Edinburgh, UK, June 30--July 4, 2003}", title = "Computing $ f({A})b $ for matrix functions $f$", volume = "47", publisher = pub-SPRINGER, address = pub-SPRINGER:adr-NY, pages = "15--24", year = "2005", DOI = "https://doi.org/10.1007/3-540-28504-0_2", MRclass = "65F30 (15A99)", MRnumber = "MR2180116", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", series = "Lecture Notes in Computational Science and Engineering", ZMnumber = "1117.65319", abstract = "For matrix functions $f$ we investigate how to compute a matrix-vector product $ f(A)b $ without explicitly computing $ f(A) $. A general method is described that applies quadrature to the matrix version of the Cauchy integral theorem. Methods specific to the logarithm, based on quadrature, and fractional matrix powers, based on solution of an ordinary differential equation initial value problem, are also presented.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", classmath = "65F30 (Other matrix algorithms); 15A54 (Matrices over function rings)", keywords = "Cauchy integral theorem; fractional matrix powers; logarithm; matrix functions; matrix-vector product; quadrature", } @Article{Hargreaves:2005:EAM, author = "Gareth I. Hargreaves and Nicholas J. Higham", title = "Efficient algorithms for the matrix cosine and sine", journal = j-NUMER-ALGORITHMS, volume = "40", number = "4", pages = "383--400", year = "2005", CODEN = "NUALEG", DOI = "https://doi.org/10.1007/s11075-005-8141-0", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", MRclass = "65F30", MRnumber = "MR2191973 (2006h:65066)", bibdate = "Wed May 19 16:29:32 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", } @Article{Higham:2005:BRS, author = "Nicholas J. Higham", title = "Book Review: {The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing. By Folkmar Bornemann, Dirk Laurie, Stan Wagon, and J{\"o}rg Waldvogel. SIAM, Philadelphia, 2004. \$57.00. xii + 306 pp., hardcover. ISBN 0-89871-561-X}", journal = j-SIAM-REVIEW, volume = "47", number = "2", pages = "382--383", month = jun, year = "2005", CODEN = "SIREAD", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Fri May 27 14:40:10 MDT 2005", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/47/2; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/97149", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @Article{Higham:2005:FPM, author = "Nicholas J. Higham and D. Steven Mackey and Niloufer Mackey and Fran{\c{c}}oise Tisseur", title = "Functions Preserving Matrix Groups and Iterations for the Matrix Square Root", journal = j-SIAM-J-MAT-ANA-APPL, volume = "26", number = "3", pages = "849--877", month = jul, year = "2005", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479804442218", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Sat Apr 16 10:32:41 MDT 2005", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/26/3; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/44221", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @TechReport{Higham:2005:IPLa, author = "Nicholas J. Higham", title = "An Interview with {Peter Lancaster}", type = "Numerical Analysis Report", number = "468", institution = inst-MCCM, address = inst-MCCM:adr, pages = "10", month = jun, year = "2005", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "2005.06.01", updated = "2005.06.01", } @Article{Higham:2005:IPLb, author = "Nicholas J. Higham", title = "An Interview with {Peter Lancaster}", journal = j-SIAM-NEWS, volume = "38", number = "6", pages = "5--6", month = jul # "/" # aug, year = "2005", ISSN = "0036-1437", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "2005.08.12", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", updated = "2005.08.12", } @Book{Higham:2005:MG, author = "Desmond J. Higham and Nicholas J. Higham", title = "{MATLAB} guide", publisher = pub-SIAM, address = pub-SIAM:adr, edition = "Second", pages = "xxiv + 382", year = "2005", ISBN = "0-89871-578-4", ISBN-13 = "978-0-89871-578-1", LCCN = "QA297 .H5217 2005", MRclass = "65-00 (00A20)", MRnumber = "MR2135945", bibdate = "Wed May 19 16:25:33 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:2005:SSM, author = "Nicholas J. Higham", title = "The Scaling and Squaring Method for the Matrix Exponential Revisited", journal = j-SIAM-J-MAT-ANA-APPL, volume = "26", number = "4", pages = "1179--1193", month = oct, year = "2005", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/04061101X", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Thu Dec 29 16:33:50 MST 2005", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/26/4; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/61101", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Guo:2006:SNM, author = "Chun-Hua Guo and Nicholas J. Higham", title = "A {Schur--Newton} Method for the Matrix {\boldmath $p$}th Root and its Inverse", journal = j-SIAM-J-MAT-ANA-APPL, volume = "28", number = "3", pages = "788--804", month = jan, year = "2006", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/050643374", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F30", MRnumber = "MR2262981 (2007k:65071)", bibdate = "Tue May 18 22:32:12 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:2006:CLM, author = "Nicholas J. Higham and D. Steven Mackey and Fran{\c{c}}oise Tisseur", title = "The Conditioning of Linearizations of Matrix Polynomials", journal = j-SIAM-J-MAT-ANA-APPL, volume = "28", number = "4", pages = "1005--1028", month = jan, year = "2006", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/050628283", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F15 (15A18)", MRnumber = "MR2276551 (2008c:65103)", MRreviewer = "Marc Van Barel", bibdate = "Tue May 18 22:32:14 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:2006:RAJ, author = "Nicholas J. Higham", title = "Review of {``Alan J. Laub. \booktitle{Matrix Analysis for Scientists and Engineers}''}", journal = j-SIAM-REVIEW, volume = "48", number = "1", pages = "170--171", month = mar, year = "2006", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/SIREAD000048000001000149000001", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Tue Feb 28 12:58:46 GMT 2006", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "2006.02.28", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", updated = "2014.07.26", } @Article{Higham:2006:RMC, author = "Nicholas J. Higham", title = "Review of {``Moody T. Chu and Gene H. Golub. \booktitle{Inverse Eigenvalue Problems: Theory, Algorithms, and Applications}''}", journal = j-J-FLUID-MECH, volume = "556", pages = "442--443", year = "2006", CODEN = "JFLSA7", ISSN = "0022-1120 (print), 1469-7645 (electronic)", ISSN-L = "0022-1120", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "2006.05.11", fjournal = "Journal of Fluid Mechanics", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=FLM", updated = "2006.05.11", } @Article{Higham:2006:SLM, author = "Nicholas J. Higham and D. Steven Mackey and Niloufer Mackey and Fran{\c{c}}oise Tisseur", title = "Symmetric linearizations for matrix polynomials", journal = j-SIAM-J-MAT-ANA-APPL, volume = "29", number = "1", pages = "143--159", year = "2006/2007", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/050646202", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F15 (15A18 15A22 93C05)", MRnumber = "MR2288018 (2008e:65123)", MRreviewer = "Rafikul Alam", bibdate = "Wed May 19 16:25:33 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @InProceedings{Corless:2007:SEA, author = "Robert M. Corless and Hui Ding and Nicholas J. Higham and David J. Jeffrey", title = "The solution of $ s \exp (s) = a $ is not always the {Lambert} $ {W} $ function of $a$", crossref = "Brown:2007:PIS", pages = "116--121", year = "2007", DOI = "https://doi.org/10.1145/1277548.1277565", bibdate = "Fri Jun 20 08:46:50 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "We study the solutions of the matrix equation $ S \exp (S) = A $. Our motivation comes from the study of systems of delay differential equations $ y'(t) = A y(t - 1) $, which occur in some models of practical interest, especially in mathematical biology. This paper concentrates on the distinction between evaluating a matrix function and solving a matrix equation. In particular, it shows that the matrix Lambert $W$ function evaluated at the matrix $A$ does not represent all possible solutions of $ S \exp (S) = A$. These results can easily be extended to more general matrix equations.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", keywords = "Lambert $W$ function; matrix function; nonlinear matrix equation", } @Article{Guo:2007:ISN, author = "Chun-Hua Guo and Nicholas J. Higham", title = "Iterative Solution of a Nonsymmetric Algebraic {Riccati} Equation", journal = j-SIAM-J-MAT-ANA-APPL, volume = "29", number = "2", pages = "396--412", month = "????", year = "2007", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/050647669", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A24 (15A48 65F30)", MRnumber = "MR2318355 (2008b:15046)", MRreviewer = "Ma. Isabel Garc{\'\i}a-Planas", bibdate = "Tue May 18 22:32:18 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:2007:BEP, author = "Nicholas J. Higham and Ren-Cang Li and Fran{\c{c}}oise Tisseur", title = "Backward error of polynomial eigenproblems solved by linearization", journal = j-SIAM-J-MAT-ANA-APPL, volume = "29", number = "4", pages = "1218--1241", year = "2007", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/060663738", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F15 (15A18)", MRnumber = "MR2369292 (2009a:65092)", MRreviewer = "Jens-Peter M. Zemke", bibdate = "Wed May 19 16:25:33 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @InCollection{Higham:2007:FM, author = "Nicholas J. Higham", title = "Functions of matrices", crossref = "Hogben:2007:HLA", pages = "??--??", year = "2007", bibdate = "Mon Aug 23 07:45:17 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @InProceedings{Higham:2007:MFA, author = "Nicholas J. Higham", title = "Matrix Factorizations and Applications: Commentary", crossref = "Chan:2007:MMC", pages = "??--??", year = "2007", bibdate = "Sat Apr 07 11:25:30 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:2007:RLT, author = "Nicholas J. Higham", title = "Review of {``Lloyd N. Trefethen and Mark Embree. \booktitle{Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators}''}", journal = j-BULL-AMS, volume = "44", number = "2", pages = "277--284", year = "2007", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881X (electronic)", ISSN-L = "0002-9904", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "2007.03.21", fjournal = "Bulletin of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/bull/", updated = "2007.03.21", } @Article{Higham:2007:SLM, author = "Nicholas J. Higham and D. Steven Mackey and Niloufer Mackey and Fran{\c{c}}oise Tisseur", title = "Symmetric Linearizations for Matrix Polynomials", journal = j-SIAM-J-MAT-ANA-APPL, volume = "29", number = "1", pages = "143--159", month = "????", year = "2007", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/050646202", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Tue May 18 22:32:16 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Al-Mohy:2008:CFD, author = "Awad H. Al-Mohy and Nicholas J. Higham", title = "Computing the {Fr{\'e}chet} derivative of the matrix exponential, with an application to condition number estimation", journal = j-SIAM-J-MAT-ANA-APPL, volume = "30", number = "4", pages = "1639--1657", year = "2008", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/080716426", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F30 (65F35)", MRnumber = "MR2486857 (2009m:65071)", MRreviewer = "Dario Fasino", bibdate = "Wed May 19 16:25:33 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Guo:2008:DSH, author = "Chun-Hua Guo and Nicholas J. Higham and Fran{\c{c}}oise Tisseur", title = "Detecting and solving hyperbolic quadratic eigenvalue problems", journal = j-SIAM-J-MAT-ANA-APPL, volume = "30", number = "4", pages = "1593--1613", year = "2008", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/070704058", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A18 (15A24 65F30 65H17)", MRnumber = "MR2486855 (2010b:15021)", MRreviewer = "Mihai Cipu", bibdate = "Wed May 19 16:25:33 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Hale:2008:CRM, author = "Nicholas Hale and Nicholas J. Higham and Lloyd N. Trefethen", title = "Computing {$ {\bf A}^\alpha, \ \log ({\bf A}) $}, and related matrix functions by contour integrals", journal = j-SIAM-J-NUMER-ANAL, volume = "46", number = "5", pages = "2505--2523", year = "2008", CODEN = "SJNAAM", DOI = "https://doi.org/10.1137/070700607", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65F30", MRnumber = "MR2421045 (2009e:65071)", MRreviewer = "Raffaella Pavani", bibdate = "Wed May 19 16:25:33 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", } @Article{Higham:2008:BEP, author = "Nicholas J. Higham and Ren-Cang Li and Fran{\c{c}}oise Tisseur", title = "Backward Error of Polynomial Eigenproblems Solved by Linearization", journal = j-SIAM-J-MAT-ANA-APPL, volume = "29", number = "4", pages = "1218--1241", month = "????", year = "2008", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/060663738", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Tue May 18 22:32:22 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:2008:CSE, author = "Nicholas J. Higham", title = "{Cayley}, {Sylvester}, and early matrix theory", journal = j-LINEAR-ALGEBRA-APPL, volume = "428", number = "1", pages = "39--43", year = "2008", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2007.10.004", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15-03 (01A55)", MRnumber = "MR2372584", bibdate = "Wed May 19 16:25:33 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Book{Higham:2008:FMT, author = "Nicholas J. Higham", title = "Functions of Matrices: Theory and Computation", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xx + 425", year = "2008", DOI = "https://doi.org/10.1137/1.9780898717778", ISBN = "0-89871-646-2", ISBN-13 = "978-0-89871-646-7", MRclass = "15-02 (93B40 93C05)", MRnumber = "MR2396439 (2009b:15001)", MRreviewer = "Daniel Kressner", bibdate = "Wed May 19 16:25:33 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/numana2000.bib", note = "Theory and computation", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:2008:HOW, author = "Nicholas J. Higham", title = "In His Own Words [Interview with {Gene Golub}]", journal = j-SIAM-NEWS, volume = "41", number = "1", pages = "3", month = jan # "/" # feb, year = "2008", ISSN = "0036-1437", ISSN-L = "0036-1437", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "Extracts from \cite{high08-ghg}.", URL = "https://www.siam.org/news/news.php?id=1290", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "2013.11.28", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", updated = "2013.11.28", } @TechReport{Higham:2008:IGG, author = "Nicholas J. Higham", title = "An Interview with {Gene Golub}", type = "{MIMS EPrint}", number = "2008.8", institution = inst-MIMS, address = inst-MIMS:adr, pages = "13", month = feb, year = "2008", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "2008.02.10", updated = "2008.02.10", } @Misc{Higham:2008:MFT, author = "Nicholas J. Higham", title = "The {Matrix Function Toolbox}", year = "2008", bibdate = "Wed Sep 9 08:03:51 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://www.maths.manchester.ac.uk/~higham/mftoolbox", acknowledgement = ack-njh, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", created = "2008.01.10", updated = "2013.12.03", } @Article{Higham:2008:SSS, author = "Nicholas J. Higham and D. Steven Mackey and Fran{\c{c}}oise Tisseur and Seamus D. Garvey", title = "Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems", journal = j-INT-J-NUMER-METHODS-ENG, volume = "73", number = "3", pages = "344--360", year = "2008", CODEN = "IJNMBH", DOI = "https://doi.org/10.1002/nme.2076", ISSN = "0029-5981 (print), 1097-0207 (electronic)", ISSN-L = "0029-5981", MRclass = "65N25 (65F15 65H17 74H45 74K05)", MRnumber = "MR2382048 (2009c:65288)", MRreviewer = "Gh. Adam", bibdate = "Wed May 19 16:25:33 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "International Journal for Numerical Methods in Engineering", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207", } @Article{Al-Mohy:2009:CFD, author = "Awad H. Al-Mohy and Nicholas J. Higham", title = "Computing the {Fr{\'e}chet} Derivative of the Matrix Exponential, with an Application to Condition Number Estimation", journal = j-SIAM-J-MAT-ANA-APPL, volume = "30", number = "4", pages = "1639--1657", month = "????", year = "2009", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/080716426", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Tue May 18 22:32:31 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Al-Mohy:2009:NSS, author = "Awad H. Al-Mohy and Nicholas J. Higham", title = "A new scaling and squaring algorithm for the matrix exponential", journal = j-SIAM-J-MAT-ANA-APPL, volume = "31", number = "3", pages = "970--989", year = "2009", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/09074721X", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A16", MRnumber = "MR2538661", bibdate = "Wed May 19 16:25:33 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Guo:2009:DSH, author = "Chun-Hua Guo and Nicholas J. Higham and Fran{\c{c}}oise Tisseur", title = "Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems", journal = j-SIAM-J-MAT-ANA-APPL, volume = "30", number = "4", pages = "1593--1613", month = "????", year = "2009", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/070704058", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Tue May 18 22:32:31 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Guo:2009:IAA, author = "Chun-Hua Guo and Nicholas J. Higham and Fran{\c{c}}oise Tisseur", title = "An improved arc algorithm for detecting definite {Hermitian} pairs", journal = j-SIAM-J-MAT-ANA-APPL, volume = "31", number = "3", pages = "1131--1151", year = "2009", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/08074218X", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A18 (65F18)", MRnumber = "MR2558816", bibdate = "Wed May 19 16:25:33 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:2009:CGP, author = "Nicholas J. Higham and Christian Mehl and Fran{\c{c}}oise Tisseur", title = "The canonical generalized polar decomposition", journal = j-SIAM-J-MAT-ANA-APPL, volume = "31", number = "4", pages = "2163--2180", year = "2009/10", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/090765018", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A23", MRnumber = "2678962 (2011i:15018)", MRreviewer = "Marek Niezgoda", bibdate = "Thu Mar 6 09:16:29 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:2009:DMP, author = "Nicholas J. Higham and D. Steven Mackey and Fran{\c{c}}oise Tisseur", title = "Definite Matrix Polynomials and their Linearization by Definite Pencils", journal = j-SIAM-J-MAT-ANA-APPL, volume = "31", number = "2", pages = "478--502", month = "????", year = "2009", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/080721406", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F15 (15A18)", MRnumber = "MR2530260", MRreviewer = "Miloud Sadkane", bibdate = "Tue May 18 22:32:35 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:2009:SSM, author = "Nicholas