%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author = "Nicholas John Higham",
%%% version = "1.61",
%%% date = "17 March 2014",
%%% time = "06:55:40 MST",
%%% filename = "higham-nicholas-john.bib",
%%% address = "Department of Mathematics
%%% University of Manchester
%%% Manchester M13 9PL
%%% England",
%%% telephone = "+44 (0)161 275 5800",
%%% FAX = "+44 (0)161 275 5819",
%%% checksum = "59497 5133 20898 215820",
%%% email = "higham at ma.man.ac.uk (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "",
%%% license = "public domain",
%%% supported = "yes",
%%% docstring = "This is a bibliography of publications of
%%% Nicholas John Higham. The companion LaTeX file
%%% higham-nicholas-john.ltx can be used to typeset
%%% this bibliography.
%%%
%%% At version 1.61, the year coverage looked
%%% like this:
%%%
%%% 1983 ( 2) 1994 ( 10) 2005 ( 7)
%%% 1984 ( 0) 1995 ( 9) 2006 ( 3)
%%% 1985 ( 1) 1996 ( 12) 2007 ( 8)
%%% 1986 ( 4) 1997 ( 12) 2008 ( 7)
%%% 1987 ( 4) 1998 ( 13) 2009 ( 8)
%%% 1988 ( 4) 1999 ( 8) 2010 ( 7)
%%% 1989 ( 6) 2000 ( 7) 2011 ( 4)
%%% 1990 ( 16) 2001 ( 9) 2012 ( 2)
%%% 1991 ( 4) 2002 ( 6) 2013 ( 5)
%%% 1992 ( 11) 2003 ( 6) 2014 ( 2)
%%% 1993 ( 12) 2004 ( 2)
%%%
%%% Article: 145
%%% Book: 11
%%% InCollection: 7
%%% InProceedings: 13
%%% MastersThesis: 1
%%% PhdThesis: 1
%%% Proceedings: 2
%%% TechReport: 31
%%%
%%% Total entries: 211
%%%
%%% 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
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%%% characters. This is produced by Robert
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%%% }
%%% ====================================================================
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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|http://www.math.utah.edu/~beebe/|"}
@String{ack-njh = "Nick Higham,
e-mail: \path|higham@vtx.ma.man.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-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-UTK-CS = "Department of Computer Science, University
of Tennessee, Knoxville"}
@String{inst-UTK-CS:adr = "Knoxville, TN 37996, USA"}
%%% ====================================================================
%%% Journal abbreviations:
@String{j-ACTA-NUMERICA = "Acta Numerica"}
@String{j-BIT = "BIT"}
@String{j-BIT-NUM-MATH = "BIT Numerical Mathematics"}
@String{j-BULL-LOND-MATH-SOC = "Bulletin of the London Mathematical Society"}
@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-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-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-LONGMAN-ST = "Longman Scientific and Technical"}
@String{pub-LONGMAN-ST:adr = "Essex, UK"}
@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-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"}
%%% ====================================================================
@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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@TechReport{Higham:1983:UBC,
author = "Nicholas J. Higham",
title = "Upper bounds for the condition number of a triangular
matrix",
type = "Numerical Analysis Report",
number = "86",
institution = inst-U-MANCHESTER,
address = inst-U-Manchester:adr,
month = may,
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@Article{Higham:1986:CPD,
author = "Nicholas J. Higham",
title = "Computing the Polar Decomposition---with
Applications",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "7",
number = "4",
pages = "1160--1174",
month = oct,
year = "1986",
CODEN = "SIJCD4",
ISSN = "0196-5204",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Scientific and Statistical Computing",
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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Scientific and Statistical Computing",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "IMA Bulletin",
}
@Article{Higham:1986:NMM,
author = "Nicholas J. Higham",
title = "{Newton}'s Method for the Matrix Square Root",
journal = j-MATH-COMPUT,
volume = "46",
number = "174",
pages = "537--549",
month = apr,
year = "1986",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F30 (65H10)",
MRnumber = "87d:65045",
MRreviewer = "Lars Eld{\'e}n",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
JSTOR database; Theory/Matrix.bib",
acknowledgement = ack-njh,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Dept. of Math., Manchester Univ., UK",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "equation; iterative methods; mathematical convergence;
matrix algebra; matrix square root; Newton iteration;
Newton method; perturbation analysis; properties;
quadratic matrix",
kwds = "nla, matrix function, matrix square root, Newton's
method",
treatment = "T Theoretical or Mathematical",
}
@Article{Higham:1987:CRS,
author = "Nicholas J. Higham",
title = "Computing Real Square Roots of a Real Matrix",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88/89",
pages = "405--430",
year = "1987",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:1987:EAB,
author = "Nicholas J. Higham",
title = "Error Analysis of the {Bj{\"o}rck}-{Pereyra}
Algorithms for Solving {Vandermonde} Systems",
journal = j-NUM-MATH,
volume = "50",
number = "5",
pages = "613--632",
year = "1987",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/16",
}
@InProceedings{Higham:1987:NLA,
author = "Nicholas J. Higham and G. W. Stewart",
editor = "A. Iserles and M. J. D. Powell",
booktitle = "The State of the Art in Numerical Analysis",
title = "Numerical Linear Algebra in Statistical Computing",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "41--57",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@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",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "See also \cite{Higham:1989:CFC}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p381-higham/;
http://www.acm.org/pubs/toc/Abstracts/0098-3500/214386.html",
abstract = "FORTRAN 77 codes SONEST and CONEST are presented for
estimating the 1-norm ( or the infinity-norm) of a real
or complex matrix, respectively. The codes are of wide
applicability in condition estimation since explicit
access to the matrix, $A$, is not required; instead,
matrix-vector products $ A x $ and $ A^T x $ are
computed by the calling program via a reverse
communication interface. The algorithms are based on a
convex optimization method for estimating the 1-norm of
a real matrix devised by Hager. We derive new results
concerning the behavior of Hager's method, extend it to
complex matrices, and make several algorithmic
modifications in order to improve the reliability and
efficiency.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:1988:FSV,
author = "Nicholas J. Higham",
title = "Fast Solution of {Vandermonde}-like Systems Involving
Orthogonal Polynomials",
journal = j-IMA-J-NUMER-ANAL,
volume = "8",
number = "4",
pages = "473--486",
month = oct,
year = "1988",
CODEN = "IJNADH",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
MathSciNet database",
abstract = "Consider the $ (n + 1) \times (n + 1) $
Vandermonde-like matrix $ P = [{pi - 1}(\alpha_{j -
1})] $, where the polynomials $ p_0 (x), \ldots {},
p_n(x) $ satisfy a three-term recurrence relation. We
develop algorithms for solving the primal and dual
systems, $ P x = b $ and $ P^T a = f $ respectively, in
$ O(n^2) $ arithmetic operations and $ O(n) $ elements
of storage. These algorithms generalize those of
Bj{\"o}rck \& Pereyra which apply to the monomial case
$ p_i(x) $. When the $ p_i(x) $ are the Chebyshev
polynomials, the algorithms are shown to be numerically
unstable. However, it is found empirically that the
addition of just one step of iterative refinement is,
in single precision, enough to make the algorithms
numerically stable.",
acknowledgement = ack-nhfb # " and " # ack-njh,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Higham:1988:SPP,
author = "Nicholas J. Higham",
title = "The Symmetric {Procrustes} Problem",
journal = j-BIT,
volume = "28",
number = "1",
pages = "133--143",
year = "1988",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F20 (41A29 73K05)",
MRnumber = "89g:65047",
MRreviewer = "N. Gass",
bibdate = "Thu Nov 12 18:12:56 MST 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh # " and " # ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Higham:1989:AST,
author = "Nicholas J. Higham",
title = "The Accuracy of Solutions to Triangular Systems",
journal = j-SIAM-J-NUMER-ANAL,
volume = "26",
number = "5",
pages = "1252--1265",
month = oct,
year = "1989",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F05 (65G05)",
MRnumber = "90i:65053",
MRreviewer = "James Weldon Demmel",
bibdate = "Mon Jan 20 15:27:00 MST 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Higham:1989:CFC,
author = "Nicholas J. Higham",
title = "Corrigendum: ``{Algorithm} 674: {FORTRAN} Codes for
Estimating the One-Norm of a Real or Complex Matrix,
with Applications to Condition Estimation''",
journal = j-TOMS,
volume = "15",
number = "2",
pages = "168--168",
month = jun,
year = "1989",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Sep 30 01:18:49 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "See \cite{Higham:1988:AFC}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p168-higham/;
http://www.acm.org/pubs/toc/Abstracts/0098-3500/214391.html",
abstract = "We omitted giving this article an ACM algorithm number
when it was first published in its entirety in the
December 1988 issue of {\em TOMS}, Vol. 14, No. 4, pp.