J. Higham", title = "The Scaling and Squaring Method for the Matrix Exponential Revisited", journal = j-SIAM-REVIEW, volume = "51", number = "4", pages = "747--764", month = "????", year = "2009", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/090768539", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "65F60 (15A16)", MRnumber = "MR2563832", bibdate = "Mon May 17 17:56:49 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/51/4; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @Article{Trefethen:2009:DHP, author = "Anne Trefethen and Nick Higham and Iain Duff and Peter Coveney", title = "Developing a High-Performance Computing\slash Numerical Analysis Roadmap", journal = j-IJHPCA, volume = "23", number = "4", pages = "423--426", month = nov, year = "2009", CODEN = "IHPCFL", DOI = "https://doi.org/10.1177/1094342009347710", ISSN = "1094-3420 (print), 1741-2846 (electronic)", ISSN-L = "1094-3420", bibdate = "Tue Aug 31 09:59:45 MDT 2010", bibsource = "http://hpc.sagepub.com/content/23/4.toc; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://hpc.sagepub.com/content/23/4/423.full.pdf+html", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", journal-URL = "http://hpc.sagepub.com/content/by/year", } @Article{Al-Mohy:2010:CSA, author = "Awad H. Al-Mohy and Nicholas J. Higham", title = "The complex step approximation to the {Fr{\'e}chet} derivative of a matrix function", journal = j-NUMER-ALGORITHMS, volume = "53", number = "1", pages = "133--148", month = jan, year = "2010", CODEN = "NUALEG", DOI = "https://doi.org/10.1007/s11075-009-9323-y", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", MRclass = "65F60", MRnumber = "MR2566131", bibdate = "Wed May 19 16:25:33 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=53&issue=1&spage=133", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", } @Article{Al-Mohy:2010:NSS, author = "Awad H. Al-Mohy and Nicholas J. Higham", title = "A New Scaling and Squaring Algorithm for the Matrix Exponential", journal = j-SIAM-J-MAT-ANA-APPL, volume = "31", number = "3", pages = "970--989", month = "????", year = "2010", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/09074721X", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Tue May 18 22:32:37 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Borsdorf:2010:CNC, author = "R{\"u}diger Borsdorf and Nicholas J. Higham and Marcos Raydan", title = "Computing a Nearest Correlation Matrix with Factor Structure", journal = j-SIAM-J-MAT-ANA-APPL, volume = "31", number = "5", pages = "2603--2622", month = "????", year = "2010", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/090776718", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F30 (62H25 90C30 90C52)", MRnumber = "2740623 (2011k:65061)", MRreviewer = "Anders Linn{\'e}r", bibdate = "Sun Nov 28 22:55:40 MST 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/31/5; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", remark = "According to \cite{Higham:2024:ONJ}, this is Nick Higham's most highly cited paper.", } @Article{Borsdorf:2010:PNA, author = "R{\"u}diger Borsdorf and Nicholas J. Higham", title = "A preconditioned {Newton} algorithm for the nearest correlation matrix", journal = j-IMA-J-NUMER-ANAL, volume = "30", number = "1", pages = "94--107", month = jan, year = "2010", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/drn085", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65F20 (62H20 65F25 65H10)", MRnumber = "MR2580548", bibdate = "Wed May 19 16:25:33 2010", bibsource = "http://imanum.oxfordjournals.org/content/vol30/issue1/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://imajna.oxfordjournals.org/cgi/content/abstract/30/1/94; http://imajna.oxfordjournals.org/cgi/reprint/30/1/94", abstract = "Various methods have been developed for computing the correlation matrix nearest in the Frobenius norm to a given matrix. We focus on a quadratically convergent Newton algorithm recently derived by Qi and Sun. Various improvements to the efficiency and reliability of the algorithm are introduced. Several of these relate to the linear algebra: the Newton equations are solved by minres instead of the conjugate gradient method, as it more quickly satisfies the inexact Newton condition; we apply a Jacobi preconditioner, which can be computed efficiently even though the coefficient matrix is not explicitly available; an efficient choice of eigensolver is identified; and a final scaling step is introduced to ensure that the returned matrix has unit diagonal. Potential difficulties caused by rounding errors in the Armijo line search are avoided by altering the step selection strategy. These and other improvements lead to a significant speed-up over the original algorithm and allow the solution of problems of dimension a few thousand in a few tens of minutes.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", } @Article{Guo:2010:IAA, author = "Chun-Hua Guo and Nicholas J. Higham and Fran{\c{c}}oise Tisseur", title = "An Improved Arc Algorithm for Detecting Definite {Hermitian} Pairs", journal = j-SIAM-J-MAT-ANA-APPL, volume = "31", number = "3", pages = "1131--1151", month = "????", year = "2010", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/08074218X", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Tue May 18 22:32:37 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:2010:CGP, author = "Nicholas J. Higham and Christian Mehl and Fran{\c{c}}oise Tisseur", title = "The Canonical Generalized Polar Decomposition", journal = j-SIAM-J-MAT-ANA-APPL, volume = "31", number = "4", pages = "2163--2180", month = "????", year = "2010", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/090765018", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A23", MRnumber = "2678962 (2011i:15018)", MRreviewer = "Marek Niezgoda", bibdate = "Sun Nov 28 22:55:37 MST 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/31/4; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Higham:2010:CMF, author = "Nicholas J. Higham and Awad H. Al-Mohy", title = "Computing matrix functions", journal = j-ACTA-NUMERICA, volume = "19", pages = "159--208", year = "2010", CODEN = "ANUMFU", DOI = "https://doi.org/10.1017/S0962492910000036", ISBN = "0-521-19284-6", ISBN-13 = "978-0-521-19284-2", ISSN = "0962-4929 (print), 1474-0508 (electronic)", ISSN-L = "0962-4929", MRclass = "65F60 (15A16)", MRnumber = "2652782 (2011g:65073)", MRreviewer = "Olexander S. Babanin", bibdate = "Sat Sep 24 10:35:17 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/actanumerica.bib", acknowledgement = ack-nhfb, ajournal = "Acta Numer.", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Acta Numerica", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU", onlinedate = "10 May 2010", } @Article{Al-Mohy:2011:CAM, author = "Awad H. Al-Mohy and Nicholas J. Higham", title = "Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators", journal = j-SIAM-J-SCI-COMP, volume = "33", number = "2", pages = "488--511", month = "????", year = "2011", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/100788860", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F60 (65P10)", MRnumber = "2785959 (2012d:65082)", MRreviewer = "Ross A. Lippert", bibdate = "Fri Mar 4 09:58:54 MST 2011", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/33/2; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", note = "See \cite{Fischer:2017:AAM}.", URL = "http://epubs.siam.org/sisc/resource/1/sjoce3/v33/i2/p488_s1", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", onlinedate = "March 01, 2011", } @Article{Grammont:2011:FAN, author = "Laurence Grammont and Nicholas J. Higham and Fran{\c{c}}oise Tisseur", title = "A framework for analyzing nonlinear eigenproblems and parametrized linear systems", journal = j-LINEAR-ALGEBRA-APPL, volume = "435", number = "3", pages = "623--640", day = "1", month = aug, year = "2011", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2009.12.038", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A18 (65F15 65F35)", MRnumber = "2794594 (2012d:15022)", MRreviewer = "Ilse C. F. Ipsen", bibdate = "Mon Jun 13 18:34:37 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Higham:2011:RSM, author = "Nicholas J. Higham and Lijing Lin", title = "On $p$-th roots of stochastic matrices", journal = j-LINEAR-ALGEBRA-APPL, volume = "435", number = "3", pages = "448--463", day = "1", month = aug, year = "2011", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2010.04.007", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15B51 (15A16 15B48 60J10)", MRnumber = "2794585 (2012d:15062)", MRreviewer = "Adolf Rhodius", bibdate = "Sat Mar 23 18:05:45 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Higham:2011:SPA, author = "Nicholas J. Higham and Lijing Lin", title = "A {Schur--Pad{\'e}} Algorithm for Fractional Powers of a Matrix", journal = j-SIAM-J-MAT-ANA-APPL, volume = "32", number = "3", pages = "1056--1078", month = "????", year = "2011", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/10081232X", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F60", MRnumber = "2837592", MRreviewer = "Jorge Sastre", bibdate = "Thu Feb 9 08:15:43 MST 2012", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/32/3; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "September 29, 2011", } @Article{Al-Mohy:2012:IIS, author = "Awad H. Al-Mohy and Nicholas J. Higham", title = "Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm", journal = j-SIAM-J-SCI-COMP, volume = "34", number = "4", pages = "C153--C169", year = "2012", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/110852553", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F30", MRnumber = "2970418", bibdate = "Tue Oct 30 14:49:05 MDT 2012", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/34/4; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", onlinedate = "January 2012", } @Article{Nakatsukasa:2012:BSI, author = "Yuji Nakatsukasa and Nicholas J. Higham", title = "Backward Stability of Iterations for Computing the Polar Decomposition", journal = j-SIAM-J-MAT-ANA-APPL, volume = "33", number = "2", pages = "460--479", month = "????", year = "2012", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/110857544", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F30 (15A23 65F20 65F25 65F35 65G50)", MRnumber = "2970215", MRreviewer = "Ilse C. F. Ipsen", bibdate = "Tue Oct 30 14:04:27 MDT 2012", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/33/2; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "January 2012", } @Article{Al-Mohy:2013:CFD, author = "Awad H. Al-Mohy and Nicholas J. Higham and Samuel D. Relton", title = "Computing the {Fr{\'e}chet} derivative of the matrix logarithm and estimating the condition number", journal = j-SIAM-J-SCI-COMP, volume = "35", number = "4", pages = "C394--C410", year = "2013", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/120885991", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F60 (65F35)", MRnumber = "3080997", bibdate = "Thu Mar 6 09:16:29 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @Article{Betcke:2013:NCN, author = "Timo Betcke and Nicholas J. Higham and Volker Mehrmann and Christian Schr{\"o}der and Fran{\c{c}}oise Tisseur", title = "{NLEVP}: a collection of nonlinear eigenvalue problems", journal = j-TOMS, volume = "39", number = "2", pages = "Art. 7, 28", year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2427023.2427024", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65H17 (65F10 65Y15)", MRnumber = "3031626", bibdate = "Thu Mar 6 09:16:29 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://dl.acm.org/pub.cfm?id=J782", } @Article{Dingle:2013:RIT, author = "Nicholas J. Dingle and Nicholas J. Higham", title = "Reducing the influence of tiny normwise relative errors on performance profiles", journal = j-TOMS, volume = "39", number = "4", pages = "24:1--24:11", month = jul, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2491491.2491494", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F35 (65G50 65Y20)", MRnumber = "3092099", MRreviewer = "Dario Fasino", bibdate = "Fri Jul 19 17:20:56 MDT 2013", bibsource = "http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "It is a widespread but little-noticed phenomenon that the normwise relative error $ || x - y || / || x || $ of vectors $x$ and $y$ of floating point numbers of the same precision, where $y$ is an approximation to x, can be many orders of magnitude smaller than the unit roundoff. We analyze this phenomenon and show that in the $ \infty $-norm it happens precisely when $x$ has components of widely varying magnitude and every component of $x$ of largest magnitude agrees with the corresponding component of $y$. Performance profiles are a popular way to compare competing algorithms according to particular measures of performance. We show that performance profiles based on normwise relative errors can give a misleading impression due to the influence of zero or tiny normwise relative errors. We propose a transformation that reduces the influence of these extreme errors in a controlled manner, while preserving the monotonicity of the underlying data and leaving the performance profile unchanged at its left end-point. Numerical examples with both artificial and genuine data illustrate the benefits of the transformation.", acknowledgement = ack-nhfb, articleno = "24", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "http://dl.acm.org/pub.cfm?id=J782", } @Article{Higham:2013:ISP, author = "Nicholas J. Higham and Lijing Lin", title = "An improved {Schur--Pad{\'e}} algorithm for fractional powers of a matrix and their {Fr{\'e}chet} derivatives", journal = j-SIAM-J-MAT-ANA-APPL, volume = "34", number = "3", pages = "1341--1360", month = "????", year = "2013", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/130906118", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F60 (15A16)", MRnumber = "3102571", bibdate = "Tue Feb 11 12:44:41 MST 2014", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/34/3; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "January 2013", } @Article{Nakatsukasa:2013:SES, author = "Yuji Nakatsukasa and Nicholas J. Higham", title = "Stable and Efficient Spectral Divide and Conquer Algorithms for the Symmetric Eigenvalue Decomposition and the {SVD}", journal = j-SIAM-J-SCI-COMP, volume = "35", number = "3", pages = "A1325--A1349", month = "????", year = "2013", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/120876605", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F15", MRnumber = "3054594", MRreviewer = "Fatemeh Panjeh Ali Beik", bibdate = "Fri Jul 19 07:43:53 MDT 2013", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/35/3; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", note = "See \cite{Sukkari:2019:QBS}.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", onlinedate = "January 2013", } @Article{Aprahamian:2014:MUF, author = "Mary Aprahamian and Nicholas J. Higham", title = "The matrix unwinding function, with an application to computing the matrix exponential", journal = j-SIAM-J-MAT-ANA-APPL, volume = "35", number = "1", pages = "88--109", month = "????", year = "2014", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/130920137", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F30 (15A24 65F60)", MRnumber = "3159979", MRreviewer = "Petko Petkov", bibdate = "Mon Mar 31 06:45:43 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "January 2014", } @Article{Bethune:2014:PAA, author = "Iain Bethune and J. Mark Bull and Nicholas J. Dingle and Nicholas J. Higham", title = "Performance analysis of asynchronous {Jacobi}'s method implemented in {MPI}, {SHMEM} and {OpenMP}", journal = j-IJHPCA, volume = "28", number = "1", pages = "97--111", month = feb, year = "2014", CODEN = "IHPCFL", DOI = "https://doi.org/10.1177/1094342013493123", ISSN = "1094-3420 (print), 1741-2846 (electronic)", ISSN-L = "1094-3420", bibdate = "Fri Mar 14 15:39:59 MDT 2014", bibsource = "http://hpc.sagepub.com/content/28/1.toc; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/ijsa.bib; https://www.math.utah.edu/pub/tex/bib/pvm.bib", URL = "http://hpc.sagepub.com/content/28/1/97.full.pdf+html", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "International Journal of High Performance Computing Applications", journal-URL = "http://hpc.sagepub.com/content/by/year", onlinedate = "July 11, 2013", } @Article{Higham:2014:ECN, author = "Nicholas J. Higham and Samuel D. Relton", title = "Estimating the condition number of the {Fr{\'e}chet} derivative of a matrix function", journal = j-SIAM-J-SCI-COMP, volume = "36", number = "6", pages = "C617--C634", year = "2014", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/130950082", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F35 (65F60)", MRnumber = "3281285", MRreviewer = "A. Bultheel", bibdate = "Wed Sep 9 06:09:29 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", ZMnumber = "06409885", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @Article{Higham:2014:HOF, author = "Nicholas J. Higham and Samuel D. Relton", title = "Higher Order {Fr{\'e}chet} Derivatives of Matrix Functions and the Level-$2$ Condition Number", journal = j-SIAM-J-MAT-ANA-APPL, volume = "35", number = "3", pages = "1019--1037", month = "????", year = "2014", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/130945259", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F35 (15A16 65F60)", MRnumber = "3233937", MRreviewer = "Boyan G. Zlatanov", bibdate = "Sat Sep 13 12:06:59 MDT 2014", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/35/3; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "January 2014", } @Article{Higham:2014:SIA, author = "Nicholas J. Higham", title = "{Sylvester}'s influence on applied mathematics", journal = j-MATH-TODAY, volume = "50", number = "4", pages = "202--206", year = "2014", ISSN = "1361-2042", ISSN-L = "1361-2042", MRclass = "01A70", MRnumber = "3241571", bibdate = "Wed Sep 9 06:09:29 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Mathematics Today", journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html", } @Article{Lin:2014:CSR, author = "Lijing Lin and Nicholas J. Higham and Jianxin Pan", title = "Covariance structure regularization via entropy loss function", journal = j-COMPUT-STAT-DATA-ANAL, volume = "72", pages = "315--327", year = "2014", CODEN = "CSDADW", DOI = "https://doi.org/10.1016/j.csda.2013.10.004", ISSN = "0167-9473 (print), 1872-7352 (electronic)", ISSN-L = "0167-9473", MRclass = "Preliminary Data", MRnumber = "3139365", bibdate = "Thu Mar 6 09:16:29 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Computational Statistics \& Data Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/01679473", } @Article{Al-Mohy:2015:NAC, author = "Awad H. Al-Mohy and Nicholas J. Higham and Samuel D. Relton", title = "New algorithms for computing the matrix sine and cosine separately or simultaneously", journal = j-SIAM-J-SCI-COMP, volume = "37", number = "1", pages = "A456--A487", year = "2015", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/140973979", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F60", MRnumber = "3311875", MRreviewer = "Petko Petkov", bibdate = "Wed Sep 9 06:09:29 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", ZMnumber = "1315.65045", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @Article{Fasi:2015:AML, author = "Massimiliano Fasi and Nicholas J. Higham and Bruno Iannazzo", title = "An algorithm for the matrix {Lambert} {$W$} function", journal = j-SIAM-J-MAT-ANA-APPL, volume = "36", number = "2", pages = "669--685", month = "????", year = "2015", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/140997610", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F60 (15A15)", MRnumber = "3354997", MRreviewer = "Thomas Mach", bibdate = "Fri Aug 7 16:43:51 MDT 2015", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/36/2; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", ZMnumber = "1317.65116", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "January 2015", } @Misc{Higham:2015:MCT, author = "Nicholas J. Higham", title = "Matrix Computation Toolbox", howpublished = "Web site.", year = "2015", bibdate = "Sat Apr 01 08:14:19 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib", URL = "http://www.ma.man.ac.uk/~higham/mctoolbox", abstract = "The Matrix Computation Toolbox is a collection of MATLAB M-files containing functions for constructing test matrices, computing matrix factorizations, visualizing matrices, and carrying out direct search optimization. Various other miscellaneous functions are also included. This toolbox supersedes the author's earlier Test Matrix Toolbox (final release 1995).