381-396. To correct this, we do so here, and reprint
the title as a pointer to the original article.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
mynote = "Published version: \cite{Higham:1991:ACT}.",
}
@Article{Higham:1989:LGF,
author = "Nicholas J. Higham and Desmond J. Higham",
title = "Large Growth Factors in {Gaussian} Elimination with
Pivoting",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "10",
number = "2",
pages = "155--164",
month = apr,
year = "1989",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:1989:MCP,
author = "Nicholas J. Higham",
title = "Matrix Computations on a {PC}",
journal = j-SIAM-NEWS,
volume = "22",
pages = "16",
month = jan,
year = "1989",
ISSN = "0036-1437",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM 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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@TechReport{Demmel:1990:IEB,
author = "J. Demmel and N. Higham",
title = "Improved Error Bounds for Underdetermined System
Solvers",
type = "LAPACK Working Note",
number = "23",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = aug,
year = "1990",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-90-113, August 1990.",
URL = "http://www.netlib.org/lapack/lawns/lawn23.ps;
http://www.netlib.org/lapack/lawnspdf/lawn23.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Demmel:1990:SBA,
author = "J. Demmel and N. Higham",
title = "Stability of Block Algorithms with Fast Level 3
{BLAS}",
type = "LAPACK Working Note",
number = "22",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = jul,
year = "1990",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-90-110, July 1990.",
URL = "http://www.netlib.org/lapack/lawns/lawn22.ps;
http://www.netlib.org/lapack/lawnspdf/lawn22.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{DuCroz:1990:SMM,
author = "J. {Du Croz} and N. Higham",
title = "Stability of Methods for Matrix Inversion",
type = "LAPACK Working Note",
number = "27",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = oct,
year = "1990",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-90-119, October, 1990.",
URL = "http://www.netlib.org/lapack/lawns/lawn27.ps;
http://www.netlib.org/lapack/lawnspdf/lawn27.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Higham:1990:ACD,
author = "Nicholas J. Higham",
editor = "M. G. Cox and S. J. Hammarling",
booktitle = "Reliable Numerical Computation",
title = "Analysis of the {Cholesky} Decomposition of a
Semi-definite Matrix",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "161--185",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@Article{Higham:1990:BEG,
author = "Nicholas J. Higham",
title = "Bounding the Error in {Gaussian} Elimination for
Tridiagonal Systems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "11",
number = "4",
pages = "521--530",
month = oct,
year = "1990",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Higham:1990:CEB,
author = "Nicholas J. Higham",
editor = "Philip J. Brown and Wayne A. Fuller",
booktitle = "Statistical Analysis of Measurement Error Models and
Applications, Contemporary Mathematics 112",
title = "Computing Error Bounds for Regression Problems",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "195--208",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@Article{Higham:1990:EFM,
author = "Nicholas J. Higham",
title = "Exploiting Fast Matrix Multiplication Within the Level
3 {BLAS}",
journal = j-TOMS,
volume = "16",
number = "4",
pages = "352--368",
month = dec,
year = "1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65-04 (65F99)",
MRnumber = "1 095 133",
bibdate = "Sun Sep 04 23:21:57 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Describes algorithms based on Strassen's method which
are asymptotically faster than the standard $ {N}^3 $
algorithm, and in practice, faster for $ {N} \approx
100 $, and examines their numerical stability. See
\cite{Dongarra:1990:ASL,Demmel:1992:SBA}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p352-higham/",
abstract = "The Level 3 BLAS (BLAS3) are a set of specifications
of FORTRAN 77 subprograms for carrying out matrix
multiplications and the solution of triangular systems
with multiple right-hand sides. They are intended to
provide efficient and portable building blocks for
linear algebra algorithms on high-performance
computers. We describe algorithms for the BLAS3
operations that are asymptotically faster than the
conventional ones. These algorithms are based on
Strassen's method for fast matrix multiplication, which
is now recognized to be a practically useful technique
once matrix dimensions exceed about 100. We pay
particular attention to the numerical stability of
these ``fast BLAS3.'' Error bounds are given and their
significance is explained and illustrated with the aid
of numerical experiments. Our conclusion is that the
fast BLAS3, although not as strongly stable as
conventional implementations, are stable enough to
merit careful consideration in many applications.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Scientific and Statistical Computing",
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",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM 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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
annote = "Prepublished as RIACS technical report 88.29 and NASA
Contractor Report 185412.",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
series = "Pitman Research Notes in Mathematics",
acknowledgement = ack-njh,
}
@TechReport{Higham:1990:IRE,
author = "Nicholas J. Higham",
title = "Iterative Refinement Enhances the Stability of {$ Q R
$} Factorization Methods for Solving Linear Equations",
type = "Numerical Analysis Report",
number = "182",
institution = inst-U-MANCHESTER,
address = inst-U-MANCHESTER:adr,
month = apr,
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
mynote = "Contains proofs in the appendix that are not in
\cite{Higham:1991:IRE}.",
}
@Article{Higham:1990:RGH,
author = "Nicholas J. Higham",
title = "Review of {``G. H. Golub and C. F. Van Loan, Matrix
Computations, Second Edition, Johns Hopkins University
Press, Baltimore, Maryland, 1989''}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "141",
pages = "289--292",
year = "1990",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:1990:RMJ,
author = "Nicholas J. Higham",
title = "Review of {``M. J. C. Gover and S. Barnett, eds.,
Applications of Matrix Theory, Oxford University Press,
1989''}",
journal = j-MATH-GAZ,
volume = "74",
number = "468",
pages = "202",
year = "1990",
CODEN = "MAGAAS",
ISSN = "0025-5572",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}
@Article{Higham:1990:SAA,
author = "Nicholas J. Higham",
title = "Stability Analysis of Algorithms for Solving Confluent
{Vandermonde}-like Systems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "11",
number = "1",
pages = "23--41",
month = jan,
year = "1990",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:1991:ACT,
author = "Nicholas J. Higham",
title = "Algorithm 694: {A} Collection of Test Matrices in
{MATLAB}",
journal = j-TOMS,
volume = "17",
number = "3",
pages = "289--305",
month = sep,
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 23:52:04 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p289-higham/",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh # " and " # ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@InCollection{Higham:1991:SLE,
author = "Nicholas J. Higham",
editor = "Christine Bondi",
booktitle = "New Applications of Mathematics",
title = "Solving Linear Equations",
publisher = pub-PENGUIN,
address = pub-PENGUIN:adr-L,
pages = "33--56",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
mynote = "Chapter 2.",
}
@Article{Higham:1991:TMP,
author = "Nicholas J. Higham",
title = "Three Measures of Precision in Floating Point
Arithmetic",
journal = j-NA-DIGEST,
volume = "91",
number = "16",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Electronic mail magazine:
\path|na.help@na-net.ornl.gov|.",
acknowledgement = ack-njh,
fjournal = "NA Digest",
mynote = "Sunday, April 21, 1991.",
}
@TechReport{Demmel:1992:BLF,
author = "James Demmel and Nick Higham and Rob Schreiber",
title = "Block {LU} Factorization",
type = "LAPACK Working Note",
number = "40",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = feb,
year = "1992",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-92-149, February 1992.",
URL = "http://www.netlib.org/lapack/lawns/lawn40.ps;
http://www.netlib.org/lapack/lawnspdf/lawn40.pdf",
acknowledgement = ack-nhfb,
}
@Article{Demmel:1992:SBA,
author = "James W. Demmel and Nicholas J. Higham",
title = "Stability of Block Algorithms with Fast Level-3
{BLAS}",
journal = j-TOMS,
volume = "18",
number = "3",
pages = "274--291",
month = sep,
year = "1992",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Sep 30 01:27:16 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "See
\cite{Dongarra:1990:ASL,Higham:1990:EFM,Dayde:1994:PBI}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p274-demmel/",
abstract = "Block algorithms are becoming increasingly popular in
matrix computations. Since their basic unit of data is
a submatrix rather than a scalar, they have a higher
level of granularity than point algorithms, and this
makes them well suited to high-performance computers.