\par The toolbox was developed in conjunction with the book Accuracy and Stability of Numerical Algorithms (SIAM, Second edition, August 2002, xxx + 680 pp.). That book is the primary documentation for the toolbox: it describes much of the underlying mathematics and many of the algorithms and matrices (it also describes many of the matrices provided by MATLAB's gallery function).", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", keywords = "floating-point arithmetic; MATLAB", } @InCollection{Higham:2015:MFS, author = "Nicholas J. Higham and Lijing Lin", editor = "Zhaojun Bai and Weiguo Gao and Yangfeng Su", booktitle = "Matrix Functions and Matrix Equations", title = "Matrix Functions: a Short Course", volume = "19", publisher = pub-WORLD-SCI, address = pub-WORLD-SCI:adr, bookpages = "vii + 137", pages = "1--27", year = "2015", ISBN = "981-4675-76-8 (hardcover), 981-4675-77-6 (e-book), 981-4675-78-4 (e-book)", ISBN-13 = "978-981-4675-76-5 (hardcover), 978-981-4675-77-2 (e-book), 978-981-4675-78-9 (e-book)", LCCN = "QA184.2 .M39 2015", MRclass = "15-01", MRnumber = "3445562", bibdate = "Sat Aug 26 17:36:15 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", series = "Ser. Contemp. Appl. Math. CAM", URL = "http://www.worldscientific.com/worldscibooks/10.1142/9590", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", tableofcontents = "Matrix Functions: A Short Course / Nicholas J. Higham and Lijing Lin / 1 \\ A Short Course on Exponential Integrators / Marlis Hochbruck / 28 \\ Matrix Equations and Model Reduction / Peter Benner, Tobias Breiten and Lihong Feng / 50 \\ Rayleigh Quotient Based Optimization Methods for Eigenvalue Problems / Ren-Cang Li / 76 \\ Factorization-Based Sparse Solvers and Preconditioners / Xiaoye Sherry Li / 109", xxaddress = "Beijing, China", xxpublisher = "Higher Education Press", } @Article{Aprahamian:2016:MEB, author = "Mary Aprahamian and Desmond J. Higham and Nicholas J. Higham", title = "Matching exponential-based and resolvent-based centrality measures", journal = j-J-COMPLEX-NETWORKS, volume = "4", number = "2", pages = "157--176", year = "2016", DOI = "https://doi.org/10.1093/comnet/cnv016", ISSN = "2051-1310 (print), 2051-1329 (electronic)", ISSN-L = "2051-1310", MRclass = "05C82", MRnumber = "3605538", bibdate = "Sat Aug 26 17:36:42 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, ajournal = "J. Complex Netw.", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Journal of Complex Networks", journal-URL = "http://www.comnet.oxfordjournals.org", } @Article{Aprahamian:2016:MIT, author = "Mary Aprahamian and Nicholas J. Higham", title = "Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms", journal = j-SIAM-J-MAT-ANA-APPL, volume = "37", number = "4", pages = "1453--1477", month = "????", year = "2016", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/16M1057577", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A24 (65F60)", MRnumber = "3556068", MRreviewer = "Mustapha Rachidi", bibdate = "Fri Aug 25 09:01:43 MDT 2017", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/37/4; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "January 2016", } @Article{Deadman:2016:TMF, author = "Edvin Deadman and Nicholas J. Higham", title = "Testing Matrix Function Algorithms Using Identities", journal = j-TOMS, volume = "42", number = "1", pages = "4:1--4:15", month = feb, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2723157", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F60", MRnumber = "3472420", bibdate = "Tue Mar 1 17:07:56 MST 2016", bibsource = "http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Algorithms for computing matrix functions are typically tested by comparing the forward error with the product of the condition number and the unit roundoff. The forward error is computed with the aid of a reference solution, typically computed at high precision. An alternative approach is to use functional identities such as the ``round-trip tests'' $ e^{\log A} = A $ and $ (A^{1 / p})^p = A $, as are currently employed in a SciPy test module. We show how a linearized perturbation analysis for a functional identity allows the determination of a maximum residual consistent with backward stability of the constituent matrix function evaluations. Comparison of this maximum residual with a computed residual provides a necessary test for backward stability. We also show how the actual linearized backward error for these relations can be computed. Our approach makes use of Fr{\'e}chet derivatives and estimates of their norms. Numerical experiments show that the proposed approaches are able both to detect instability and to confirm stability.", acknowledgement = ack-nhfb, articleno = "4", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "http://dl.acm.org/pub.cfm?id=J782", } @Article{Higham:2016:AAA, author = "Nicholas J. Higham and Nata{\v{s}}a Strabi{\'c}", title = "{Anderson} acceleration of the alternating projections method for computing the nearest correlation matrix", journal = j-NUMER-ALGORITHMS, volume = "72", number = "4", pages = "1021--1042", month = aug, year = "2016", CODEN = "NUALEG", DOI = "https://doi.org/10.1007/s11075-015-0078-3", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", MRclass = "65F30 (15B57)", MRnumber = "3529831", MRreviewer = "Hassane Abbas", bibdate = "Tue Sep 20 10:57:47 MDT 2016", bibsource = "http://link.springer.com/journal/11075/72/4; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib", URL = "http://link.springer.com/content/pdf/10.1007/s11075-015-0078-3.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", } @Article{Higham:2016:ACP, author = "Nicholas J. Higham and Vanni Noferini", title = "An algorithm to compute the polar decomposition of a $ 3 \times 3 $ matrix", journal = j-NUMER-ALGORITHMS, volume = "73", number = "2", pages = "349--369", month = oct, year = "2016", CODEN = "NUALEG", DOI = "https://doi.org/10.1007/s11075-016-0098-7", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", MRclass = "65F99 (15A21)", MRnumber = "3549082", bibdate = "Tue Sep 20 10:57:48 MDT 2016", bibsource = "http://link.springer.com/journal/11075/73/2; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib", URL = "http://link.springer.com/content/pdf/10.1007/s11075-016-0098-7.pdf", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", keywords = "$3 \times 3$ matrix; Numerical stability; Polar decomposition; Quaternions; Singular value decomposition", } @Article{Higham:2016:BDN, author = "Nicholas J. Higham and Natasa Strabi{\'c}", title = "Bounds for the Distance to the Nearest Correlation Matrix", journal = j-SIAM-J-MAT-ANA-APPL, volume = "37", number = "3", pages = "1088--1102", month = "????", year = "2016", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/15M1052007", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A45 (65F05 65F30)", MRnumber = "3537883", MRreviewer = "Antonio Cicone", bibdate = "Tue Nov 8 08:41:57 MST 2016", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/37/3; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "January 2016", } @Article{Higham:2016:ELE, author = "Nicholas J. Higham and Samuel D. Relton", title = "Estimating the Largest Elements of a Matrix", journal = j-SIAM-J-SCI-COMP, volume = "38", number = "5", pages = "C584--C601", month = "????", year = "2016", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/15M1053645", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F99 (65F35)", MRnumber = "3561776", MRreviewer = "Jo\~ao Ribeiro Cardoso", bibdate = "Sun Mar 12 07:28:39 MDT 2017", bibsource = "http://epubs.siam.org/toc/sjoce3/38/5; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", onlinedate = "January 2016", } @Article{Higham:2016:KGS, author = "Nicholas J. Higham", title = "{Knuth} Gives Satisfaction in {SIAM von Neumann Lecture}", journal = j-SIAM-NEWS, volume = "49", number = "6", pages = "??--??", month = jul # "\slash " # aug, year = "2016", ISSN = "0036-1437", ISSN-L = "0036-1437", bibdate = "Fri Sep 30 15:20:42 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "https://sinews.siam.org/DetailsPage/TabId/900/ArtMID/2243/ArticleID/820/Knuth-Gives-Satisfaction-in-SIAM-von-Neumann-Lecture.aspx", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", keywords = "2016 SIAM John von Neumann lecture prize; Art of Computer Programming; Donald E. Knuth; Satisfiability and Combinatorics", } @Article{Higham:2016:MWP, author = "Nicholas J. Higham", title = "Mathematical Word Processing: Historical Snippets", journal = j-SIAM-NEWS, volume = "49", number = "6", pages = "??--??", month = jul # "\slash " # aug, year = "2016", ISSN = "0036-1437", ISSN-L = "0036-1437", bibdate = "Fri Sep 30 12:32:57 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "https://sinews.siam.org/DetailsPage/TabId/900/ArtMID/2243/ArticleID/1655/Mathematical-Word-Processing-Historical-Snippets.aspx", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", } @Article{Higham:2016:RDS, author = "Nicholas J. Higham and Nata{\v{s}}a Strabi{\'c} and Vedran {\v{S}}ego", title = "Restoring Definiteness via Shrinking, with an Application to Correlation Matrices with a Fixed Block", journal = j-SIAM-REVIEW, volume = "58", number = "2", pages = "245--263", month = "????", year = "2016", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/140996112", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "15B57 (65F30)", MRnumber = "3493945", MRreviewer = "Yang Cao", bibdate = "Fri May 27 07:15:57 MDT 2016", bibsource = "http://epubs.siam.org/toc/siread/58/2; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "January 2016", } @Article{Zhang:2016:MDE, author = "Weijian Zhang and Nicholas J. Higham", title = "{Matrix Depot}: an extensible test matrix collection for {Julia}", journal = "PeerJ Computer Science", volume = "2", pages = "e58:1--e58:25", month = apr, year = "2016", DOI = "https://doi.org/10.7717/peerj-cs.58", ISSN = "2376-5992", bibdate = "Tue Apr 23 06:36:55 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/julia.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", journal-URL = "https://peerj.com/cs/", } @Article{Carson:2017:NAI, author = "Erin Carson and Nicholas J. Higham", title = "A new analysis of iterative refinement and its application to accurate solution of ill-conditioned sparse linear systems", journal = j-SIAM-J-SCI-COMP, volume = "39", number = "6", pages = "A2834--A2856", year = "2017", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/17M1122918", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65G50 (65F10 65F35 65F50)", MRnumber = "3732948", bibdate = "Tue May 8 08:38:21 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "http://eprints.maths.manchester.ac.uk/2537/", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @Article{Fischer:2017:AAM, author = "Thomas M. Fischer", title = "On the algorithm by {Al-Mohy} and {Higham} for computing the action of the matrix exponential: a posteriori roundoff error estimation", journal = j-LINEAR-ALGEBRA-APPL, volume = "531", number = "??", pages = "141--168", day = "15", month = oct, year = "2017", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2017.05.042", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Sat Aug 26 17:24:35 MDT 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", note = "See \cite{Al-Mohy:2011:CAM}.", URL = "http://www.sciencedirect.com/science/article/pii/S0024379517303427", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Higham:2017:CAT, author = "Nicholas J. Higham and Peter Kandolf", title = "Computing the Action of Trigonometric and Hyperbolic Matrix Functions", journal = j-SIAM-J-SCI-COMP, volume = "39", number = "2", pages = "A613--A627", month = "????", year = "2017", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/16M1084225", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F60 (15A16)", MRnumber = "3636536", MRreviewer = "Ralf Zimmermann", bibdate = "Fri Aug 25 09:17:35 MDT 2017", bibsource = "http://epubs.siam.org/toc/sjoce3/39/2; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", onlinedate = "January 2017", } @Article{Higham:2017:CHB, author = "Nicholas J. Higham and Neville J. Ford", title = "{Christopher T. H. Baker} (1939--2017)", journal = j-MATH-TODAY, volume = "53", number = "6", pages = "257", year = "2017", ISSN = "1361-2042", ISSN-L = "1361-2042", MRclass = "01A70", MRnumber = "3702305", bibdate = "Tue May 8 08:39:11 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Mathematics Today", journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html", } @Book{Higham:2017:MG, author = "Desmond J. Higham and Nicholas J. Higham", title = "{MATLAB} guide", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xxvi + 476", year = "2017", ISBN = "1-61197-465-8", ISBN-13 = "978-1-61197-465-2", MRclass = "65-00 (00A20)", MRnumber = "3601107", bibdate = "Sat Aug 26 17:40:10 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/numana2010.bib", abstract = "MATLAB is an interactive system for numerical computation that is widely used for teaching and research in industry and academia. It provides a modern programming language and problem solving environment, with powerful data structures, customizable graphics, and easy-to-use editing and debugging tools. This third edition of MATLAB Guide completely revises and updates the best-selling second edition and is more than 25 percent longer. The book remains a lively, concise introduction to the most popular and important features of MATLAB and the Symbolic Math Toolbox. Key features are a tutorial in Chapter 1 that gives a hands-on overview of MATLAB, a thorough treatment of MATLAB mathematics, including the linear algebra and numerical analysis functions and the differential equation solvers, and a web page that provides a link to example program files, updates, and links to MATLAB resources. The new edition contains color figures throughout, includes pithy discussions of related topics in new `Asides' boxes that augment the text, has new chapters on the Parallel Computing Toolbox, object-oriented programming, graphs, and large data sets, covers important new MATLAB data types such as categorical arrays, string arrays, tall arrays, tables, and timetables, contains more on MATLAB workflow, including the Live Editor and unit tests, and fully reflects major updates to the MATLAB graphics system.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", remark = "Third edition of \cite{Higham:2000:MG,Higham:2005:MG}.", subject = "MATLAB (logiciel).; Analyse num{\'e}rique; Logiciels.; Numerical analysis; Data processing; Data processing.", tableofcontents = "1: A Brief Tutorial \\ 2: Basics \\ 3: Distinctive Features of MATLAB \\ 4: Arithmetic \\ 5: Matrices \\ 6: Operators and Flow Control \\ 7: Program Files \\ 8: Graphics \\ 9: Linear Algebra \\ 10: More on Functions \\ 11: Numerical Methods: Part I \\ 12: Numerical Methods: Part II \\ 13: Input and Output \\ 14: Troubleshooting \\ 15: Sparse Matrices \\ 16: More on Coding \\ 17: Advanced Graphics \\ 18: Other Data Types and Multidimensional Arrays \\ 19: Object-Oriented Programming \\ 20: The Symbolic Math Toolbox \\ 21: Graphs \\ 22: Large Data Sets \\ 23: Optimizing Codes \\ 24: Tricks and Tips \\ 25: The Parallel Computing Toolbox \\ 26: Case Studies", } @InProceedings{Higham:2017:RMA, author = "N. J. Higham", title = "The Rise of Multiprecision Arithmetic", crossref = "Burgess:2017:ISC", pages = "1--1", month = jul, year = "2017", DOI = "https://doi.org/10.1109/ARITH.2017.24", ISSN = "1063-6889", bibdate = "Fri Nov 17 09:10:14 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", abstract = "There is a growing demand for and availability of multiprecision arithmetic: floating point arithmetic supporting multiple, possibly arbitrary, precisions. For an increasing body of applications, including in supernova simulations, electromagnetic scattering theory, and computational number theory, double precision arithmetic is insufficient to provide results of the required accuracy. On the other hand, for climate modelling and deep learning half precision (about four significant decimal digits) has been shown to be sufficient in some studies. We discuss a number of topics involving multiprecision arithmetic, including: The need for, availability of, and ways to exploit, higher precision arithmetic (e.g., quadruple precision arithmetic). How to derive linear algebra algorithms that will run in any precision, as opposed to be being optimized (as some key algorithms are) for double precision. For solving linear systems with the use of iterative refinement, the benefits of suitably combining three different precisions of arithmetic (say, half, single, and double). How a new form of preconditioned iterative refinement can be used to solve very ill conditioned sparse linear systems to high accuracy.