The numerical stability of the block algorithms in the
new linear algebra program library LAPACK is
investigated here. It is shown that these algorithms
have backward error analyses in which the backward
error bounds are commensurate with the error bounds for
the underlying level-3 BLAS (BLAS3). One implication is
that the block algorithms are as stable as the
corresponding point algorithms when conventional BLAS3
are used. A second implication is that the use of BLAS3
based on fast matrix multiplication techniques affects
the stability only insofar as it increases the constant
terms in the normwise backward error bounds. For linear
equation solvers employing {\em LU} factorization, it
is shown that fixed precision iterative refinement
helps to mitigate the effect of the larger error
constants. Despite the positive results presented here,
not all plausible block algorithms are stable; we
illustrate this with the example of {\em LU}
factorization with block triangular factors and
describe how to check a block algorithm for stability
without doing a full error analysis.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
MathSciNet database",
abstract = "Inversion of a triangular matrix can be accomplished
in several ways. The standard methods are characterized
by the loop ordering, whether matrix-vector
multiplication, solution of a triangular system, or a
rank-1 update is done inside the outer loop, and
whether the method is blocked or unblocked. The
numerical stability properties of these methods are
investigated. It is shown that unblocked methods
satisfy pleasing bounds on the left or right residual.
However, for one of the block methods it is necessary
to convert a matrix multiplication into the solution of
a multiple right-hand side triangular system in order
to have an acceptable residual bound. The inversion of
a full matrix given a factorization PA=LU is also
considered, including the special cases of symmetric
indefinite and symmetric positive definite matrices.
Three popular methods are shown to possess satisfactory
residual bounds, subject to a certain requirement on
the implementation, and an attractive new method is
described. This work was motivated by the question of
what inversion methods should be used in LAPACK.",
acknowledgement = ack-nhfb # " and " # ack-njh,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Higham:1992:BEC,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "Backward Error and Condition of Structured Linear
Systems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "1",
pages = "162--175",
month = jan,
year = "1992",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:1992:CPT,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "Componentwise Perturbation Theory for Linear Systems
with Multiple Right-Hand Sides",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "174",
pages = "111--129",
year = "1992",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:1992:EMN,
author = "Nicholas J. Higham",
title = "Estimating the Matrix {$p$}-norm",
journal = j-NUM-MATH,
volume = "62",
pages = "539--555",
year = "1992",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/16",
}
@Article{Higham:1992:IWP,
author = "Nicholas J. Higham",
title = "{IMA} Workshop Participants {F}{\^e}te {Golub} on 60th
Birthday",
journal = j-SIAM-NEWS,
volume = "25",
pages = "3--??",
month = may,
year = "1992",
ISSN = "0036-1437",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM News",
}
@Article{Higham:1992:JAF,
author = "Nicholas J. Higham",
title = "The Joy of Anonymous {FTP}",
journal = j-IMA-NUM-ANA-NEWSLETTER,
volume = "17",
number = "1",
pages = "61--64",
month = oct,
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "IMA Numerical Analysis Newsletter",
}
@Article{Higham:1992:LRM,
author = "Nicholas J. Higham",
title = "{LAPACK} Released in {March}",
journal = j-SIAM-NEWS,
volume = "25",
pages = "20",
month = may,
year = "1992",
ISSN = "0036-1437",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM News",
}
@TechReport{Higham:1992:PTB,
author = "Nick Higham",
title = "Perturbation Theory and Backward Error for {$ 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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-92-153, April, 1992.",
URL = "http://www.netlib.org/lapack/lawns/lawn42.ps;
http://www.netlib.org/lapack/lawnspdf/lawn42.pdf",
acknowledgement = ack-nhfb,
}
@Article{Higham:1992:SMM,
author = "Nicholas J. Higham",
title = "Stability of a Method for Multiplying Complex Matrices
with Three Real Matrix Multiplications",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "3",
pages = "681--687",
month = jul,
year = "1992",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@TechReport{Balle:1993:STM,
author = "Susanne M. Balle and Per Christian Hansen and Nicholas
J. Higham",
title = "A {Strassen}-Type Matrix Inversion Algorithm for the
{Connection Machine}",
number = "CNC/1993/028",
institution = "Centre for Novel Computing, " # inst-U-Manchester,
address = inst-U-Manchester:adr,
type = "Technical Report",
pages = "29",
month = oct,
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@Article{Demmel:1993:IEB,
author = "James W. Demmel and Nicholas J. Higham",
title = "Improved Error Bounds for Underdetermined System
Solvers",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "14",
number = "1",
pages = "1--14",
month = jan,
year = "1993",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
mynote = "Also LAPACK Working Note \#23.",
}
@Article{Hammarling:1993:CHW,
author = "Sven Hammarling and Nicholas J. Higham and Bo
K{\aa}gstr{\"o}m",
title = "{CERFACS} Hosts Workshop on Reliability of
Computations",
journal = j-SIAM-NEWS,
volume = "26",
pages = "4",
month = jul,
year = "1993",
ISSN = "0036-1437",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM 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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://citeseer.nj.nec.com/higham93accuracy.html;
http://citeseer.nj.nec.com/rd/4651150%2C296147%2C1%2C0.25%2CDownload/http%253A%252F%252Fciteseer.nj.nec.com/cache/papers2/cs/14280/http%253AzSzzSzwww.maths.man.ac.ukzSz%257EnareportszSznarep198.pdf/higham93accuracy.pdf;
http://citeseer.nj.nec.com/rd/4651150%2C296147%2C1%2C0.25%2CDownload/http%253A%252F%252Fwww.maths.man.ac.uk/%257Enareports/narep198.ps.gz",
abstract = "The usual recursive summation technique is just one of
several ways of computing the sum of $n$ floating point
numbers. Five summation methods and their variations
are analyzed. The accuracy of the methods is compared
using rounding error analysis and numerical
experiments. Four of the methods are shown to be
special cases of a general class of methods, and an
error analysis is given for this class. No one method
is uniformly more accurate than the others, but some
guidelines are given on the choice of method in
particular cases.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Manchester Univ., UK",
classification = "C4110 (Error analysis in numerical methods); C5230
(Digital arithmetic methods)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "Floating point numbers; Floating point summation;
Numerical experiments; Recursive summation technique;
Rounding error analysis",
language = "English",
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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear.",
acknowledgement = ack-njh,
}
@InProceedings{Higham:1993:CEA,
author = "Nicholas J. Higham and Philip A. Knight",
editor = "Carl D. Meyer and Robert J. Plemmons",
booktitle = "Linear Algebra, Markov Chains, and Queueing Models",
title = "Componentwise Error Analysis for Stationary Iterative
Methods",
volume = "48",
publisher = pub-SPRINGER,
address = pub-SPRINGER:adr-NY,
pages = "29--46",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
series = "IMA Volumes in Mathematics and its Applications",
acknowledgement = ack-njh,
}
@Article{Higham:1993:FPB,
author = "Nicholas J. Higham and Philip A. Knight",
title = "Finite Precision Behavior of Stationary Iteration for
Solving Singular Systems",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "192",
pages = "165--186",
year = "1993",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
mynote = "Special issue for Proceedings of Workshop on
Computational Linear Algebra in Algebraic and Related
Problems.",
}
@Book{Higham:1993:HWM,
author = "Nicholas J. Higham",
title = "Handbook of Writing for the Mathematical Sciences",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xii + 241",
month = jun,
year = "1993",
ISBN = "0-89871-314-5",
ISBN-13 = "978-0-89871-314-5",
LCCN = "QA42.H54 1993",
bibdate = "Tue Sep 2 16:32:32 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
price = "US\$21.50",
acknowledgement = ack-njh,
note-1 = "[From the publisher]: Having trouble with your latest
math paper? Giving a presentation that you just can't
pull together? Struggling with your thesis or trying to
get your first article published in a technical
journal? Handbook of Writing for the Mathematical
Sciences is the book for you!
This handy volume provides information on virtually
every issue you will face when writing a technical
paper or talk, from choosing the right journal to
handling your references. You'll also get an overview
of the entire publication process--invaluable for
anyone hoping to publish in a technical journal.",
note-2 = "To write a truly impressive paper, you'll need to
understand the anatomy of a research paper and the
steps involved in revising a draft. This book offers
discussions of these fundamental topics, along with
illustrative and provocative examples. Also included
are chapters on standard English usage, using computers
for writing and research, and writing technical
material when English is a foreign language.
This handbook provides much-needed advice on handling
the basic ingredients of a research paper, like
definitions, theorems, examples, and equations. In
addition, appendices provide essential reference
material, including summaries of \LaTeX{} symbols and
Emacs commands, addresses of mathematical societies,
and a list of papers that have won expository writing
prizes.",
note-3 = "This book is ideal for graduate students and teachers.
Among its special features:
\begin{itemize} \item Detail and extensive use of
examples make it an excellent teaching tool
\item Discusses \TeX{} and other software tools for
preparing publications
\item Thorough treatment, with examples, of how to
write slides (transparencies) for a mathematical
talk.
\item Comprehensive index and extensive bibliography
make it an excellent reference
\item Readable for everyone in the field--from
undergraduates to seasoned professionals
\end{itemize}",
note-4 = "Contents \\
Preface; \\
Chapter 1: General Principles; \\
Chapter 2: Writer's Tools and Recommended Reading; \\
Chapter 3: Mathematical Writing; \\
Chapter 4: English Usage; \\
Chapter 5: When English is a Foreign Language; \\
Chapter 6: Writing a Paper; \\
Chapter 7: Revising a Draft; \\
Chapter 8: Publishing a Paper; \\
Chapter 9: Writing a Talk; \\
Chapter 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.\\
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.",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@TechReport{Higham:1993:PSV,
author = "Nicholas J. Higham and Pythagoras Papadimitriou",
title = "Parallel Singular Value Decomposition via the Polar
Decomposition",
type = "Numerical Analysis Report",
number = "239",
institution = inst-MCCM,
address = inst-MCCM:adr,
month = oct,
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
mynote = "Longer version of \cite{Higham:1994:PAC}.",
}
@Article{Higham:1993:PTB,
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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit33.html",
acknowledgement = ack-njh # " and " # ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@TechReport{Higham:1993:TMT,
author = "Nicholas J. Higham",
title = "The {Test Matrix Toolbox} for {Matlab}",
type = "Numerical Analysis Report",
number = "237",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "76",
month = dec,
year = "1993",
bibdate = "Tue Mar 30 17:06:37 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
abstract-1 = "We describe version 2.0 of the Test Matrix Toolbox for
Matlab 4. The toolbox contains a collection of test
matrices, routines for visualizing matrices, and
miscellaneous routines that provide useful additions to
Matlab's existing set of functions. There are 58
parametrized test matrices, which are mostly square,
dense, nonrandom, and of arbitrary dimension. The test
matrices include ones with known inverses or known
eigenvalues; ill-conditioned or rank deficient
matrices; and symmetric, positive definite, orthogonal,
defective, involutary, and totally positive matrices.",
abstract-2 = "We describe version 2.0 of the Test Matrix Toolbox for
Matlab The visualization routines display surface plots
of a matrix and its (pseudo-) inverse, the field of
values, Gershgorin disks, and two- and
three-dimensional views of pseudospectra. We explain
the need for collections of test matrices and summarize
the features of the collection in the toolbox. We give
examples of the use of the toolbox and explain some of
the interesting properties of the Frank and Pascal
matrices, and of random, magic square and companion
matrices. The leading comment lines from all the
toolbox routines are listed.",
acknowledgement = ack-njh,
keywords = "test matrix, Matlab, pseudospectrum, visualization,
Frank matrix, Pascal matrix, companion matrix, magic
square matrix, random matrix",
}
@Article{Higham:1994:BVT,
author = "Nicholas J. Higham",
title = "{\BibTeX}: {A} Versatile Tool for {\LaTeX} Users",
journal = j-SIAM-NEWS,
volume = "27",
pages = "10, 11, 19",
month = jan,
year = "1994",
ISSN = "0036-1437",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM 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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Japanese edition of \cite{Higham:1993:HWM}, translated
by Shoji Okumura and Takemitsu Hasegawa.",
acknowledgement = ack-njh,
}
@Article{Higham:1994:MSD,
author = "Nicholas J. Higham",
title = "The Matrix Sign Decomposition and Its Relation to the
Polar Decomposition",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "212/213",
pages = "3--20",
year = "1994",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Tue Jan 3 12:21:48 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@InProceedings{Higham:1994:NPA,
author = "Nicholas J. Higham and Pythagoras Papadimitriou",
editor = "John G. Lewis",
booktitle = "Proceedings of the Fifth SIAM Conference on Applied
Linear Algebra",
title = "A New Parallel Algorithm for Computing the Singular
Value Decomposition",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "80--84",
year = "1994",
ISBN = "0-89871-336-6",
ISBN-13 = "978-0-89871-336-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@Article{Higham:1994:PAC,
author = "Nicholas J. Higham and Pythagoras Papadimitriou",
title = "A Parallel Algorithm for Computing the Polar
Decomposition",
journal = j-PARALLEL-COMPUTING,
volume = "20",
number = "8",
pages = "1161--1173",
month = aug,
year = "1994",
CODEN = "PACOEJ",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
}
@TechReport{Higham:1994:SCPa,
author = "Nicholas J. Higham",
title = "A Survey of Componentwise Perturbation Theory in
Numerical Linear Algebra",
type = "Numerical Analysis Report",
number = "241",
institution = inst-U-MANCHESTER,
address = inst-U-Manchester:adr,
month = feb,
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in Mathematics of Computation 1943--1993, W.