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", keywords = "climate modelling; Computational modeling; deep learning half precision; Digital arithmetic; double precision arithmetic; Electromagnetic scattering; floating point arithmetic; Floating-point arithmetic; iterative methods; iterative refinement; linear algebra; linear algebra algorithms; linear systems; Linear systems; Mathematical model; multiprecision arithmetic; sparse linear systems", } @Article{Carson:2018:ASL, author = "Erin Carson and Nicholas J. Higham", title = "Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions", journal = j-SIAM-J-SCI-COMP, volume = "40", number = "2", pages = "A817--A847", month = "????", year = "2018", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/17M1140819", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F10 (65F05 65F35 65G50)", MRnumber = "3775138", MRreviewer = "Dimitrios Christou", bibdate = "Tue May 8 15:57:34 MDT 2018", bibsource = "http://epubs.siam.org/toc/sjoce3/40/2; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", onlinedate = "January 2018", } @Article{Fasi:2018:MAC, author = "Massimiliano Fasi and Nicholas J. Higham", title = "Multiprecision algorithms for computing the matrix logarithm", journal = j-SIAM-J-MAT-ANA-APPL, volume = "39", number = "1", pages = "472--491", year = "2018", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/17M1129866", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F60 (15A16 15A60)", MRnumber = "3775134", MRreviewer = "Javier Pastor", bibdate = "Tue May 8 08:39:52 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Freeman:2018:JWF, author = "T. L. Freeman and Nicholas J. Higham", title = "{Joan E. Walsh FIMA} (1932--2017)", journal = j-MATH-TODAY, volume = "54", number = "3", pages = "89", year = "2018", ISSN = "1361-2042", ISSN-L = "1361-2042", MRclass = "01A70", MRnumber = "3820884", bibdate = "Sat Oct 6 15:34:30 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Mathematics Today", journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html", } @Article{Georgescu:2018:ESC, author = "Dan I. Georgescu and Nicholas J. Higham and Gareth W. Peters", title = "Explicit solutions to correlation matrix completion problems, with an application to risk management and insurance", journal = j-R-SOC-OPEN-SCI, volume = "5", number = "3", pages = "172348:1--172348:11", month = mar, year = "2018", CODEN = "RSOSAV", DOI = "https://doi.org/10.1098/rsos.172348", ISSN = "2054-5703", ISSN-L = "2054-5703", MRclass = "65F99 (15A83 91B30)", MRnumber = "3815440", bibdate = "Sat Oct 6 15:34:30 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, ajournal = "R. Soc. Open Sci.", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Royal Society Open Science", journal-URL = "http://rsos.royalsocietypublishing.org/", } @InProceedings{Haidar:2018:HGT, author = "Azzam Haidar and Stanimire Tomov and Jack Dongarra and Nicholas J. Higham", editor = "{IEEE}", booktitle = "{SC '18 Proceedings of the International Conference for High Performance Computing, Networking, Storage, and Analysis, Dallas, Texas, November 11--16, 2018}", title = "Harnessing {GPU} tensor cores for fast {FP16} arithmetic to speed up mixed-precision iterative refinement solvers", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "47:1--47:11", year = "2018", ISBN = "1-5386-8384-9", ISBN-13 = "978-1-5386-8384-2", LCCN = "????", bibdate = "Sat Jan 19 18:51:19 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "https://dl.acm.org/citation.cfm?id=3291656.3291719", abstract = "Low-precision floating-point arithmetic is a powerful tool for accelerating scientific computing applications, especially those in artificial intelligence. Here, we present an investigation showing that other high-performance computing (HPC) applications can also harness this power. Specifically, we use the general HPC problem, Ax = b, where A is a large dense matrix, and a double precision (FP64) solution is needed for accuracy. Our approach is based on mixed-precision (FP16 $ \to $ FP64) iterative refinement, and we generalize and extend prior advances into a framework, for which we develop architecture-specific algorithms and highly tuned implementations. These new methods show how using half-precision Tensor Cores (FP16-TC) for the arithmetic can provide up to 4X speedup. This is due to the performance boost that the FP16-TC provide as well as to the improved accuracy over the classical FP16 arithmetic that is obtained because the GEMM accumulation occurs in FP32 arithmetic.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:2018:DD, author = "Nicholas Higham", title = "Differentiation with(out) a difference", journal = j-SIAM-NEWS, volume = "51", number = "5", pages = "2", year = "2018", ISSN = "1557-9573", ISSN-L = "1557-9573", MRclass = "65D25 (41A80 65G50)", MRnumber = "3823048", bibdate = "Tue Jan 22 15:10:07 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", } @Misc{Higham:2018:HPA, author = "Nicholas J. Higham", title = "Half Precision Arithmetic: fp16 Versus bfloat16", howpublished = "Web site.", day = "3", month = dec, year = "2018", bibdate = "Sat Jan 19 18:43:15 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "https://nickhigham.wordpress.com/2018/12/03/half-precision-arithmetic-fp16-versus-bfloat16/", abstract = "The 2008 revision of the IEEE Standard for Floating-Point Arithmetic introduced a half precision 16-bit floating point format, known as fp16, as a storage format. Various manufacturers have adopted fp16 for computation, using the obvious extension of the rules for the fp32 (single precision) and fp64 (double precision) formats. For example, fp16 is supported by the NVIDIA P100 and V100 GPUs and the AMD Radeon Instinct MI25 GPU, as well as the A64FX Arm processor that will power the Fujitsu Post-K exascale computer.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Higham:2018:RAB, author = "Nicholas Higham", title = "Rhapsodizing about {Bohemian} matrices", journal = j-SIAM-NEWS, volume = "51", number = "10", pages = "2", year = "2018", ISSN = "1557-9573", ISSN-L = "1557-9573", MRclass = "15B34", MRnumber = "3929646", bibdate = "Fri Jul 9 15:09:12 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", } @Article{Higham:2018:SS, author = "Nicholas Higham", title = "Snap to structure", journal = j-SIAM-NEWS, volume = "51", number = "1", pages = "2", year = "2018", ISSN = "1557-9573", ISSN-L = "1557-9573", MRclass = "65G99 (68W30)", MRnumber = "3823054", bibdate = "Tue Jan 22 15:10:07 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", } @Article{Higham:2018:TFD, author = "Nicholas Higham", title = "A timely focus on data science", journal = j-SIAM-NEWS, volume = "51", number = "9", pages = "2", year = "2018", ISSN = "1557-9573", ISSN-L = "1557-9573", MRclass = "68T01", MRnumber = "3889491", bibdate = "Fri Jul 9 15:09:43 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", } @Article{Higham:2018:UN, author = "Nicholas J. Higham", title = "The Unwinding Number", journal = j-SIAM-NEWS, volume = "51", number = "8", pages = "2--2", month = oct, year = "2018", ISSN = "0036-1437", ISSN-L = "0036-1437", MRclass = "65E05 (68N15)", MRnumber = "3823081", bibdate = "Sat Oct 06 08:46:15 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "https://sinews.siam.org/Details-Page/the-unwinding-number", abstract = "While Fortran 66 had a complex data type, this was not true of most other early programming languages, such as Algol 60. As a result, programmers had to write their own procedures to implement complex arithmetic and transcendental functions in terms of separately stored real and imaginary parts. They quickly realized that this is not a trivial task; in the early 1960s, it took five published attempts over three years to obtain a correct implementation of the complex logarithm in Algol 60.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Article{Nadukandi:2018:CWK, author = "Prashanth Nadukandi and Nicholas J. Higham", title = "Computing the Wave-Kernel Matrix Functions", journal = j-SIAM-J-SCI-COMP, volume = "40", number = "6", pages = "A4060--A4082", month = "????", year = "2018", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/18M1170352", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F60 (15A60 41A21)", MRnumber = "3884228", MRreviewer = "Fazlollah Soleymani", bibdate = "Tue Jan 22 15:10:07 2019", bibsource = "http://epubs.siam.org/toc/sjoce3/40/6; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", onlinedate = "January 2018", } @Article{Anzt:2019:APB, author = "Hartwig Anzt and Jack Dongarra and Goran Flegar and Nicholas J. Higham and Enrique S. Quintana-Ort{\'\i}", title = "Adaptive precision in block-{Jacobi} preconditioning for iterative sparse linear system solvers", journal = j-CCPE, volume = "31", number = "6", pages = "e4460:1--e4460:??", day = "25", month = mar, year = "2019", CODEN = "CCPEBO", DOI = "https://doi.org/10.1002/cpe.4460", ISSN = "1532-0626 (print), 1532-0634 (electronic)", ISSN-L = "1532-0626", bibdate = "Thu Mar 28 08:07:56 MDT 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/ccpe.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Concurrency and Computation: Practice and Experience", journal-URL = "http://www.interscience.wiley.com/jpages/1532-0626", onlinedate = "12 March 2018", } @TechReport{Blanchard:2019:MPB, author = "Pierre Blanchard and Nicholas J. Higham and Florent Lopez and Theo Mary and Srikara Pranesh", title = "Mixed Precision Block Fused Multiply-Add: Error Analysis and Application to {GPU} Tensor Cores", type = "MIMS EPrint", number = "2019.18", institution = "Manchester Institute for Mathematical Sciences, School of Mathematics, The University of Manchester", address = "Manchester, UK", day = "24", month = sep, year = "2019", ISSN = "1749-9097", bibdate = "Thu Dec 05 10:14:37 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://eprints.maths.manchester.ac.uk/2733/; https://en.wikipedia.org/wiki/Bfloat16 floating-point format", abstract = "Computing units that carry out a fused multiply-add (FMA) operation with matrix arguments, referred to as tensor units by some vendors, have great potential for use in scientific computing. However, these units are inherently mixed precision and existing rounding error analyses do not support them. We consider a mixed precision block FMA that generalizes both the usual scalar FMA and existing tensor units. We describe how to exploit such a block FMA in the numerical linear algebra kernels of matrix multiplication and LU factorization and give rounding error analyses of both kernels. An important application is to GMRES-based iterative refinement with block FMAs, for which our analysis provides new insight. Our framework is applicable to the tensor core units in the NVIDIA Volta and Turing GPUs. For these we compare matrix multiplication and LU factorization with TC16 and TC32 forms of FMA, which differ in the precision used for the output of the tensor cores. Our experiments on an NVDIA V100 GPU confirm the predictions of the analysis that the TC32 variant is much more accurate than the TC16 one, while achieving almost the same performance.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", keywords = "floating-point arithmetic; fused multiply-add; LU factorization; matrix multiplication; rounding error analysis, NVIDIA GPU; tensor cores", } @Article{Fasi:2019:APS, author = "Massimiliano Fasi and Nicholas J. Higham", title = "An arbitrary precision scaling and squaring algorithm for the matrix exponential", journal = j-SIAM-J-MAT-ANA-APPL, volume = "40", number = "4", pages = "1233--1256", year = "2019", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/18M1228876", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F60 (15A16)", MRnumber = "4014393", MRreviewer = "Ralf Zimmermann", bibdate = "Fri Jul 9 15:12:06 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Hammarling:2019:CJH, author = "Sven J. Hammarling and Nicholas J. Higham", title = "Celebrating {James Hardy Wilkinson}", journal = j-MATH-TODAY, volume = "55", number = "4", pages = "131--131", year = "2019", ISSN = "1361-2042", MRclass = "01A70", MRnumber = "3967944", bibdate = "Fri Jul 9 15:12:06 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Mathematics Today", journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html", } @Article{Higham:2019:NAP, author = "Nicholas J. Higham and Theo Mary", title = "A New Approach to Probabilistic Rounding Error Analysis", journal = j-SIAM-J-SCI-COMP, volume = "41", number = "5", pages = "A2815--A2835", month = "????", year = "2019", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/18M1226312", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65G50 (60E15 65F05)", MRnumber = "4002728", MRreviewer = "A. Bultheel", bibdate = "Tue Nov 5 05:24:19 MST 2019", bibsource = "http://epubs.siam.org/toc/sjoce3/41/5; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", keywords = "floating-point arithmetic; MATLAB; numerical linear algebra; rounding error analysis", onlinedate = "January 2019", } @Article{Higham:2019:NPE, author = "Nicholas J. Higham and Theo Mary", title = "A New Preconditioner that Exploits Low-Rank Approximations to Factorization Error", journal = j-SIAM-J-SCI-COMP, volume = "41", number = "1", pages = "A59--A82", month = "????", year = "2019", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/18M1182802", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F22 (65F05 65F08 65F10 68W20)", MRnumber = "3895124", bibdate = "Thu Oct 10 06:58:01 MDT 2019", bibsource = "http://epubs.siam.org/toc/sjoce3/41/1; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", onlinedate = "January 2019", } @Article{Higham:2019:SLP, author = "Nicholas J. Higham and Srikara Pranesh", title = "Simulating Low Precision Floating-Point Arithmetic", journal = j-SIAM-J-SCI-COMP, volume = "41", number = "5", pages = "C585--C602", month = "????", year = "2019", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/19M1251308", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F05 (65G50 65Y04)", MRnumber = "4024753", MRreviewer = "Jin Yun Yuan", bibdate = "Tue Nov 5 05:24:19 MST 2019", bibsource = "http://epubs.siam.org/toc/sjoce3/41/5; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", keywords = "bfloat16; bit flips; directed rounding; floating-point arithmetic; fp16; half precision; IEEE arithmetic; low precision; MATLAB; mixed precision; round to nearest; rounding error analysis; simulation; stochastic rounding; subnormal numbers", onlinedate = "January 2019", } @Article{Higham:2019:SMH, author = "Nicholas J. Higham and Srikara Pranesh and Mawussi Zounon", title = "Squeezing a Matrix into Half Precision, with an Application to Solving Linear Systems", journal = j-SIAM-J-SCI-COMP, volume = "41", number = "4", pages = "A2536--A2551", month = "????", year = "2019", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/18M1229511", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F35 (65F05 65F08 65F10 65G50)", MRnumber = "3987532", MRreviewer = "A. Bultheel", bibdate = "Thu Oct 10 06:58:08 MDT 2019", bibsource = "http://epubs.siam.org/toc/sjoce3/41/4; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", keywords = "diagonal scaling; fp16; GMRES; half precision arithmetic; iterative refinement; linear system; MATLAB; mixed precision; overflow; preconditioning; subnormal numbers; underflow", onlinedate = "January 2019", } @Article{Blanchard:2020:CFA, author = "Pierre Blanchard and Nicholas J. Higham and Theo Mary", title = "A Class of Fast and Accurate Summation Algorithms", journal = j-SIAM-J-SCI-COMP, volume = "42", number = "3", pages = "A1541--A1557", month = "????", year = "2020", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/19M1257780", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65B10 (65F05 65G50)", MRnumber = "4094754", MRreviewer = "S. Hitotumatu", bibdate = "Fri Mar 12 11:39:57 MST 2021", bibsource = "http://epubs.siam.org/toc/sjoce3/42/3; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", abstract = "The need to sum floating-point numbers is ubiquitous in scientific computing. Standard recursive summation of $n$ summands, often implemented in a blocked form, has a backward error bound proportional to $ n u$, where $u$ is the unit roundoff. With the growing interest in low precision floating-point arithmetic and ever increasing $n$ in applications, computed sums are more likely to have insufficient accuracy. We propose a class of summation algorithms called FABsum (for fast and accurate block summation'') that applies a fast summation algorithm (such as recursive summation) blockwise and then sums the partial sums using an accurate summation algorithm (such as compensated summation, or recursive summation in higher precision). We give a rounding error analysis to show that FABsum with a fixed block size $b$ has a backward error bound $ (b + 1)u + O(u^2)$, which is independent of $n$ to first order. Our computational experiments show that with a suitable choice of $b$ (independent of $n$) FABsum can deliver substantially more accurate results than blocked recursive summation, with only a modest drop in performance. FABsum is especially attractive for low precisions, where it can provide correct digits for much larger $n$ than recursive summation.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", keywords = "accurate floating-point summation; floating-point arithmetic; rounding errors", onlinedate = "January 2020", } @Article{Blanchard:2020:MPB, author = "Pierre Blanchard and Nicholas J. Higham and Florent Lopez and Theo Mary and Srikara Pranesh", title = "Mixed precision block fused multiply-add: error analysis and application to {GPU} tensor cores", journal = j-SIAM-J-SCI-COMP, volume = "42", number = "3", pages = "C124--C141", year = "2020", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/19M1289546", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F05 (65G50 65Y04 68M07)", MRnumber = "4103291", bibdate = "Fri Jul 9 15:12:06 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @Article{Carson:2020:TPG, author = "Erin Carson and Nicholas J. Higham and Srikara Pranesh", title = "Three-precision {GMRES}-based iterative refinement for least squares problems", journal = j-SIAM-J-SCI-COMP, volume = "42", number = "6", pages = "A4063--A4083", year = "2020", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/20M1316822", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F05 (65F08 65F20)", MRnumber = "4188846", bibdate = "Fri Jul 9 15:12:06 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @Article{Dongarra:2020:NAH, author = "Jack Dongarra and Laura Grigori and Nicholas J. Higham", title = "Numerical algorithms for high-performance computational science", journal = j-PHILOS-TRANS-R-SOC-LOND-SER-A, volume = "378", number = "2166", pages = "20190066:1--20190066:18", year = "2020", DOI = "https://doi.org/10.1098/rsta.2019.0066", ISSN = "1364-503X (print), 1471-2962 (electronic)", MRclass = "65Y10", MRnumber = "4072450", bibdate = "Fri Jul 9 15:12:06 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, ajournal = "Philos. Trans. Roy. Soc. A", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Philosophical Transactions of the Royal Society A. Mathematical, Physical and Engineering Sciences", } @Article{Haidar:2020:MPI, author = "Azzam Haidar and Harun Bayraktar and Stanimire Tomov and Jack Dongarra and Nicholas J. Higham", title = "Mixed-precision iterative refinement using tensor cores on {GPUs} to accelerate solution of linear systems", journal = j-PROC-R-SOC-LOND-SER-A, volume = "476", number = "2243", pages = "20200110:1--2020011030", year = "2020", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2020.0110", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", MRclass = "65F10 (65Y10)", MRnumber = "4187936", bibdate = "Fri Jul 9 15:12:06 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Proceedings of the Royal Society of London. Series A", journal-URL = "http://rspa.royalsocietypublishing.org/", } @Book{Higham:2020:HWM, author = "Nicholas J. Higham", title = "Handbook of Writing for the Mathematical Sciences", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xxi + 353", year = "2020", DOI = "https://doi.org/10.1137/1.9781611976106", ISBN = "91-611-9760-9-X (paperback), 1-61197-610-3 (e-book)", ISBN-13 = "91-611-9760-9-X (paperback), 978-1-61197-610-6 (e-book)", LCCN = "QA42 .H54 2020", MRclass = "00A20", MRnumber = "4050520", bibdate = "Fri Jul 9 15:12:06 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", abstract = "{{\booktitle{Handbook of Writing for the Mathematical Sciences}}} provides advice on all aspects of scientific writing, with a particular focus on writing mathematics. Its readable style and handy format, coupled with an extensive bibliography and comprehensive index, make it useful for everyone from undergraduates to seasoned professionals. This third edition revises, updates, and expands the best-selling second edition to reflect modern writing and publishing practices and builds on the author's extensive experience in writing and speaking about mathematics. Key features are coverage of fundamentals of writing, including English usage, revising a draft, and writing when your first language is not English; thorough treatment of mathematical writing, including how to choose notation, how to choose between words and symbols, and how to format equations; many tips for exploiting \LaTeX{} and \BibTeX{}; advice on how to write and publish a paper, covering the entire publication process; and anecdotes, quotes, and unusual facts that enliven the presentation. The new edition has been reorganized to make the book easier to use for reference; treats modern developments in publishing such as open access, DOIs, and ORCID; has a new chapter on workflow covering text editors, markup languages, version control, and much more; has a new chapter that discusses the principles of indexing and how to prepare an index in \LaTeX; has a new chapter on reviewing a paper, book proposal, or book; has a new chapter ``Writing a Book'' that includes advice on choosing a publisher and \LaTeX tips particular to books; contains more on poster design, and discusses e-posters and the poster blitz; and has a new chapter giving advice on writing a blog post.