Gautschi, ed. Proceedings of Symposia in Applied
Mathematics, American Mathematical Society.",
acknowledgement = ack-njh,
}
@InProceedings{Higham:1994:SCPb,
author = "Nicholas J. Higham",
editor = "Walter Gautschi",
booktitle = "{Mathematics of Computation} 1943--1993: {A} Half
Century of Computational Mathematics",
title = "A Survey of Componentwise Perturbation Theory in
Numerical Linear Algebra",
volume = "48",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "49--77",
year = "1994",
bibdate = "Fri Mar 24 08:51:18 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
series = "Proceedings of Symposia in Applied Mathematics",
acknowledgement = ack-njh,
}
@Article{Higham:1994:SPI,
author = "Nicholas J. Higham and Alex Pothen",
title = "Stability of the Partitioned Inverse Method for
Parallel Solution of Sparse Triangular Systems",
journal = j-SIAM-J-SCI-COMP,
volume = "15",
number = "1",
pages = "139--148",
month = jan,
year = "1994",
CODEN = "SJOCE3",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Higham:1994:WDM,
author = "Nicholas J. Higham",
title = "Which Dictionary for the Mathematical Scientist?",
journal = j-IMA-BULL,
volume = "30",
number = "5/6",
pages = "81--88",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "IMA Bulletin",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear.",
acknowledgement = ack-njh,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
}
@TechReport{Higham:1995:DPS,
author = "Nicholas J. Higham",
title = "Diagonal Pivoting Stability \dots",
type = "Numerical Analysis Report",
number = "2xx",
institution = inst-U-MANCHESTER,
address = inst-U-Manchester:adr,
month = jun,
year = "1995",
bibdate = "Tue Mar 21 16:31:40 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "In preparation.",
acknowledgement = ack-njh,
}
@TechReport{Higham:1995:IRLa,
author = "Nicholas J. Higham",
title = "Iterative Refinement for Linear Systems and {LAPACK}",
type = "Numerical Analysis Report",
number = "277",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "17",
month = sep,
year = "1995",
bibdate = "Mon Apr 21 19:26:38 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in " # j-IMA-J-NUMER-ANAL # " (14) 1997.",
acknowledgement = ack-njh,
mynote = "Also LAPACK Working Note 104.",
}
@TechReport{Higham:1995:IRLb,
author = "N. J. Higham",
title = "Iterative Refinement and {LAPACK}",
type = "LAPACK Working Note",
number = "104",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = oct,
year = "1995",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-95-308, October 1995.",
URL = "http://www.netlib.org/lapack/lawns/lawn104.ps;
http://www.netlib.org/lapack/lawnspdf/lawn104.pdf",
acknowledgement = ack-nhfb,
mynote = "Also Manchester Numerical Analysis Report 277.",
}
@Article{Higham:1995:MPF,
author = "Nicholas J. Higham and Philip A. Knight",
title = "Matrix Powers in Finite Precision Arithmetic",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "16",
number = "2",
pages = "343--358",
month = apr,
year = "1995",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Tue Aug 29 09:11:08 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
mynote = "Page numbers from SIAM.",
}
@Article{Higham:1995:RHA,
author = "Nicholas J. Higham",
title = "Review of {``Howard Anton and Chris Rorres, Elementary
Linear Algebra: Applications Version, Seventh edition,
Wiley, New York, 1994.''}",
journal = j-IMA-BULL,
volume = "31",
number = "7/8",
pages = "122--123",
year = "1995",
bibdate = "Mon Aug 14 03:43:49 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "IMA Bulletin",
}
@TechReport{Higham:1995:SDP,
author = "N. J. Higham",
title = "Stability of the Diagonal Pivoting Method with Partial
Pivoting",
type = "LAPACK Working Note",
number = "105",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = oct,
year = "1995",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-95-309, October 1995.",
URL = "http://www.netlib.org/lapack/lawns/lawn105.ps;
http://www.netlib.org/lapack/lawnspdf/lawn105.pdf",
acknowledgement = ack-nhfb,
}
@Article{Higham:1995:SPT,
author = "Nicholas J. Higham",
title = "Stability of Parallel Triangular System Solvers",
journal = j-SIAM-J-SCI-COMP,
volume = "16",
number = "2",
pages = "400--413",
month = mar,
year = "1995",
CODEN = "SJOCE3",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed Jul 5 10:32:41 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
mynote = "Page numbers from SIAM.",
xxnote = "Check month: apr or mar??",
}
@TechReport{Higham:1995:TMT,
author = "Nicholas J. Higham",
title = "The {Test Matrix Toolbox} for {{\sc Matlab}}, Version
3.0",
type = "Numerical Analysis Report",
number = "276",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "70",
month = sep,
year = "1995",
bibdate = "Thu Sep 28 10:50:20 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Supersedes Numerical Analysis Report No. 237. In
preparation.",
URL = "http://p2chpd-cluster.univ-lyon1.fr/P2CHPD/matlab/pdf_doc/otherdocs/testmatrix.pdf",
acknowledgement = ack-njh,
}
@Article{Braconnier:1996:CFV,
author = "Thierry Braconnier and Nicholas J. Higham",
title = "Computing the Field of Values and Pseudospectra Using
the {Lanczos} Method with Continuation",
journal = j-BIT-NUM-MATH,
volume = "36",
number = "3",
pages = "422--440",
month = sep,
year = "1996",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
MRclass = "65F15",
MRnumber = "97d:65015",
bibdate = "Fri Nov 13 07:00:34 MST 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "International Linear Algebra Year (Toulouse, 1995).",
URL = "http://www.mai.liu.se/BIT/contents/bit36.html",
acknowledgement = ack-njh # " and " # ack-nhfb,
journal-URL = "http://link.springer.com/journal/16",
}
@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",
bibdate = "Mon Feb 19 08:51:53 GMT 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM 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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in " # j-SIAM-J-MAT-ANA-APPL # ".",
acknowledgement = ack-njh,
}
@Article{Hammarling:1996:HPP,
author = "Sven Hammarling and Nicholas J. Higham",
title = "How to Prepare a Poster",
journal = j-SIAM-NEWS,
volume = "29",
number = "4",
pages = "20, 19",
month = may,
year = "1996",
ISSN = "0036-1437",
bibdate = "Tue May 14 11:26:42 GMT 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM 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",
bibdate = "Tue Jan 30 11:01:35 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Typeset with \LaTeX2e.",
price = "US\$39.00",
acknowledgement = ack-njh # " and " # ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "To appear",
acknowledgement = ack-nhfb,
}
@TechReport{Higham:1996:FCS,
author = "Nicholas J. Higham",
title = "Factorizing Complex Symmetric Matrices with Positive
Definite Real and Imaginary Parts",
type = "Numerical Analysis Report",
number = "298",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "12",
month = nov,
year = "1996",
bibdate = "Mon May 19 12:01:10 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Published in \cite{Higham:1998:FCS}.",
acknowledgement = ack-njh,
}
@TechReport{Higham:1996:MIM,
author = "Nicholas J. Higham and Sheung Hun Cheng",
title = "Modifying the Inertia of Matrices Arising in
Optimization",
type = "Numerical Analysis Report",
number = "295",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "17",
month = sep,
year = "1996",
bibdate = "Mon Feb 24 12:42:49 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in " # j-LINEAR-ALGEBRA-APPL # ".",
acknowledgement = ack-njh,
}
@Article{Higham:1996:RAN,
author = "Nicholas J. Higham",
title = "Review of {``Acta Numerica 1994 and Acta Numerica
1995, Cambridge University Press''}",
journal = j-MATH-TODAY,
volume = "32",
number = "1/2",
pages = "28--??",
year = "1996",
ISSN = "1361-2042",
ISSN-L = "1361-2042",
bibdate = "Sat Sep 24 08:44:10 2011",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/Bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
acknowledgement = ack-nhfb # " and " # ack-njh,
fjournal = "Mathematics Today",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Higham:1996:RMB,
author = "Nicholas J. Higham",
title = "Review of {``Are Magnus Bruaset. A Survey of
Preconditioned Iterative Methods, volume 328 of Pitman
Research Notes in Mathematics. Longman Scientific and
Technical, Essex, UK, 1995.''}",
journal = j-IMA-BULL,
volume = "32",
number = "3/4",
pages = "60",
year = "1996",
bibdate = "Wed Apr 17 16:22:01 GMT 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "IMA Bulletin",
}
@TechReport{Higham:1996:SBE,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "Structured Backward Error and Condition of Generalized
Eigenvalue Problems",
type = "Numerical Analysis Report",
number = "297",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "24",