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", remark = "Third edition of \cite{Higham:1998:HWM} (MR1223778).", tableofcontents = "General principles \\ Mathematical writing \\ English usage \\ The writer's bookshelf \\ When English is a foreign language \\ Writing a paper \\ Revising a draft \\ \TeX{}, \LaTeX{}, and \BibTeX{} \\ Workflow \\ Publishing a paper \\ Refereeing and reviewing \\ Writing a talk \\ Giving a talk \\ Preparing a poster \\ Writing and defending a thesis \\ Writing a book \\ Preparing an index \\ Writing a blog post \\ Information sources", } @Article{Higham:2020:SPB, author = "Nicholas J. Higham and Theo Mary", title = "Sharper probabilistic backward error analysis for basic linear algebra kernels with random data", journal = j-SIAM-J-SCI-COMP, volume = "42", number = "5", pages = "A3427--A3446", year = "2020", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/20M1314355", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F35 (60E15 65F05 65G50)", MRnumber = "4165945", bibdate = "Fri Jul 9 15:12:06 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @Article{Abdelfattah:2021:SBB, author = "Ahmad Abdelfattah and Timothy Costa and Jack Dongarra and Mark Gates and Azzam Haidar and Sven Hammarling and Nicholas J. Higham and Jakub Kurzak and Piotr Luszczek and Stanimire Tomov and Mawussi Zounon", title = "A Set of Batched Basic Linear Algebra Subprograms and {LAPACK} Routines", journal = j-TOMS, volume = "47", number = "3", pages = "21:1--21:23", month = jun, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3431921", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Jun 27 07:42:02 MDT 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3431921", abstract = "This article describes a standard API for a set of Batched Basic Linear Algebra Subprograms (Batched BLAS or BBLAS). The focus is on many independent BLAS operations on small matrices that are grouped together and processed by a single routine, called a Batched BLAS routine. The matrices are grouped together in uniformly sized groups, with just one group if all the matrices are of equal size. The aim is to provide more efficient, but portable, implementations of algorithms on high-performance many-core platforms. These include multicore and many-core CPU processors, GPUs and coprocessors, and other hardware accelerators with floating-point compute facility. As well as the standard types of single and double precision, we also include half and quadruple precision in the standard. In particular, half precision is used in many very large scale applications, such as those associated with machine learning.", acknowledgement = ack-nhfb, articleno = "21", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Blanchard:2021:ACL, author = "Pierre Blanchard and Desmond J. Higham and Nicholas J. Higham", title = "Accurately computing the log-sum-exp and softmax functions", journal = j-IMA-J-NUMER-ANAL, volume = "41", number = "4", pages = "2311--2330", month = oct, year = "2021", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/draa038", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", bibdate = "Sat Oct 23 16:14:21 MDT 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib", URL = "http://academic.oup.com/imajna/article/41/4/2311/5893596", abstract = "Evaluating the log-sum-exp function or the softmax function is a key step in many modern data science algorithms, notably in inference and classification. Because of the exponentials that these functions contain, the evaluation is prone to overflow and underflow, especially in low-precision arithmetic. Software implementations commonly use alternative formulas that avoid overflow and reduce the chance of harmful underflow, employing a shift or another rewriting. Although mathematically equivalent, these variants behave differently in floating-point arithmetic and shifting can introduce subtractive cancellation. We give rounding error analyses of different evaluation algorithms and interpret the error bounds using condition numbers for the functions. We conclude, based on the analysis and numerical experiments, that the shifted formulas are of similar accuracy to the unshifted ones, so can safely be used, but that a division-free variant of softmax can suffer from loss of accuracy.", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", } @Article{Connolly:2021:SRP, author = "Michael P. Connolly and Nicholas J. Higham and Theo Mary", title = "Stochastic rounding and its probabilistic backward error analysis", journal = j-SIAM-J-SCI-COMP, volume = "43", number = "1", pages = "A566--A585", year = "2021", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/20M1334796", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65G50 (60G42 65F35)", MRnumber = "4214365", bibdate = "Fri Jul 9 15:12:06 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @Article{Fasi:2021:GES, author = "Massimiliano Fasi and Nicholas J. Higham", title = "Generating extreme-scale matrices with specified singular values or condition number", journal = j-SIAM-J-SCI-COMP, volume = "43", number = "1", pages = "A663--A684", year = "2021", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/20M1327938", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F18 (65F35 65Y05)", MRnumber = "4218408", bibdate = "Fri Jul 9 15:12:06 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @Article{Fasi:2021:MTI, author = "Massimiliano Fasi and Nicholas J. Higham", title = "Matrices with Tunable Infinity-Norm Condition Number and No Need for Pivoting in {$ L U $} Factorization", journal = j-SIAM-J-MAT-ANA-APPL, volume = "42", number = "1", pages = "417--435", month = "????", year = "2021", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/20M1357238", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F35 (65Y05)", MRnumber = "4232450", bibdate = "Fri Jul 9 15:12:06 2021", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/42/1; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "January 2021", } @Article{Fasi:2021:NBN, author = "Massimiliano Fasi and Nicholas J. Higham and Mantas Mikaitis and Srikara Pranesh", title = "Numerical behavior of {NVIDIA} tensor cores", journal = "PeerJ Computer Science", volume = "7", pages = "e330:1--e330:19", month = feb, year = "2021", DOI = "https://doi.org/10.7717/peerj-cs.330", ISSN = "2376-5992", bibdate = "Mon Apr 22 14:18:25 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", journal-URL = "https://peerj.com/cs/", } @Article{Higham:2021:ELP, author = "Nicholas J. Higham and Srikara Pranesh", title = "Exploiting lower precision arithmetic in solving symmetric positive definite linear systems and least squares problems", journal = j-SIAM-J-SCI-COMP, volume = "43", number = "1", pages = "A258--A277", year = "2021", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/19M1298263", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F05 (65F08 65F10 65F35)", MRnumber = "4201445", bibdate = "Fri Jul 9 15:12:06 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @Article{Higham:2021:IMF, author = "Nicholas J. Higham and Matthew C. Lettington and Karl Michael Schmidt", title = "Integer matrix factorisations, superalgebras and the quadratic form obstruction", journal = j-LINEAR-ALGEBRA-APPL, volume = "622", pages = "250--267", year = "2021", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2021.03.028", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15B36 (05B15 11E12 15A15 15A23 15A30)", MRnumber = "4241259", bibdate = "Fri Jul 9 15:12:06 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Higham:2021:MDF, author = "Nicholas J. Higham and Xiaobo Liu", title = "A Multiprecision Derivative-Free {Schur--Parlett} Algorithm for Computing Matrix Functions", journal = j-SIAM-J-MAT-ANA-APPL, volume = "42", number = "3", pages = "1401--1422", month = "????", year = "2021", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/20M1365326", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F60", MRnumber = "4313845", bibdate = "Tue Jan 18 10:51:55 MST 2022", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/42/3; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "January 2021", } @Article{Higham:2021:RMG, author = "Desmond J. Higham and Nicholas J. Higham and Srikara Pranesh", title = "Random Matrices Generating Large Growth in {$ L U $} Factorization with Pivoting", journal = j-SIAM-J-MAT-ANA-APPL, volume = "42", number = "1", pages = "185--201", month = "????", year = "2021", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/20M1338149", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F05 (15B52 65F35)", MRnumber = "4207902", bibdate = "Fri Jul 9 15:12:06 2021", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/42/1; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "January 2021", } @Article{Al-Mohy:2022:APA, author = "Awad H. Al-Mohy and Nicholas J. Higham and Xiaobo Liu", title = "Arbitrary Precision Algorithms for Computing the Matrix Cosine and its {Fr{\'e}chet} Derivative", journal = j-SIAM-J-MAT-ANA-APPL, volume = "43", number = "1", pages = "233--256", month = "????", year = "2022", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/21M1441043", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Thu Apr 14 12:31:00 MDT 2022", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/43/1; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", URL = "https://epubs.siam.org/doi/10.1137/21M1441043", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Hammarling:2022:ICJ, author = "Sven Hammarling and Nicholas J. Higham", title = "The Influence and Contribution of {Jack Dongarra} to Numerical Linear Algebra", journal = j-COMPUT-SCI-ENG, volume = "24", number = "4", pages = "6--11", month = jul # "\slash " # aug, year = "2022", CODEN = "CSENFA", DOI = "https://doi.org/10.1109/MCSE.2022.3198330", ISSN = "1521-9615 (print), 1558-366X (electronic)", ISSN-L = "1521-9615", bibdate = "Fri Mar 3 06:06:17 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/computscieng.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Computing in Science and Engineering", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992", } @Article{Higham:2022:AEM, author = "Nicholas J. Higham and Mantas Mikaitis", title = "\pkg{Anymatrix}: an extensible {MATLAB} matrix collection", journal = j-NUMER-ALGORITHMS, volume = "90", number = "3", pages = "1175--1196", month = jul, year = "2022", CODEN = "NUALEG", DOI = "https://doi.org/10.1007/s11075-021-01226-2", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", bibdate = "Thu Jun 9 09:50:52 MDT 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib", URL = "https://link.springer.com/article/10.1007/s11075-021-01226-2", acknowledgement = ack-nhfb, ajournal = "Numer. Algorithms", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", } @Book{Higham:2022:HCP, author = "Nicholas J. Higham and Dennis Sherwood", title = "How to Be Creative: a Practical Guide for the Mathematical Sciences", volume = "179", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xii + 109", year = "2022", ISBN = "1-61197-702-9 (paperback), 1-61197-703-7 (e-book)", ISBN-13 = "978-1-61197-702-8 (paperback), 978-1-61197-703-5 (e-book)", LCCN = "QA63 .H54 2022", bibdate = "Mon Apr 22 14:50:13 MDT 2024", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", series = "OT", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", tableofcontents = "A process for generating great ideas \\ More idea generation processes \\ Creativity in mathematics \\ Creativity workshops", } @Article{Higham:2022:MPA, author = "Nicholas J. Higham and Theo Mary", title = "Mixed precision algorithms in numerical linear algebra", journal = j-ACTA-NUMERICA, volume = "31", pages = "347--414", month = may, year = "2022", CODEN = "ANUMFU", DOI = "https://doi.org/10.1017/S0962492922000022", ISSN = "0962-4929 (print), 1474-0508 (electronic)", ISSN-L = "0962-4929", bibdate = "Wed Jun 15 09:10:34 MDT 2022", bibsource = "http://journals.cambridge.org/action/displayIssue?jid=ANU&volumeId=31&issueId=00; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/actanumerica.bib", URL = "https://www.cambridge.org/core/journals/acta-numerica/article/mixed-precision-algorithms-in-numerical-linear-algebra/43CA701BA29251B5790C653E66F46197", acknowledgement = ack-nhfb, ajournal = "Acta Numer.", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "Acta Numerica", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU", onlinedate = "09 June 2022", } @Article{Higham:2022:OFW, author = "Nicholas J. Higham and Matthew C. Lettington", title = "Optimizing and Factorizing the {Wilson} Matrix", journal = j-AMER-MATH-MONTHLY, volume = "129", number = "5", pages = "454--465", year = "2022", CODEN = "AMMYAE", DOI = "https://doi.org/10.1080/00029890.2022.2038006", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Wed Jun 8 08:16:36 MDT 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20", onlinedate = "13 Apr 2022", } @Article{Higham:2022:SBL, author = "Nicholas J. Higham and Theo Mary", title = "Solving block low-rank linear systems by {$ L U $} factorization is numerically stable", journal = j-IMA-J-NUMER-ANAL, volume = "42", number = "2", pages = "951--980", month = apr, year = "2022", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/drab020", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", bibdate = "Sat Apr 23 13:25:36 MDT 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib", URL = "http://academic.oup.com/imajna/article/42/2/951/6238550", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", } @Article{Zounon:2022:PIP, author = "Mawussi Zounon and Nicholas J. Higham and Craig Lucas and Fran{\c{c}}oise Tisseur", title = "Performance impact of precision reduction in sparse linear systems solvers", journal = "PeerJ Computer Science", volume = "8", pages = "e778:a--e778:22", month = jan, year = "2022", DOI = "https://doi.org/10.7717/peerj-cs.778", ISSN = "2376-5992", bibdate = "Tue Apr 23 06:39:24 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", journal-URL = "https://peerj.com/cs/", } @Article{Amestoy:2023:CSA, author = "Patrick Amestoy and Alfredo Buttari and Nicholas J. Higham and Jean-Yves L'Excellent and Theo Mary and Bastien Vieubl{\'e}", title = "Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement", journal = j-TOMS, volume = "49", number = "1", pages = "4:1--4:??", month = mar, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3582493", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3582493", abstract = "The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision \ldots{}", acknowledgement = ack-nhfb, articleno = "4", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Connolly:2023:PRE, author = "Michael P. Connolly and Nicholas J. Higham", title = "Probabilistic Rounding Error Analysis of {Householder} {QR} Factorization", journal = j-SIAM-J-MAT-ANA-APPL, volume = "44", number = "3", pages = "1146--1163", month = "????", year = "2023", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/22M1514817", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Tue Oct 17 16:49:22 MDT 2023", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/44/3; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", URL = "https://epubs.siam.org/doi/10.1137/22M1514817", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Fasi:2023:CSR, author = "Massimiliano Fasi and Nicholas J. Higham and Xiaobo Liu", title = "Computing the Square Root of a Low-Rank Perturbation of the Scaled Identity Matrix", journal = j-SIAM-J-MAT-ANA-APPL, volume = "44", number = "1", pages = "156--174", month = "????", year = "2023", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/22M1471559", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Thu Mar 23 07:10:33 MDT 2023", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/44/1; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", URL = "https://epubs.siam.org/doi/10.1137/22M1471559", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Fasi:2023:MMM, author = "Massimiliano Fasi and Nicholas J. Higham and Florent Lopez and Theo Mary and Mantas Mikaitis", title = "Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to {GPU} Tensor Cores", journal = j-SIAM-J-SCI-COMP, volume = "45", number = "1", pages = "C1--C19", month = "????", year = "2023", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/21M1465032", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", bibdate = "Thu Mar 23 07:38:32 MDT 2023", bibsource = "http://epubs.siam.org/toc/sjoce3/45/1; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", URL = "https://epubs.siam.org/doi/10.1137/21M1465032", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @Article{Higham:2023:HDQ, author = "Nicholas J. Higham and Dennis Sherwood", title = "{Hamilton}'s discovery of the quaternions and creativity in mathematics", journal = "London Mathematical Society. Newsletter", number = "507", pages = "28--31", year = "2023", ISSN = "2516-3841, 2516-385X", MRclass = "00A35", MRnumber = "4640878", bibdate = "Mon Apr 22 15:08:26 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, ajournal = "Lond. Math. Soc. Newsl.", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", fjournal = "London Mathematical Society. Newsletter", } @InProceedings{Higham:2023:NSA, author = "Nicholas J. Higham", editor = "????", booktitle = "{ICM --- International Congress of Mathematicians}. Vol. 7. Sections 15--20", title = "Numerical stability of algorithms at extreme scale and low precisions", publisher = "EMS Press", address = "Berlin, Germany", pages = "5098--5117", year = "2023", ISBN = "3-9854706-5-0, 3-9854756-5-2, 3-9854705-8-8", ISBN-13 = "978-3-9854706-5-5, 978-3-9854756-5-0, 978-3-9854705-8-7", bibdate = "Mon Apr 22 15:10:05 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", }

%%% ==================================================================== %%% Part 2 (of 2): Publications about Nicholas Higham and his works.

@Misc{Anonymous:2022:ANL, author = "Anonymous", title = "Advances in Numerical Linear Algebra: Celebrating the 60th Birthday of {Nick Higham, 6--8 July 2022}", howpublished = "Web site", year = "2022", bibdate = "Mon Apr 22 14:30:57 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "https://nla-group.org/njh60/", acknowledgement = ack-nhfb, subject-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Misc{Anonymous:2024:NH, author = "Anonymous", title = "{Nicholas Higham}", howpublished = "Web site", day = "14", month = feb, year = "2024", bibdate = "Mon Apr 22 14:24:57 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "https://en.wikipedia.org/wiki/Nicholas_Higham", acknowledgement = ack-nhfb, subject-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Misc{Anonymous:2024:RNH, author = "Anonymous", title = "Remembering {Nick Higham}: 1961--2024", howpublished = "SIAM Web site", day = "1", month = may, year = "2024", bibdate = "Mon May 13 14:45:48 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "https://sinews.siam.org/Details-Page/obituary-nicholas-j-higham", acknowledgement = ack-nhfb, subject-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", } @Misc{Higham:2024:ONJ, author = "Desmond J. Higham and Fran{\c{c}}oise Tisseur", title = "Obituary: {Nicholas J. Higham}", howpublished = "SIAM Web site", day = "1", month = may, year = "2024", bibdate = "Mon May 13 14:45:48 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", URL = "https://sinews.siam.org/Details-Page/obituary-nicholas-j-higham", acknowledgement = ack-nhfb, subject-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", }

%%% ==================================================================== %%% Cross-referenced entries must come last:

@Article{Dongarra:1990:ASL, author = "Jack J. Dongarra and Jeremy {Du Croz} and Sven Hammarling and Iain Duff", title = "{Algorithm 679}: {A} Set of {Level 3 Basic Linear Algebra Subprograms}: Model Implementation and Test Programs", journal = j-TOMS, volume = "16", number = "1", pages = "18--28", month = mar, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/77626.77627", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Mar 22 15:39:54 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "See also \cite{Higham:1990:EFM,Demmel:1992:SBA,Dayde:1994:PBI}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p18-dongarra/; http://www.netlib.org/utk/people/JackDongarra/PAPERS/ALGORITHM-679-A-Set-of-Level-3-BLAS.pdf", acknowledgement = ack-nhfb, classcodes = "C4140 (Linear algebra); C7310 (Mathematics)", corpsource = "Oak Ridge Nat. Lab., TN, USA", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://dl.acm.org/pub.cfm?id=J782", keywords = "computers; Fortran 77; high-performance; level 3 basic linear algebra subprograms; mathematics computing; matrix algebra; matrix-matrix operations; portable; program testing; subroutines; test programs", treatment = "P Practical", } @Article{Dayde:1994:PBI, author = "Michael J. Dayd{\'e} and Iain S. Duff and Antoine Petitet", title = "A Parallel Block Implementation of Level-3 {BLAS} for {MIMD} Vector Processors", journal = j-TOMS, volume = "20", number = "2", pages = "178--193", month = jun, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 09 13:52:29 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "See \cite{Dongarra:1990:ASL,Higham:1990:EFM,Demmel:1992:SBA}.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://dl.acm.org/pub.cfm?id=J782", keywords = "algorithms; Level-3 BLAS; matrix-matrix kernels; measurement; parallelization; performance; vectorization", subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems--computations on matrices; G.1.0 [Numerical Analysis]: General--numerical algorithms; G.1.3 [Numerical Analysis]: Numerical Linear Algebra--linear systems (direct and iterative methods); G.4 [Mathematics of Computing]: Mathematical Software--certification and testing; efficiency; portability; reliability and robustness; verification", } @Book{Ainsworth:1999:GSG, editor = "Mark Ainsworth and Jeremy Levesley and Marco Marletta", title = "The Graduate Student's Guide to Numerical Analysis '98: Lecture Notes from the {VIII EPSRC Summer School in Numerical Analysis}", volume = "26", publisher = pub-SPRINGER, address = pub-SPRINGER:adr-B, pages = "x + 250", year = "1999", ISBN = "3-540-65752-5 (hardcover)", ISBN-13 = "978-3-540-65752-1 (hardcover)", ISSN = "0179-3632", LCCN = "QA 297 G67 1999", bibdate = "Wed Nov 3 09:30:14 MST 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "The Eighth EPSRC Numerical Analysis Summer School was held at the University of Leicester from the 5th to the 17th of July, 1998.", series = "Springer series in computational mathematics", acknowledgement = ack-nhfb, keywords = "numerical analysis", } @Proceedings{Watson:2000:NAD, editor = "George Alistair Watson and David Francis Griffiths", booktitle = "{Numerical analysis 1999: [the 18th Dundee Biennial Conference on Numerical Analysis was held at the University of Dundee during the 4 days 29th June--2nd Julay 1999]}", title = "{Numerical analysis 1999: [the 18th Dundee Biennial Conference on Numerical Analysis was held at the University of Dundee during the 4 days 29th June--2nd July, 1999]}", volume = "420", publisher = pub-CHAPMAN-HALL-CRC, address = pub-CHAPMAN-HALL-CRC:adr, pages = "279", year = "2000", DOI = "https://doi.org/10.1201/9781482280937", ISBN = "1-58488-020-1 (paperback)", ISBN-13 = "978-1-58488-020-2 (paperback)", LCCN = "QA297 .D85 1999; QA297 .N825 2000; QA297 .N853 1999", MRclass = "65D20 (41A30 65F10 93E24)", MRnumber = "1751115", MRreviewer = "Donald Myers", bibdate = "Sat Nov 18 08:33:59 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib", series = "Chapman \& Hall/CRC Research Notes in Mathematics", acknowledgement = ack-nhfb, author-dates = "Michael James David Powell (29 July 1936--19 April 2015)", tableofcontents = "Preface \\ M. Ainsworth, P. Coggins and B. Senior / Mixed hp-finite element methods for incompressible flow / 1 \\ R. Becker, H. Kapp and R. Rannacher / Adaptive finite element methods for optimization problems / 21 \\ P. Blomgren, T. F. Chan, P. Mulet, L. Vese and W. L. Wan / Variational PDE models and methods for image processing / 43 \\ F. Brezzi / Interacting with the subgrid world / 69 \\ F. Chaitin-Chatelin / The computing power of Geometry / 83 \\ C. M. Elliott and V. M. Styles / Numerical approximation of vortex density evolution in a superconductor / 93 \\ A. C. Faul and M. J. D. Powell / Krylov subspace methods for radial basis function interpolation / 115 \\ M. C. Ferris, T. S. Munson and D. Ralph / A homotopy method for mixed complementarity problems based on the PATH solver / 143 \\ E. Hairer and Ch. Lubich / Energy conservation by Stormer-type numerical integrators / 169 \\ A. Klawonn and O. B. Widlund / New results on FETI methods for elliptic problems with discontinuous coefficients / 191 \\ I. H. Sloan and R. S. Womersley / The search for good polynomial interpolation points on the sphere / 211 \\ P. M. Van Dooren / Gramian based model reduction of large-scale dynamical systems / 231 \\ G. A. Watson / Solving data fitting problems in $l_p$ norms with bounded uncertainties in the data / 249 \\ Contributed Papers / 267", } @Article{Sukkari:2019:QBS, author = "Dalal Sukkari and Hatem Ltaief and Aniello Esposito and David Keyes", title = "A {QDWH}-based {SVD} Software Framework on Distributed-memory Manycore Systems", journal = j-TOMS, volume = "45", number = "2", pages = "18:1--18:21", month = apr, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3309548", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Nakatsukasa:2013:SES}.", URL = "https://dl.acm.org/citation.cfm?id=3309548", subject-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", abstract = "This article presents a high-performance software framework for computing a dense SVD on distributed-memory manycore systems. Originally introduced by Nakatsukasa et al. (2010) and Nakatsukasa and Higham (2013), the SVD solver relies on the polar decomposition using the QR Dynamically Weighted Halley algorithm (QDWH). Although the QDWH-based SVD algorithm performs a significant amount of extra floating-point operations compared to the traditional SVD with the one-stage bidiagonal reduction, the inherent high level of concurrency associated with Level 3 BLAS compute-bound kernels ultimately compensates for the arithmetic complexity overhead. Using the ScaLAPACK two-dimensional block cyclic data distribution with a rectangular processor topology, the resulting QDWH-SVD further reduces excessive communications during the panel factorization, while increasing the degree of parallelism during the update of the trailing submatrix, as opposed to relying on the default square processor grid. After detailing the algorithmic complexity and the memory footprint of the algorithm, we conduct a thorough performance analysis and study the impact of the grid topology on the performance by looking at the communication and computation profiling trade-offs. We report performance results against state-of-the-art existing QDWH software implementations (e.g., Elemental) and their SVD extensions on large-scale distributed-memory manycore systems based on commodity Intel x86 Haswell processors and Knights Landing (KNL) architecture. The QDWH-SVD framework achieves up to 3/8-fold speedups on the Haswell/KNL-based platforms, respectively, against ScaLAPACK PDGESVD and turns out to be a competitive alternative for well- and ill-conditioned matrices. We finally come up herein with a performance model based on these empirical results. Our QDWH-based polar decomposition and its SVD extension are freely available at https://github.com/ecrc/qdwh.git and https://github.com/ecrc/ksvd.git, respectively, and have been integrated into the Cray Scientific numerical library LibSci v17.11.1.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "http://dl.acm.org/pub.cfm?id=J782", }

%%% Last MathSciNet search: Tue Jan 18 11:02:38 2022

@Proceedings{Iserles:1987:SAN, editor = "A. Iserles and M. J. D. Powell", booktitle = "{State of the Art in Numerical Analysis. Proceedings of the Joint IMA\slash SIAM Conference held at the University of Birmingham, 14--18 April 1986}", title = "{State of the Art in Numerical Analysis. Proceedings of the Joint IMA\slash SIAM Conference held at the University of Birmingham, 14--18 April 1986}", volume = "9", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "x + 719", year = "1987", ISBN = "0-19-853614-3", ISBN-13 = "978-0-19-853614-7", LCCN = "QA297.J65 1986", bibdate = "Mon Sep 9 14:56:14 MDT 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib", series = "The Institute of Mathematics and Its Applications conference series; new series", URL = "http://www.gbv.de/dms/hbz/toc/ht002967923.pdf; http://zbmath.org/?q=an:0611.00024", ZMnumber = "0611.00024", acknowledgement = ack-nhfb, confdate = "14--18 April 1986", conflocation = "Birmingham, UK", confsponsor = "Inst. Math. Appl.; SIAM", pubcountry = "UK", tableofcontents = "Contributors / / xiii \\ 1. Eigenvalue problems / J. H. Wilkinson / 1 \\ 2. Numerical linear algebra in statistical computing / N. J. Higham and G. W. Stewart / 41 \\ 3. Sparse matrices / J. K. Reid / 59 \\ 4. Multivariate approximation / Carl de Boor / 87 \\ 5. Data approximation by splines in one and two independent variables / M. G. Cox / 111 \\ 6. Methods for best approximation and regression problems / G. A. Watson / 139 \\ 7. Branch cuts for complex elementary functions / W. Kahan / 165 \\ 8. Recent developments in linear and quadratic programming / R. Fletcher / 213 \\ 9. Solving systems of nonlinear equations by tensor methods / R. B. Schnabel and P. D. Frank / 245 \\ 10. Numerical methods for bifurcation problems / A. D. Jepson and A. Spence / 273 \\ 11. On the iterative solution of differential and integral equations using secant updating techniques / A. Griewank / 299 \\ 12. Methods for nonlinear constraints in optimization calculations / M. J. D. Powell / 325 \\ 13. The influence of vector and parallel processors on numerical analysis / I. S. Duff / 359 \\ 14. Developments in stability theory for ordinary differential equations / J. D. Lambert / 409 \\ 15. Stiff ODE initial value problems and their solution / A. R. Curtis / 433 \\ 16. Order stars and stability / G. Wanner / 451 \\ 17. The state of the art in the numerical treatment of integral equations / C. T. H. Baker / 473 \\ 18. Strongly elliptic boundary integral equations / W. L. Wendland / 511 \\ 19. Collocation methods for one-dimensional Fredholm and Volterra integral equations / H. Brunner / 563 \\ 20. Numerical methods for free and moving boundary problems / C. W. Cryer / 601 \\ 21. Multigrid methods for elliptic equations / J. Walsh / 623 \\ 22. Galerkin finite element methods and their generalizations / K. W. Morton / 645 \\ 23. Recent developments in the numerical solution of nonlinear conservation laws / S. Osher and P. K. Sweby / 681 \\ Index / 701", } @Proceedings{Meyer:1993:LAM, editor = "C. D. (Carl Dean) Meyer and Robert J. Plemmons", booktitle = "{Linear algebra, Markov chains, and queueing models: [\ldots{} some of the lectures given at the Workshop Linear Algebra, Markov Chains, and Queueing Models held January 13--17, 1992, as part of the Year of Applied Linear Algebra at the Institute for Mathematics and its Applications]}", title = "{Linear algebra, Markov chains, and queueing models: [\ldots{} some of the lectures given at the Workshop Linear Algebra, Markov Chains, and Queueing Models held January 13--17, 1992, as part of the Year of Applied Linear Algebra at the Institute for Mathematics and its Applications]}", volume = "48", publisher = pub-SV, address = pub-SV:adr, pages = "xvi + 294", year = "1993", ISBN = "0-387-94085-5 (New York), 3-540-94085-5 (Berlin)", ISBN-13 = "978-0-387-94085-4 (New York), 978-3-540-94085-2 (Berlin)", LCCN = "QA184 .L545 1993", bibdate = "Wed May 28 17:58:34 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; z3950.loc.gov:7090/Voyager", series = "The IMA volumes in mathematics and its applications", URL = "http://catalog.hathitrust.org/api/volumes/oclc/28182134.html; http://www.gbv.de/dms/ilmenau/toc/126000387.PDF; http://www.zentralblatt-math.org/zmath/en/search/?an=0779.00020", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", subject = "Algebras, Linear; Congresses; Markov processes; Queuing theory", tableofcontents = "Error bounds for the computation of null vectors with applications to Markov chains / Jesse L. Barlow \\ The influence of nonnormality on matrix computations / Fran{\c{c}}oise Chatelin \\ Componentwise error analysis for stationary iterative methods / Nicholas J. Higham and Philip A. Knight \\ The character of a finite Markov chain / Carl D. Meyer \\ Gaussian elimination, perturbation theory, and Markov chains / G. W. Stewart \\ Algorithms for periodic Markov chains / Fran{\c{c}}ois Bonhoure, Yves Dallery, and William J. Stewart \\ Iterative methods for queueing networks with irregular state-spaces / Raymond H. Chan \\ Analysis of $p$-cyclic iterations for Markov chains / Apostolos Hadjidimos and Robert J. Plemmons \\ Iterative methods for finding the stationary vector for Markov chains / Dianne P. O'Leary \\ Local convergence of (exact and inexact) iterative aggregation / Daniel B. Szyld \\ Automated generation and analysis of Markov reward models using stochastic reward nets / Gianfranco Ciardo \ldots{} [et al.] \\ Means and variances in Markov reward systems / Winfried K. Grassman \\ A direct algorithm for computing the stationary distribution of a $p$-cyclic Markov chain / Daniel P. Heyman \\ Approximate analysis of a discrete-time queueing model of the shared buffer ATM switch / S. Hong, H. G. Perros, and H. Yamashita \\ Algorithms for infinite Markov chains with repeating columms / Guy Latouche \\ Cray-2 memory organization and interprocessor memory contention / Robert W. Numrich", } @Proceedings{Moonen:1993:LAL, editor = "Marc S. Moonen and Gene H. Golub and Bart L. R. {De Moor}", booktitle = "{Linear Algebra for Large Scale and Real-Time Applications: Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3--14, 1992}", title = "{Linear Algebra for Large Scale and Real-Time Applications: Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3--14, 1992}", volume = "232", publisher = pub-KLUWER, address = pub-KLUWER:adr, pages = "ix + 435", year = "1993", ISBN = "0-7923-2151-0", ISBN-13 = "978-0-7923-2151-4", LCCN = "QA185.D37 L56 1993", MRclass = "65-06 (65Fxx 65Y05)", MRnumber = "94e:65009", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", bibdate = "Mon Jan 15 17:53:04 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", series = "NATO ASI series. Series E, Applied sciences", URL = "http://catdir.loc.gov/catdir/enhancements/fy0823/92046135-d.html; http://www.gbv.de/dms/hbz/toc/ht004938330.pdf; http://zbmath.org/?q=an:0810.00029", ZMnumber = "0810.00029", abstract = "In recent years there has been great interest in large scale and real-time matrix computations; these computations arise in a variety of fields, such as computer graphics, imaging, speech and image processing, telecommunication, biomedical signal processing, optimization and so on. This volume, which is an outgrowth of a NATO ASI, held at Leuven, Belgium, August 1992, gives an account of recent research advances in numerical techniques used in large scale and real-time computations and their implementation on high performance computers.", acknowledgement = ack-nhfb, tableofcontents = "Preface / / xi \\ Invited Lectures / / 1 \\ Large scale structural analysis on massively parallel computers / P. E. Bj{\o}rstad and J. Cook / 3 \\ Data-parallel BLAS as a basis for LAPACK on massively parallel computers / P. E. Bj{\o}rstad and T. S{\o}revik / 13 \\ a Large-scale nonlinear constrained optimization / A. R. Conn, N. Gould and Ph. L. Toint / 21 \\ Trading off parallelism and numerical stability / J. W. Demmel / 49 \\ Subband filtering: CORDIC modulation and systolic quadrature mirror filter tree / E. F. Deprettere / 69 \\ A parallel image rendering algorithm and architecture based on ray tracing and radiosity shading / E. F. Deprettere and L.