month = nov,
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Submitted to " # j-SIAM-J-MAT-ANA-APPL,
bibdate = "Fri Nov 15 12:27:07 GMT 1996",
acknowledgement = ack-njh,
}
@TechReport{Cox:1997:ASN,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Accuracy and Stability of the Null Space Method for
Solving the Equality Constrained Least Squares
Problem",
type = "Numerical Analysis Report",
number = "306",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "20",
month = aug,
year = "1997",
bibdate = "Sat Oct 31 10:24:09 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in " # j-BIT # ", 39(1): 1999",
acknowledgement = ack-njh,
}
@TechReport{Cox:1997:SHQ,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Stability of {Householder $ Q R $} Factorization for
Weighted Least Squares Problems",
type = "Numerical Analysis Report",
number = "301",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "17",
month = feb,
year = "1997",
bibdate = "Mon May 19 14:24:46 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in Numerical Analysis 1997, Proceedings of
the 17th Dundee Conference.",
acknowledgement = ack-njh,
}
@InCollection{Higham:1997:CCL,
author = "Nicholas J. Higham",
editor = "William R. Davis and others",
booktitle = "Cornelius Lanczos Collected Published Papers with
Commentaries",
title = "{Commentary on C. Lanczos, ``Introduction'' to
``Tables of Chebyshev Polynomials $ S_n(x) $ and $
C_n(x) $'', Nat.\ Bur.\ Stand., Appl.\ Math.\ Series 9,
1952, v--xxvi}",
volume = "VI(3)",
publisher = "????",
address = "????",
pages = "557--559",
year = "1997",
bibdate = "Wed Aug 13 08:39:47 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear.",
acknowledgement = ack-njh,
mynote = "Volume VI, Part 3, pp. 557--559.",
}
@Article{Higham:1997:IRL,
author = "Nicholas J. Higham",
title = "Iterative refinement for linear systems and {LAPACK}",
journal = j-IMA-J-NUMER-ANAL,
volume = "17",
number = "4",
pages = "495--509",
month = oct,
year = "1997",
CODEN = "IJNADH",
DOI = "http://dx.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://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www3.oup.co.uk/imanum/hdb/Volume_17/Issue_04/;
MathSciNet database",
note = "Preprint published as Numerical Analysis Report 277,
Manchester Centre for Computational Mathematics,
Manchester, England, and as LAPACK Working Note 104.",
URL = "http://www3.oup.co.uk/imanum/hdb/Volume_17/Issue_04/170495.sgm.abs.html",
abstract = "The technique of iterative refinement for improving
the computed solution to a linear system was used on
desk calculators and computers in the 1940s and has
remained popular. In the 1990s iterative refinement is
well supported in software libraries, notably in
LAPACK. Although the behaviour of iterative refinement
in floating point arithmetic is reasonably well
understood, the existing theory is not sufficient to
justify the use of fixed precision iterative refinement
in all the LAPACK routines in which it is implemented.
We present analysis that provides the theoretical
support needed for LAPACK. The analysis covers both
mixed and fixed precision iterative refinement with an
arbitrary number of iterations, makes only a general
assumption on the underlying solver, and is relatively
short. We identify some remaining open problems.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Higham:1997:MHI,
author = "Nicholas J. Higham",
title = "{Manchester} Hosts Inaugural Meeting of {UK} and
{Irish SIAM Section}",
journal = j-SIAM-NEWS,
volume = "30",
number = "3",
pages = "3",
month = apr,
year = "1997",
ISSN = "0036-1437",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM News",
}
@InProceedings{Higham:1997:RDD,
author = "Nicholas J. Higham",
editor = "I. S. Duff and G. A. Watson",
booktitle = "The State of the Art in Numerical Analysis",
title = "Recent Developments in Dense Numerical Linear
Algebra",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "1--26",
year = "1997",
bibdate = "Fri Jul 11 16:11:28 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@Article{Higham:1997:RJR,
author = "Nicholas J. Higham",
title = "Review of {``James R. Schott, Matrix Analysis for
Statistics, Wiley, 1997''}",
journal = j-MATH-TODAY,
volume = "33",
number = "5",
pages = "161--162",
year = "1997",
ISSN = "1361-2042",
bibdate = "Sun Oct 12 15:29:25 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Mathematics Today",
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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "In preparation.",
acknowledgement = ack-njh,
}
@Article{Higham:1997:SDP,
author = "Nicholas J. Higham",
title = "Stability of the Diagonal Pivoting Method with Partial
Pivoting",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "18",
number = "1",
pages = "52--65",
month = jan,
year = "1997",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Sun Mar 2 11:16:54 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@TechReport{Higham:1997:SIMa,
author = "Nicholas J. Higham",
title = "Stable Iterations for the Matrix Square Root",
type = "Numerical Analysis Report",
number = "305",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "20",
month = apr,
year = "1997",
bibdate = "Mon Jun 16 12:13:21 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Published in \cite{Higham:1997:SIMb}.",
acknowledgement = ack-njh,
}
@Article{Higham:1997:SIMb,
author = "Nicholas J. Higham",
title = "Stable iterations for the matrix square root",
journal = j-NUMER-ALGORITHMS,
volume = "15",
number = "2",
pages = "227--242",
month = "????",
year = "1997",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F30 (65F05)",
MRnumber = "98d:65055",
bibdate = "Mon Sep 29 08:36:51 MDT 2003",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
http://www.math.psu.edu/dna/contents/na.html;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/7/6/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/5058/7/6/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@InProceedings{Higham:1997:TLA,
author = "Nicholas J. Higham",
editor = "Ronald F. Boisvert",
booktitle = "Quality of Numerical Software: {Assessment} and
Enhancement",
title = "Testing Linear Algebra Software",
publisher = pub-CH,
address = pub-CH:adr-L,
pages = "109--122",
year = "1997",
bibdate = "Mon Feb 3 09:14:23 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@Article{Cheng:1998:MCA,
author = "Sheung Hun Cheng and Nicholas J. Higham",
title = "A Modified {Cholesky} Algorithm Based on a Symmetric
Indefinite Factorization",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "19",
number = "4",
pages = "1097--1110",
month = oct,
year = "1998",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Dec 4 12:14:09 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/19/4;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/30289",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@TechReport{Cheng:1998:NDP,
author = "Sheung Hun Cheng and Nicholas J. Higham",
title = "The Nearest Definite Pair for the {Hermitian}
Generalized Eigenvalue Problem",
type = "Numerical Analysis Report",
number = "325",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "15",
month = may,
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Submitted to " # j-LINEAR-ALGEBRA-APPL,
bibdate = "Mon May 11 14:55:05 GMT 1998",
acknowledgement = ack-njh,
oldlabel = "chhi98",
}
@TechReport{Cox:1998:BEB,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Backward Error Bounds for Constrained Least Squares
Problems",
type = "Numerical Analysis Report",
number = "321",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "20",
month = apr,
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Submitted to " # j-BIT,
bibdate = "Fri Apr 17 12:13:36 GMT 1998",
acknowledgement = ack-njh,
oldlabel = "cohi98c",
}
@TechReport{Cox:1998:RWB,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Row-Wise Backward Stable Elimination Methods for the
Equality Constrained Least Squares Problem",
type = "Numerical Analysis Report",
number = "319",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "18",
month = mar,
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in " # j-SIAM-J-MAT-ANA-APPL,
bibdate = "Fri Aug 14 18:34:14 GMT 1998",
acknowledgement = ack-njh,
oldlabel = "cohi98r",
}
@InProceedings{Cox:1998:SHQ,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Stability of {Householder QR} Factorization for
Weighted Least Squares Problems",
crossref = "Higham:1998:NAP",
pages = "57--73",
year = "1998",
bibdate = "Mon Aug 29 22:30:58 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
series = "Pitman Research Notes in Mathematics",
acknowledgement = ack-nhfb,
}
@Article{Higham:1998:BNR,
author = "Nicholas J. Higham",
title = "Book News \& Reviews: Review of {``Christoph W.
Ueberhuber, Numerical Computation: Methods, Software
and Analysis, Springer-Verlag, 1997''}",
journal = j-IEEE-COMPUT-SCI-ENG,
volume = "5",
number = "1",
pages = "79--79",
month = jan # "\slash " # mar,
year = "1998",
CODEN = "ISCEE4",
ISSN = "1070-9924 (print), 1558-190X (electronic)",
ISSN-L = "1070-9924",
bibdate = "Sat Jan 9 08:57:23 MST 1999",
bibsource = "http://www.computer.org/cse/cs1998;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://dlib.computer.org/cs/books/cs1998/pdf/c1079.pdf",
acknowledgement = ack-njh # " and " # ack-nhfb,
fjournal = "IEEE Computational Science \& Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=99",
mynote = "Jan-Mar",
oldlabel = "high98:uebe97",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Higham:1998:HWM,
author = "Nicholas J. Higham",
title = "Handbook of writing for the mathematical sciences",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Second",
pages = "xvi + 302",
year = "1998",
ISBN = "0-89871-420-6",
ISBN-13 = "978-0-89871-420-3",
LCCN = "QA42 .H54 1998",
bibdate = "Wed Oct 30 14:21:33 2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
oldlabel = "hich98",
}
@TechReport{Higham:1998:NAS,
author = "Nicholas J. Higham",
title = "Notes on Accuracy and Stability of Algorithms in
Numerical Linear Algebra",
type = "Numerical Analysis Report",
number = "333",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "42",
month = aug,
year = "1998",
bibdate = "Mon Sep 7 09:59:00 GMT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in proceedings of EPSRC Numerical Analysis
Summer School, Leicester University, July 1998.",
acknowledgement = ack-njh,
oldlabel = "high98a",
}
@Article{Higham:1998:NWE,
author = "Nicholas J. Higham and David J. Silvester",
title = "``{Nothing was Ever the Same Again}''",
journal = j-SIAM-NEWS,
volume = "31",
number = "7",
pages = "1, 8",
month = sep,
year = "1998",
ISSN = "0036-1437",
bibdate = "Wed Sep 16 11:49:30 GMT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM News",
}
@TechReport{Higham:1998:QFC,
author = "Nicholas J. Higham",
title = "{QR} 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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Submitted to " # j-LINEAR-ALGEBRA-APPL,
bibdate = "Mon Sep 14 14:06:12 GMT 1998",
acknowledgement = ack-njh,
oldlabel = "high98q",
}
@Article{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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/117/25/30/abstract.html;
http://www.elsevier.nl/gej-ng/10/30/19/117/25/30/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Cox:1999:ASN,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Accuracy and Stability of the Null Space Method for
Solving the Equality Constrained Least Squares
Problem",
journal = j-BIT-NUM-MATH,
volume = "39",
number = "1",
pages = "34--49",
month = "????",
year = "1999",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
bibdate = "Thu Oct 16 08:15:34 2003",
bibsource = "http://www.mai.liu.se/BIT/contents/bit39.html;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
OCLC Article1st database",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/16",
}
@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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
OCLC Article1st database",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/16",
}
@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 = "http://dx.doi.org/10.1112/S0024609397264167",
ISSN = "0024-6093",
ISSN-L = "0024-6093",
bibdate = "Thu Aug 25 10:49:37 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://blms.oxfordjournals.org/content/31/3/374.full.pdf",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the London Mathematical Society",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
}
@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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/31318",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:1999:SBL,
author = "Nicholas J. Higham",
title = "Stability of block {LDL$^T$} factorization of a
symmetric tridiagonal matrix",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "287",
number = "1--3",
pages = "181--189",
day = "15",
month = jan,
year = "1999",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Fri May 28 08:42:54 MDT 1999",
bibsource = "http://www.elsevier.com/locate/laa;
http://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=19
99&volume=287&issue=1-3&aid=6193",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/33595",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Davies:2000:NSG,
author = "Philip I. Davies and Nicholas J. Higham",
title = "Numerically Stable Generation of Correlation Matrices
and Their Factors",
journal = j-BIT-NUM-MATH,
volume = "40",
number = "4",
pages = "640--651",
month = dec,
year = "2000",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=40&issue=4&spage=640",
acknowledgement = ack-nhfb,
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/16",
}
@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 = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/35608",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2000:FCP,
author = "Nicholas J. Higham",
title = "{$ Q R $} factorization with complete pivoting and
accurate computation of the {SVD}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "309",
number = "1--3",
pages = "153--174",
year = "2000",
CODEN = "LAAPAW",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
remark = "Proceedings of the International Workshop on Accurate
Solution of Eigenvalue Problems (University Park, PA,
1998)",
}
@Book{Higham:2000:MG,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "{MATLAB} Guide",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxii + 283",
year = "2000",
ISBN = "0-89871-469-9",
ISBN-13 = "978-0-89871-469-2",
LCCN = "QA297 .H5217 2000",
MRclass = "65-04 (00A20)",
MRnumber = "MR1787308 (2001e:65003)",
bibdate = "Tue Jan 23 09:04:18 2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
keywords = "Matlab; numerical analysis -- data processing",
}
@Article{Higham:2000:NAQ,
author = "Nicholas J. Higham and Hyun-Min Kim",
title = "Numerical analysis of a quadratic matrix equation",
journal = j-IMA-J-NUMER-ANAL,
volume = "20",
number = "4",
pages = "499--519",
month = oct,
year = "2000",
CODEN = "IJNADH",
DOI = "http://dx.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://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www3.oup.co.uk/imanum/hdb/Volume_20/Issue_04/",
URL = "http://www3.oup.co.uk/imanum/hdb/Volume_20/Issue_04/200499abs.pdf;
http://www3.oup.co.uk/imanum/hdb/Volume_20/Issue_04/pdf/200499.pdf",
abstract = "The quadratic matrix equation $ A X^2 + B X + C = 0 $
in $ n \times n $ matrices arises in applications and
is of intrinsic interest as one of the simplest
nonlinear matrix equations. We give a complete
characterization of solutions in terms of the
generalized Schur decomposition and describe and
compare various numerical solution techniques. In
particular, we give a thorough treatment of functional
iteration methods based on Bernoulli's method. Other
methods considered include Newton's method with exact
line searches, symbolic solution and continued
fractions. We show that functional iteration applied to
the quadratic matrix equation can provide an efficient
way to solve the associated quadratic eigenvalue
problem $ (\lambda^2 A + \lambda B + C) x = 0 $.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Higham:2000:QFC,
author = "Nicholas J. Higham",
title = "{QR} factorization with complete pivoting and accurate
computation of the {SVD}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "309",
number = "1--3",
pages = "153--174",
day = "15",
month = apr,
year = "2000",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Mon Oct 9 10:54:41 MDT 2000",
bibsource = "http://www.elsevier.com/locate/laa;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/126/25/34/abstract.html;
http://www.elsevier.nl/gej-ng/10/30/19/126/25/34/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@TechReport{Cheng:2001:ILB,
author = "S. Cheng and N. Higham",
title = "Implementation for {LAPACK} of a Block Algorithm for
Matrix $1$-Norm Estimation",
type = "LAPACK Working Note",
number = "152",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = aug,
year = "2001",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-01-470, August 2001.",
URL = "http://www.netlib.org/lapack/lawns/lawn152.ps;
http://www.netlib.org/lapack/lawnspdf/lawn152.pdf",
acknowledgement = ack-nhfb,
}
@Article{Cheng:2001:PIB,
author = "Sheung Hun Cheng and Nicholas J. Higham",
title = "Parallel Implementation of a Block Algorithm for
Matrix $1$-Norm Estimation",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2150",
pages = "568--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:05:53 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2150.htm;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2150/21500568.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2150/21500568.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
}
@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 = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/37349",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2001:P,
author = "Nicholas Higham and Roger Horn and Thomas J. Laffey
and Ferran Puerta",