-S. Shen / 91 \\ Reduction and approximation of linear computational circuits / P. Dewilde and A.-J. van der Veen / 109 \\ The look-ahead Lanczos process for large nonsymmetric matrices and related algorithms / R. W. Freund / 137 \\ Case studies of real-time processing in robotics / W. M. Gentleman / 165 \\ Adaptive signal processing with emphasis on QRD-least squares lattice / S. Haykin / 183 \\ A direct method for reordering eigenvalues in the generalized real Schur form of a regular matrix pair (A, B) / B. K{\aa}gstr{\"o}m / 195 \\ Block shift invariance and efficient system identification algorithms / N. Kalouptsidis / 219 \\ Computing the singular value decomposition on a fat-tree architecture / T. J. Lee, F. T. Luk and D. L. Boley / 231 \\ A new matrix decomposition for signal processing / F. T. Luk and S. Qiao / 241 \\ The linear algebra of perfect reconstruction filtering / M. Stewart and G. Cybenko / 249 \\ Determining rank in the presence of error / G. W. Stewart / 275 \\ Approximation with Kronecker products / C. F. Van Loan and N. Pitsianis / 293 \\ Some linear algebra issues in large-scale optimization / M. H. Wright / 315 \\ Contributed Lectures / / 339 \\ Direct and inverse unitary eigenproblems in signal processing: an overview / G. S. Ammar, W. B. Gragg and L. Reichel / 341 \\ Block implementations of the symmetric QR and Jacobi algorithms / P. Arbenz and M. Oettli / 345 \\ Linear algebra for large-scale information retrieval applications / M. W. Berry / 347 \\ Matched filter vs. least-squares approximation / L. H. J. Bierens / 349 \\ Reordering diagonal blocks in real Schur form / A. W. Bojanczyk and P. Van Dooren / 351 \\ Placing zeroes and the Kronecker canonical form / D. L. Boley and P. Van Dooren / 353 \\ Analysis of the recursive least squares lattice algorithm / J. R. Bunch and R. C. LeBorne / 355 \\ Adaptive Chebyshev iteration based on modified moments / D. Calvetti, G. H. Golub and L. Reichel / 357 \\ Continuous realization methods and their applications / M. T. Chu / 359 \\ Asymptotic behavior of orthogonal polynomials / T. Dehn / 361 \\ CADCS and parallel computing / F. Dumortier, A. Van Cauwenberghe and L. Boullart / 363 \\ Eigenvalue roulette and random test matrices / A. Edelman / 365 \\ On numerical methods for unitary eigenvalue problems / H. Fa{\sas}bender / 369 \\ Accurate singular values and differential qd algorithms / K. V. Fernando and B. N. Parlett / 371 \\ Orthogonal projection and total least squares / R. D. Fierro and J. R. Bunch / 375 \\ Gauss quadratures associated with the Arnoldi process and the Lanczos algorithm / R. W. Freund and M. Hochbruck / 377 \\ An implementation of the QMR method based on coupled two-term recurrences / R. W. Freund and N. M. Nachtigal / 381 \\ Computationally efficient homotopies for the H 2 model order reduction problem / Y. Ge, L. T. Watson, E. G. Collins, Jr. and L. D. Davis / 385 \\ A fast algorithm for QR decomposition of Toeplitz matrices / G. O. Glentis / 387 \\ Unitary Hessenberg methods for Toeplitz approximations and applications / Ch. He and A. Bunse-Gerstner / 389 \\ Perturbation theory and backward error for $A X - X B = C$ / N. J. Higham / 391 \\ Fast transforms and elliptic problems / T. Huckle / 393 \\ An interior-point method for minimizing the maximum eigenvalue of a linear combination of matrices / F. Jarre / 395 \\ The lattice-ladder with generalized forgetting / J. Kadlec / 397 \\ Solving a least squares problem with boundary constraints / L. Kaufman / 399 \\ Estimating the extremal eigenvalues and condition number by the Lanczos algorithm with a random start / J. Kuczy{\'n}ski and H. Wo{\'z}niakowski / 401 \\ A generalized ADI iterative method / N. Levenberg and L. Reichel / 403 \\ Quaternions and the symmetric eigenvalue problem / N. Mackey / 405 \\ Application of the Gauss-Seidel iteration to the RLS algorithm / {\"O}. Morg{\"u}l and A. Mala{\c{s}} / 407 \\ Ranks of submatrices of a matrix and its inverse / C. C. Paige and M. Wei / 409 \\ A QRD-based least-squares algorithm for multipulse antenna array signal processing / I. K. Proudler / 411 \\ On displacement structures for covariance matrices and lossless functions / P. A. Regalia and F. Desbouvries / 413 \\ Application of vector extrapolation and conjugate gradient type methods to the semiconductor device problem / W. H. A. Schilders / 415 \\ Accurate symmetric eigenreduction by a Jacobi method / I. Slapni{\v{c}}ar / 417 \\ The order-recursive Chandrasekhar equations for fast square-root Kalman filtering / D. T. M. Slock / 419 \\ Hybrid iterative methods based on Faber polynomials / G. Starke / 421 \\ Aspects of implementing a 'C' matrix library / D. E. Stewart / 423 \\ Intermediate fill-in in sparse QR decomposition / M. T{\r{u}}ma / 425 \\ Shifting strategies for the parallel QR algorithm / D. S. Watkins / 427 \\ List of Participants / / 429 \\ Authors Index / / 437", } @Proceedings{Duff:1997:SAN, editor = "Iain S. Duff and G. Alistair Watson", booktitle = "The state of the art in numerical analysis", title = "The state of the art in numerical analysis", volume = "63", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "xiv + 562", year = "1997", ISBN = "0-19-850014-9", ISBN-13 = "978-0-19-850014-8", LCCN = "QA297.S775 1997", MRclass = "65-06 (00B25)", MRnumber = "MR1628339 (99a:65008)", bibdate = "Thu Sep 16 11:59:48 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/g/gould-nicholas-ian.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib; https://www.math.utah.edu/pub/tex/bib/numana1990.bib", note = "Based on the proceedings of a conference on the state of the art in numerical analysis. Organized by the Institute of Mathematics and Its Applications and held at York University in April 1996.", series = "The Institute of Mathematics and Its Applications conference series: new series", URL = "https://global.oup.com/academic/product/the-state-of-the-art-in-numerical-analysis-9780198500148", acknowledgement = ack-nhfb, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", tableofcontents = "1. Recent Developments in Dense Numerical Linear Algebra / N. J. Higham \\ 2. Sparse Numerical Linear Algebra: Direct Methods and Preconditioning / I. S. Duff \\ 3. Closer to the Solution: Iterative Linear Solvers / G. H. Golub and H. A. van der Vorst \\ 4. 150 Years Old and Still Alive: Eigenproblems / H. A. van der Vorst and G. H. Golub \\ 5. Geometric Integration / J. M. Sanz-Serna \\ 6. Convergence and Stability in the Numerical Approximation of Dynamical Systems / A. Stuart \\ 7. Beyond the Classical Theory of Computational Ordinary Differential Equations / A. Iserles \\ 8. Numerical Analysis of Volterra Functional and Integral Equations / C. T. H. Baker \\ 9. The Numerical Solution of Boundary Integral Equations / K. E. Atkinson \\ 10. Aspects of Approximation with Emphasis on the Univariate Case / G. A. Watson \\ 11. A Review of Methods for Multivariable Interpolation at Scattered Data Points / M. J. D. Powell \\ 12. Large Scale Unconstrained Optimization / J. Nocedal \\ 13. Interior Point Methods for Linear and Nonlinear Programming / D. F. Shanno and E. M. Simantiraki \\ 14. Methods for Nonlinear Constraints in Optimization Calculations / A. R. Conn, N. I. M. Gould and Ph. L. Toint \\ 15. Stabilization Techniques and Subgrid Scales Capturing, F. Brezzi, L. P. Franca / T. J. R. Hughes and A. Russo \\ 16. Approximation of Curvature Dependent Interface Motion / C. M. Elliott \\ 17. Finite Element Methods for Hyperbolic Problems: a Posteriori Error Analysis and Adaptivity / E. S{\"u}li and P. Houston \\ 18. Approximation of Multidimensional Hyperbolic Partial Differential Equations / K. W. Morton \\ 19. Algorithms in Tomography / F. Natterer \\ 20. Partial Differential Equations and Image Iterative Filtering / F. Guichard and J.-M. Morel", } @Proceedings{Higham:1998:NAP, editor = "D. J. (Desmond J.) Higham and G. A. Watson and D. F. (David Francis) Griffiths", booktitle = "{Numerical analysis 1997: Proceedings of the 17th Dundee Biennial Conference, June 24--27, 1997}", title = "{Numerical analysis 1997: proceedings of the 17th Dundee Biennial Conference, June 24--27, 1997}", volume = "380", publisher = pub-LONGMAN-ST, address = pub-LONGMAN-ST:adr, pages = "254", year = "1998", ISBN = "0-582-31261-2 (paperback)", ISBN-13 = "978-0-582-31261-6 (paperback)", ISSN = "0269-3674", LCCN = "QA297 .D85 1997", bibdate = "Tue Jan 3 15:19:05 MST 2006", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib; melvyl.cdlib.org:210/CDL90", series = "Pitman Research Notes in Mathematics", acknowledgement = ack-nhfb, meetingname = "Dundee Conference on Numerical Analysis (17th: 1997)", subject = "Numerical analysis; Congresses", } @Proceedings{Higham:2001:PEC, editor-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", editor = "Nicholas J. Higham and Roger Horn and Thomas J. Laffey", booktitle = "Proceedings of the {Eighth Conference of the International Linear Algebra Society}", title = "Proceedings of the {Eighth Conference of the International Linear Algebra Society}", publisher = pub-ELS, address = pub-ELS:adr, pages = "x--xii + 1--609", year = "2001", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", MRclass = "00B25 (15-06)", MRnumber = "MR1839422", bibdate = "Sat Apr 16 17:55:00 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib", note = "Held at the Universitat Politecnica de Catalunya, Barcelona, July 19--22, 1999, Linear Algebra Appl. {\bf 332/334} (2001)", acknowledgement = ack-nhfb, } @Proceedings{Brown:2007:PIS, editor = "C. W. Brown", booktitle = "{Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, July 29--August 1, 2007, University of Waterloo, Waterloo, Ontario, Canada}", title = "{Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, July 29--August 1, 2007, University of Waterloo, Waterloo, Ontario, Canada}", publisher = pub-ACM, address = pub-ACM:adr, pages = "????", year = "2007", ISBN = "1-59593-743-9 (print), 1-59593-742-0 (CD-ROM)", ISBN-13 = "978-1-59593-743-8 (print), 978-1-59593-742-1 (CD-ROM)", LCCN = "QA76.5 S98 2007", bibdate = "Fri Jun 20 08:53:37 2008", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/axiom.bib; https://www.math.utah.edu/pub/tex/bib/issac.bib; https://www.math.utah.edu/pub/tex/bib/maple-extract.bib", note = "ACM order number 505070.", acknowledgement = ack-nhfb, } @Book{Chan:2007:MMC, author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", editor = "Raymond H. Chan and Chen Greif and Dianne P. O'Leary", booktitle = "Milestones in Matrix Computation: the Selected Works of {Gene H. Golub} with Commentaries", title = "Milestones in Matrix Computation: the Selected Works of {Gene H. Golub} with Commentaries", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "xi + 565 + 3", year = "2007", ISBN = "0-19-920681-3", ISBN-13 = "978-0-19-920681-0", LCCN = "QA188 .G67 2007", MRclass = "65-06 (01A75 65Fxx)", MRnumber = "MR2281939 (2008b:65004)", MRreviewer = "David Scott Watkins", bibdate = "Sat Apr 07 10:23:33 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/numana2000.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib; https://www.math.utah.edu/pub/tex/bib/technometrics1970.bib", URL = "http://www.loc.gov/catdir/enhancements/fy0737/2007276086-d.html", abstract = "The text presents and discusses some of the most influential papers in Matrix Computation authored by Gene H. Golub, one of the founding fathers of the field. The collection of 21 papers in divided into five main areas: iterative methods for linear systems, solution of least squares problems, matrix factorizations and applications, orthogonal polynomials and quadrature, and eigenvalue problems an commentaries for each area are provided by leading experts: Anne Greenbaum, {\AA}ke Bj{\"o}rck, Nicholas Higham, Walter Gautschi, and G. W. (Pete) Stewart. Comments on each paper are also provided by the original authors, providing the reader with historical information on how the paper came to be written and under what circumstances the collaboration was undertaken. Including a brief biography and facsimiles of the original papers, this text will be of great interest to students and researchers in numerical analysis and scientific computation.", acknowledgement = ack-nhfb, tableofcontents = "List of Plates / x \\ I: Gene H. Golub \\ 1 Gene H. Golub Biography, by Chen Greif / 3 \\ 2 Publications of Gene H. Golub / 13 \\ 3 Major Awards / 30 \\ 4 Students of Gene H. Golub / 32 \\ II: Iterative Methods for Linear Systems \\ 5 Commentary, by Anne Greenbaum / 35 \\ References / 43 \\ 6 Chebyshev semi-iterative methods, successive over-relaxation iterative methods, and second-order Richardson iterative methods, Parts I and II (with R. S. Varga) / 45 \\ 7 A generalized conjugate gradient method for non-symmetric systems of linear equations (with Paul Concus) / 68 \\ 8 A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations (with Paul Concus and Dianne P. O'Leary) / 79 \\ 9 Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems (with Zhong-Zhi Bai and Michael K. Ng) / 102 \\ III: Solution of Least Squares Problems \\ 10 Commentary, by {\AA}ke Bj{\"o}rck / 129 \\ References / 141 \\ 11 Numerical methods for solving linear least squares problems / 148 \\ 12 Singular value decomposition and least squares solutions (with C. Reinsch) / 160 \\ 13 The differentiation of pseudo-inverses and non-linear least squares problems whose variables separate (with V. Pereyra) / 181 \\ 14 Generalized cross-validation as a method for choosing a good ridge parameter (with M. Heath and G. Wahba) / 202 \\ 15 An analysis of the total least squares problem (with C. Van Loan) / 213 \\ IV: Matrix Factorizations and Applications \\ 16 Commentary, by Nicholas Higham / 227 \\ References / 233 \\ 17 Calculating the singular values and pseudo-inverse of a matrix (with W. Kahan) / 236 \\ 18 The simplex method of linear programming using $ L U $ decomposition (with R. H. Bartels) / 257 \\ 19 On direct methods for solving Poisson's equation (with B. L. Buzbee and C. W. Nielson) / 261 \\ 20 Numerical methods for computing angles between linear subspaces (with {\AA}. Bj{\"o}rck) / 292 \\ 21 Methods for modifying matrix factorizations (with P. E. Gill, W. Murray and M. A. Saunders) / 309 \\ V: Orthogonal Polynomials and Quadrature \\ 22 Commentary, by Walter Gautschi / 345 \\ References / 354 \\ 23 Calculation of Gauss quadrature rules (with J. H. Welsch) / 359 \\ 24 Matrices, moments, and quadrature (with G{\'e}rard Meurant) / 380 \\ 25 Computation of Gauss--Kronrod Quadrature Rules (with D. Calvetti, W. B. Gragg and L. Reichel) / 434 \\ VI: Eigenvalue Problems \\ 26 Commentary, by G. W. Stewart / 457 \\ References / 465 \\ 27 Some modified matrix eigenvalue problems / 467 \\ 28 Ill-conditioned eigensystems and the computation of the Jordan canonical form (with J. H. Wilkinson) / 485 \\ 29 The block Lanczos method for computing eigenvalues (with R. Underwood) / 528 \\ 30 The numerically stable reconstruction of a Jacobi matrix from spectral data (with C. de Boor) / 546 Index / 563", } @Book{Hogben:2007:HLA, editor = "Leslie Hogben", booktitle = "Handbook of Linear Algebra", title = "Handbook of Linear Algebra", publisher = pub-CHAPMAN-HALL-CRC, address = pub-CHAPMAN-HALL-CRC:adr, pages = "xxx + 1370", year = "2007", ISBN = "1-58488-510-6 (hardcover), 1-4200-1057-3 (e-book)", ISBN-13 = "978-1-58488-510-8 (hardcover), 978-1-4200-1057-2 (e-book)", LCCN = "QA184.2 .H36 2007", MRclass = "15-00 (00A20)", MRnumber = "2279160 (2007j:15001)", bibdate = "Fri Nov 21 06:49:56 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib; https://www.math.utah.edu/pub/tex/bib/maple-extract.bib; https://www.math.utah.edu/pub/tex/bib/numana2000.bib; z3950.loc.gov:7090/Voyager", note = "Associate editors: Richard Brualdi, Anne Greenbaum and Roy Mathias.", series = "Discrete Mathematics and its Applications (Boca Raton)", URL = "http://www.crcnetbase.com/isbn/9781420010572; http://www.crcnetbase.com/isbn/9781584885108; http://www.loc.gov/catdir/enhancements/fy0647/2006045491-d.html", abstract = "\booktitle{Handbook of Linear Algebra} covers all aspects of linear algebra, including fundamentals, numerical linear algebra, software packages for computation in linear algebra, and various applications, such as quantum computing, control theory, image compression, and computational biology. The author addresses combinatorial Matrix theory and features Matrix notation throughout the text. The book includes a chapter on software that provides extensive coverage of MATLAB, Maple, and Mathematica and contains details of Fortran subroutines available for linear algebra such as LAPACK and ARPACK. Rather than presenting long mathematical proofs, the text provides numerous references for additional information.", acknowledgement = ack-nhfb # " and " # ack-rah, keywords = "Maple", remark = "Associate editors: Richard Brualdi, Anne Greenbaum, and Roy Mathias.", subject = "Algebras, Linear", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", tableofcontents = "Preliminaries \\ I. Linear algebra \\ 1: Vectors, matrices and systems of linear equations / Jane Day \\ 2: Linear independence, span, and bases / Mark Mills \\ 3: Linear transformations / Francesco Barioli \\ 4: Determinants and eigenvalues / Luz M. DeAlba \\ 5: Inner product spaces, orthogonal projection, least squares and singular value decomposition / Lixing Han and Michael Neumann \\ 6: Canonical forms / Leslie Hogben \\ 7: Unitary similarity, normal matrices, and spectral theory / Helene Shapiro \\ 8: Hermitian and positive definite matrices / Wayne Barrett \\ 9: Nonnegative and stochastic matrices / Uriel G. Rothblum \\ 10: Partitioned matrices / Robert Reams \\ 11: Functions of matrices / Nicholas J. Higham \\ 12: Quadratic, bilinear and sesquilinear forms / Raphael Lowey \\ 13: Multilinear algebra / J. A. Dias de Silva and Armando Machado \\ 14: Matrix equalities and inequalities / Michael Tsatsomeros \\ 15: Matrix perturbation theory / Ren-Cang Li \\ 16: Pseudospectra / Mark Embree \\ 17: Singular values and singular value inequalities / Roy Mathias \\ 18: Numerical range / Chi-Kwong Li \\ 19: Matrix stability and inertia / Daniel Hershkowitz \\ 20: Inverse eigenvalue problems / Alberto Borobia \\ 21: Totally positive and totally negative matrices / Shaun M. Fallat \\ 22: Linear preserver problems / Peter \v Semrl \\ 23: Matrices over integral domains / Shmuel Friedland \\ 24: Similarities of families of matrices / Shmuel Friedland \\ 25: Max-plus algebra / Marianne Akian, Ravindra Bapat, St{\'e}phane Gaubert \\ 26: Matrices leaving a cone invariant / Bit-Shun Tam and Hans Schneider \\ II. Combinatorial matrix theory and graphs \\ 27: Combinatorial matrix theory / Richard A. Brualdi \\ 28: Matrices and graphs / Willem H. Haemers \\ 29: Digraphs and matrices / Jeffrey L. Stuart \\ 30: Bipartite graphs and matrices / Bryan L. Shader \\ 31: Permanents / Ian M. Wanless \\ 32: D-optimal designs / Michael G. Neubauer and William Watkins \\ 33: Sign pattern matrices / Frank J. Hall and Zhongshan Li \\ 34: Multiplicity lists for the eigenvalues of symmetric matrices with a given graph / Charles R. Johnson, Ant{\'o}nio Leal Duarte, and Carlos M. Saiago \\ 35: Matrix completion problems / Leslie Hogben and Amy Wangsness \\ 36: Algebraic connectivity / Steve Kirkland \\ III. Numerical methods \\ 37: Vector and matrix norms, error analysis, efficiency and stability / Ralph Byers and Biswa Nath Datta \\ 38: Matrix factorizations, and direct solution of linear systems / Christopher Beattie \\ 39: Least squares solution of linear systems / Per Christian Hansen and Hans Bruun Nielsen \\ 40: Sparse matrix methods / Esmond G. Ng \\ 41: Iterative solution methods for linear systems / Anne Greenbaum \\ 42: Symmetric matrix eigenvalue techniques / Ivan Slapni\v car \\ 43: Unsymmetric matrix eigenvalue techniques / David S. Watkins \\ 44: The implicitly restarted Arnoldi method / D. C. Sorensen \\ 45: Computation of the singular value decomposition / Alan Kaylor Cline and Inderjit S. Dhillon \\ 46: Computing eigenvalues and singular values to high relative accuracy / Zlatko Drma{\v{c}} \\ 47: Fast matrix multiplication / Dario A. Bini \\ 48: Structured matrix computations / Michael Ng \\ 49: Large-scale matrix computations / Roland W. Freund \\ IV. Applications \\ 50: Linear programming / Leonid S. Vaserstein \\ 51: Semidefinite programming / Henry Wolkowicz \\ 52: Random vectors and linear statistical models / Simo Puntanen and George P. H. Styan \\ 53: Multivariate statistical analysis / Simo Puntanen, George A. F. Seber, and George P. H. Styan \\ 54: Markov chains / Beatrice Meini \\ 55: Differential equations and stability / Volker Mehrmann and Tatjana Stykel \\ 56: Dynamical systems and linear algebra / Fritz Colonius and Wolfgang Kliemann \\ 57: Control theory / Peter Benner \\ 58: Fourier analysis / Kenneth Howell \\ 59: Linear algebra and mathematical physics / Lorenzo Sadun \\ 60: Linear algebra in biomolecular modeling / Zhijun Wu \\ 61: Coding theory / Joachim Rosenthal and Paul Weiner \\ 62: Quantum computation / Zijian Diao \\ 63: Information retrieval and web search / Amy Langville and Carl Meyer \\ 64: Signal processing / Michael Stewart \\ 65: Geometry / Mark Hunacek \\ 66: Some applications of matrices and graphs in Euclidean geometry / Miroslav Fiedler \\ 67: Matrix groups / Peter J. Cameron \\ 68: Group representations / Randall Holmes and T. Y. Tam \\ 69: Nonassociative algebras / Murray R. Bremner, Lucia I. Muakami and Ivan P. Shestakov \\ 70: Lie algebras / Robert Wilson \\ V. Computational software \\ 71: METLAB / Steven J. Leon \\ 72: Linear algebra in Maple / David J. Jeffrey and Robert M. Corless \\ 73: Mathematica / Heikki Ruskeep{\"a}{\"a} \\ 74: BLAS / Jack Dongarra, Victor Eijkhout, and Julien Langou \\ 75: LAPACK / Zhaojun Bai \\ 76: Use of ARPACK and EIGS / D. C. Sorensen \\ 77: Summary of Software for Linear Algebra Freely Available on the Web / Jack Dongarra, Victor Eijkhout, Julien Langou \\ G-1: Glossary \\ H-1: Notation Index", } @Book{Higham:2015:PCA, editor-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and Paul A. Martin and Fadil Santosa and Jared Tanner", booktitle = "The {Princeton} Companion to Applied Mathematics", title = "The {Princeton} Companion to Applied Mathematics", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "xvii + 3 + 994 + 16", year = "2015", ISBN = "0-691-15039-7 (hardcover)", ISBN-13 = "978-0-691-15039-0 (hardcover)", LCCN = "QA155 .P75 2015", bibdate = "Wed Sep 9 05:32:49 MDT 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/subjects/companion-applied-mathematics.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", URL = "http://press.princeton.edu/titles/10592.html", abstract = "This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important questions, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics.", acknowledgement = ack-njh, subject = "Algebra; Mathematics; Mathematical models", tableofcontents = "Preface / ix \\ Contributors / xiii \\ Part I: Introduction to Applied Mathematics \\ I.1 What Is Applied Mathematics? / 1 \\ I.2 The Language of Applied Mathematics / 8 \\ I.3 Methods of Solution / 27 \\ I.4 Algorithms / 40 \\ I.5 Goals of Applied Mathematical Research / 48 \\ I.6 The History of Applied Mathematics / 55 \\ Part II: Concepts \\ II.1 Asymptotics / 81 \\ II.2 Boundary Layer / 82 \\ II.3 Chaos and Ergodicity / 82 \\ II.4 Complex Systems / 83 \\ II.5 Conformal Mapping / 84 \\ II.6 Conservation Laws / 86 \\ II.7 Control / 88 \\ II.8 Convexity / 89 \\ II.9 Dimensional Analysis and Scaling / 90 \\ II.10 The Fast Fourier Transform / 94 \\ II.11 Finite Differences / 95 \\ II.12 The Finite-Element Method / 96 \\ II.13 Floating-Point Arithmetic / 96 \\ II.14 Functions of Matrices / 97 \\ II.15 Function Spaces / 99 \\ II.16 Graph Theory / 101 \\ II.17 Homogenization / 103 \\ II.18 Hybrid Systems / 103 \\ II.19 Integral Transforms and Convolution / 104 \\ II.20 Interval Analysis / 105 \\ II.21 Invariants and Conservation Laws / 106 \\ II.22 The Jordan Canonical Form / 112 \\ II.23 Krylov Subspaces / 113 \\ II.24 The Level Set Method / 114 \\ II.25 Markov Chains / 116 \\ II.26 Model Reduction / 117 \\ II.27 Multiscale Modeling / 119 \\ II.28 Nonlinear Equations and Newton's Method / 120 \\ II.29 Orthogonal Polynomials / 122 \\ II.30 Shocks / 122 \\ II.31 Singularities / 124 \\ II.32 The Singular Value Decomposition / 126 \\ II.33 Tensors and Manifolds / 127 \\ II.34 Uncertainty Quantification / 131 \\ II.35 Variational Principle / 134 \\ II.36 Wave Phenomena / 134 \\ Part III: Equations, Laws, and Functions of Applied Mathematics \\ III.1 Benford's Law / 135 \\ III.2 Bessel Functions / 137 \\ III.3 The Black--Scholes Equation / 137 \\ III.4 The Burgers Equation / 138 \\ III.5 The Cahn--Hilliard Equation / 138 \\ III.6 The Cauchy--Riemann Equations / 139 \\ III.7 The Delta Function and Generalized Functions / 139 \\ III.8 The Diffusion Equation / 142 \\ III.9 The Dirac Equation / 142 \\ III.10 Einstein's Field Equations / 144 \\ III.11 The Euler Equations / 146 \\ III.12 The Euler--Lagrange Equations / 147 \\ III.13 The Gamma Function / 148 \\ III.14 The Ginzburg--Landau Equation / 148 \\ III.15 Hooke's Law / 149 \\ III.16 The Korteweg--de Vries Equation / 150 \\ III.17 The Lambert $W$ Function / 151 \\ III.18 Laplace's Equation / 155 \\ III.19 The Logistic Equation / 156 \\ III.20 The Lorenz Equations / 158 \\ III.21 Mathieu Functions / 159 \\ III.22 Maxwell's Equations / 160 \\ III.23 The Navier--Stokes Equations / 162 \\ III.24 The Painlev{\'e} Equations / 163 \\ III.25 The Riccati Equation / 165 \\ III.26 Schr{\"o}dinger's Equation / 167 \\ III.27 The Shallow-Water Equations / 167 \\ III.28 The Sylvester and Lyapunov Equations / 168 \\ III.29 The Thin-Film Equation / 169 \\ III.30 The Tricomi Equation / 170 \\ III.31 The Wave Equation / 171 \\ Part IV: Areas of Applied Mathematics \\ IV.1 Complex Analysis / 173 \\ IV.2 Ordinary Differential Equations / 181 \\ IV.3 Partial Differential Equations / 190 \\ IV.4 Integral Equations / 200 \\ IV.5 Perturbation Theory and Asymptotics / 208 \\ IV.6 Calculus of Variations / 218 \\ IV.7 Special Functions / 227 \\ IV.8 Spectral Theory / 236 \\ IV.9 Approximation Theory / 248 \\ IV.10 Numerical Linear Algebra and Matrix Analysis / 263 \\ IV.11 Continuous Optimization (Nonlinear and Linear Programming) / 281 \\ IV.12 Numerical Solution of Ordinary Differential Equations / 293 \\ IV.13 Numerical Solution of Partial Differential Equations / 306 \\ IV.14 Applications of Stochastic Analysis / 319 \\ IV.15 Inverse Problems / 327 \\ IV.16 Computational Science / 335 \\ IV.17 Data Mining and Analysis / 350 \\ IV.18 Network Analysis / 360 \\ IV.19 Classical Mechanics / 374 \\ IV.20 Dynamical Systems / 383 \\ IV.21 Bifurcation Theory / 393 \\ IV.22 Symmetry in Applied Mathematics / 402 \\ IV.23 Quantum Mechanics / 411 \\ IV.24 Random-Matrix Theory / 419 \\ IV.25 Kinetic Theory / 428 \\ IV.26 Continuum Mechanics / 446 \\ IV.27 Pattern Formation / 458 \\ IV.28 Fluid Dynamics / 467 \\ IV.29 Magnetohydrodynamics / 476 \\ IV.30 Earth System Dynamics / 485 \\ IV.31 Effective Medium Theories / 500 \\ IV.32 Mechanics of Solids / 505 \\ IV.33 Soft Matter / 516 \\ IV.34 Control Theory / 523 \\ IV.35 Signal Processing / 533 \\ IV.36 Information Theory / 545 \\ IV.37 Applied Combinatorics and Graph Theory / 552 \\ IV.38 Combinatorial Optimization / 564 \\ IV.39 Algebraic Geometry / 570 \\ IV.40 General Relativity and Cosmology / 579 \\ Part V: Modeling \\ V.1 The Mathematics of Adaptation (Or the Ten Avatars of Vishnu) / 591 \\ V.2 Sport / 598 \\ V.3 Inerters / 604 \\ V.4 Mathematical Biomechanics / 609 \\ V.5 Mathematical Physiology / 616 \\ V.6 Cardiac Modeling / 623 \\ V.7 Chemical Reactions / 627 \\ V.8 Divergent Series: Taming the Tails / 634 \\ V.9 Financial Mathematics / 640 \\ V.10 Portfolio Theory / 648 \\ V.11 Bayesian Inference in Applied Mathematics / 658 \\ V.12 A Symmetric Framework with Many Applications / 661 \\ V.13 Granular Flows / 665 \\ V.14 Modern Optics / 673 \\ V.15 Numerical Relativity / 680 \\ V.16 The Spread of Infectious Diseases / 687 \\ V.17 The Mathematics of Sea Ice / 694 \\ V.18 Numerical Weather Prediction / 705 \\ V.19 Tsunami Modeling / 712 \\ V.20 Shock Waves / 720 \\ V.21 Turbulence / 724 \\ Part VI: Example Problems \\ VI.1 Cloaking / 733 \\ VI.2 Bubbles / 735 \\ VI.3 Foams / 737 \\ VI.4 Inverted Pendulums / 741 \\ VI.5 Insect Flight / 743 \\ VI.6 The Flight of a Golf Ball / 746 \\ VI.7 Automatic Differentiation / 749 \\ VI.8 Knotting and Linking of Macromolecules / 752 \\ VI.9 Ranking Web Pages / 755 \\ VI.10 Searching a Graph / 757 \\ VI.11 Evaluating Elementary Functions / 759 \\ VI.12 Random Number Generation / 761 \\ VI.13 Optimal Sensor Location in the Control of Energy-Efficient Buildings / 763 \\ VI.14 Robotics / 767 \\ VI.15 Slipping, Sliding, Rattling, and Impact: Nonsmooth Dynamics and Its Applications / 769 \\ VI.16 From the $N$-Body Problem to Astronomy and Dark Matter / 771 \\ VI.17 The $N$-Body Problem and the Fast Multipole Method / 775 \\ VI.18 The Traveling Salesman Problem / 778 \\ Part VII: Application Areas \\ VII.1 Aircraft Noise / 783 \\ VII.2 A Hybrid Symbolic--Numeric Approach to Geometry Processing and Modeling / 787 \\ VII.3 Computer-Aided Proofs via Interval Analysis / 790 \\ VII.4 Applications of Max-Plus Algebra / 795 \\ VII.5 Evolving Social Networks, Attitudes, and Beliefs --- and Counterterrorism / 800 \\ VII.6 Chip Design / 804 \\ VII.7 Color Spaces and Digital Imaging / 808 \\ VII.8 Mathematical Image Processing / 813 \\ VII.9 Medical Imaging / 816 \\ VII.10 Compressed Sensing / 823 \\ VII.11 Programming Languages: An Applied Mathematics View / 828 \\ VII.12 High-Performance Computing / 839 \\ VII.13 Visualization / 843 \\ VII.14 Electronic Structure Calculations (Solid State Physics) / 847 \\ VII.15 Flame Propagation / 852 \\ VII.16 Imaging the Earth Using Green's Theorem / 857 \\ VII.17 Radar Imaging / 860 \\ VII.18 Modeling a Pregnancy Testing Kit / 864 \\ VII.19 Airport Baggage Screening with X-Ray Tomography / 866 \\ VII.20 Mathematical Economics / 868 \\ VII.21 Mathematical Neuroscience / 873 \\ VII.22 Systems Biology / 879 \\ VII.23 Communication Networks / 883 \\ VII.24 Text Mining / 887 \\ VII.25 Voting Systems / 891 \\ Part VIII: Final Perspectives \\ VIII.1 Mathematical Writing / 897 \\ VIII.2 How to Read and Understand a Paper / 903 \\ VIII.3 How to Write a General Interest Mathematics Book / 906 \\ VIII.4 Workflow / 912 \\ VIII.5 Reproducible Research in the Mathematical Sciences / 916 \\ VIII.6 Experimental Applied Mathematics / 925 \\ VIII.7 Teaching Applied Mathematics / 933 \\ VIII.8 Mediated Mathematics: Representations of Mathematics in Popular Culture and Why These Matter / 943 \\ VIII.9 Mathematics and Policy / 953 \\ Index / 963", } @Proceedings{Burgess:2017:ISC, editor = "Neil Burgess and Javier Bruguera and Florent de Dinechin", booktitle = "{24th IEEE Symposium on Computer Arithmetic (ARITH 24), London, UK, 24--26 July 2017}", title = "{2017 IEEE 24th Symposium on Computer Arithmetic (ARITH 24), London, UK, 24--26 July 2017}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "xii + 198", year = "2017", ISBN = "1-5386-1966-0 (print), 1-5386-1965-2, 1-5386-1964-4", ISBN-13 = "978-1-5386-1966-7 (print), 978-1-5386-1965-0, 978-1-5386-1964-3", ISSN = "1063-6889", LCCN = "QA76.9.C62 S95 2017", bibdate = "Fri Nov 17 10:14:11 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/gnu.bib", URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=8019911", acknowledgement = ack-nhfb, keywords = "computer arithmetic units; correctness proofs; cryptography; domain specific designs; error analysis; exascale computing; floating point arithmetic; floating-point error analysis; formal verification; function approximation; modular arithmetic; theorem proving; verification", author-dates = "Nicholas John Higham (25 December 1961--20 January 2024)", }