title = "Preface",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "332--334",
number = "1",
pages = "1--1",
day = "1",
month = aug,
year = "2001",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Jul 25 17:54:46 MDT 2001",
bibsource = "http://www.elsevier.com/locate/laa;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/157/25/25/abstract.html;
http://www.elsevier.nl/gej-ng/10/30/19/157/25/25/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:2001: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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Tisseur:2001:SPP,
author = "Fran{\c{c}}oise Tisseur and Nicholas J. Higham",
title = "Structured pseudospectra for polynomial eigenvalue
problems, with applications",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "23",
number = "1",
pages = "187--208",
year = "2001",
CODEN = "SJMAEL",
ISSN = "1095-7162",
ISSN-L = "0895-4798",
MRclass = "15A18 (15A22 65F15)",
MRnumber = "MR1856605 (2002k:15024)",
MRreviewer = "Jesse L. Barlow",
bibdate = "Sat Apr 16 17:55:00 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Book{Higham:2002:ASN,
author = "Nicholas J. Higham",
title = "Accuracy and Stability of Numerical Algorithms",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Second",
pages = "xxx + 680",
year = "2002",
ISBN = "0-89871-521-0",
ISBN-13 = "978-0-89871-521-7",
LCCN = "QA297 .H53 2002",
MRclass = "65G50 (65-02)",
MRnumber = "MR1927606 (2003g:65064)",
bibdate = "Wed Oct 30 14:20:02 2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.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://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www3.oup.co.uk/imanum/hdb/Volume_22/Issue_03/",
URL = "http://www3.oup.co.uk/imanum/hdb/Volume_22/Issue_03/220329.sgm.abs.html;
http://www3.oup.co.uk/imanum/hdb/Volume_22/Issue_03/pdf/220329.pdf",
abstract = "Given a symmetric matrix, what is the nearest
correlation matrix that is, the nearest symmetric
positive semidefinite matrix with unit diagonal? This
problem arises in the finance industry, where the
correlations are between stocks. For distance measured
in two weighted Frobenius norms we characterize the
solution using convex analysis. We show how the
modified alternating projections method can be used to
compute the solution for the more commonly used of the
weighted Frobenius norms. In the finance application
the original matrix has many zero or negative
eigenvalues; we show that for a certain class of
weights the nearest correlation matrix has
correspondingly many zero eigenvalues and that this
fact can be exploited in the computation.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "convex analysis; correlation matrix; nearness problem;
positive semidefinite matrix; weighted",
}
@Article{Higham:2002:DDH,
author = "Nicholas J. Higham and Fran{\c{c}}oise Tisseur and
Paul M. Van Dooren",
title = "Detecting a definite {Hermitian} pair and a hyperbolic
or elliptic quadratic eigenvalue problem, and
associated nearness problems",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "351--352",
pages = "455--474",
day = "15",
month = aug,
year = "2002",
CODEN = "LAAPAW",
DOI = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Fourth special issue on linear systems and control",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:2002: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 = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Fourth special issue on linear systems and control",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:2002: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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/35097",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Tisseur:2002:SPP,
author = "Fran{\c{c}}oise Tisseur and Nicholas J. Higham",
title = "Structured Pseudospectra for Polynomial Eigenvalue
Problems, with Applications",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "23",
number = "1",
pages = "187--208",
month = jan,
year = "2002",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Wed Oct 23 08:36:32 MDT 2002",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/23/1;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/37145",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Bojanczyk:2003:ECI,
author = "Adam Bojanczyk and Nicholas J. Higham and Harikrishna
Patel",
title = "The equality constrained indefinite least squares
problem: theory and algorithms",
journal = j-BIT,
volume = "43",
number = "3",
pages = "505--517",
year = "2003",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Bojanczyk:2003:SIL,
author = "Adam Bojanczyk and Nicholas J. Higham and Harikrishna
Patel",
title = "Solving the Indefinite Least Squares Problem by
Hyperbolic {QR} Factorization",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "24",
number = "4",
pages = "914--931",
month = oct,
year = "2003",
CODEN = "SJMAEL",
DOI = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/40149",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Davies:2003:SPA,
author = "Philip I. Davies and Nicholas J. Higham",
title = "A {Schur--Parlett} Algorithm for Computing Matrix
Functions",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "25",
number = "2",
pages = "464--485",
month = apr,
year = "2003",
CODEN = "SJMAEL",
DOI = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/41081",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2003:BEM,
author = "Nicholas J. Higham and Fran{\c{c}}oise Tisseur",
title = "Bounds for eigenvalues of matrix polynomials",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "358",
number = "1--3",
pages = "5--22",
day = "1",
month = jan,
year = "2003",
CODEN = "LAAPAW",
DOI = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Special issue on accurate solution of eigenvalue
problems (Hagen, 2000)",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/207/25/27/abstract.html;
http://www.sciencedirect.com/science?_ob=GatewayURL&_origin=SOCJLA&_urlversion=4&_method=citationSearch&_version=1&_piikey=S0024379501003160&_volkey=00243795%23358%235&_refkey=Higham%232003%235%2322&md5=51223bc8229cca92374c1fcdbfa6b770",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:2003:CMC,
author = "Nicholas J. Higham and Matthew I. Smith",
title = "Computing the Matrix Cosine",
journal = j-NUMER-ALGORITHMS,
volume = "34",
number = "1",
pages = "13--26",
month = sep,
year = "2003",
CODEN = "NUALEG",
DOI = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://ipsapp008.kluweronline.com/content/getfile/5058/47/2/abstract.htm;
http://ipsapp008.kluweronline.com/content/getfile/5058/47/2/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Higham:2003:OMP,
author = "Nicholas J. Higham",
title = "{$J$}-Orthogonal Matrices: Properties and Generation",
journal = j-SIAM-REVIEW,
volume = "45",
number = "3",
pages = "504--519",
month = sep,
year = "2003",
CODEN = "SIREAD",
DOI = "http://dx.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 = "Wed Aug 20 06:58:15 MDT 2003",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/45/3;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/41493",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Higham: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 = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/42664",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2004:NSB,
author = "Nicholas J. Higham",
title = "The numerical stability of barycentric {Lagrange}
interpolation",
journal = j-IMA-J-NUMER-ANAL,
volume = "24",
number = "4",
pages = "547--556",
month = oct,
year = "2004",
CODEN = "IJNADH",
DOI = "http://dx.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/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://imanum.oupjournals.org/cgi/content/abstract/24/4/547;
http://imanum.oupjournals.org/cgi/reprint/24/4/547",
abstract = "The Lagrange representation of the interpolating
polynomial can be rewritten in two more computationally
attractive forms: a modified Lagrange form and a
barycentric form. We give an error analysis of the
evaluation of the interpolating polynomial using these
two forms. The modified Lagrange formula is shown to be
backward stable. The barycentric formula has a less
favourable error analysis, but is forward stable for
any set of interpolating points with a small Lebesgue
constant. Therefore the barycentric formula can be
significantly less accurate than the modified Lagrange
formula only for a poor choice of interpolating points.
This analysis provides further weight to the argument
of Berrut and Trefethen that barycentric Lagrange
interpolation should be the polynomial interpolation
method of choice.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Bini:2005:AMR,
author = "Dario A. Bini and Nicholas J. Higham and Beatrice
Meini",
title = "Algorithms for the matrix $p$ th root",
journal = j-NUMER-ALGORITHMS,
volume = "39",
number = "4",
pages = "349--378",
month = aug,
year = "2005",
CODEN = "NUALEG",
DOI = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@InProceedings{Davies:2005:CMF,
author = "Philip I. Davies and Nicholas J. Higham",
editor = "Artan Bori{\c{c}i} and others",
booktitle = "{QCD and numerical analysis III. Proceedings of the
third international workshop on numerical analysis and
lattice QCD, Edinburgh, UK, June 30--July 4, 2003}",
title = "Computing $ f({A})b $ for matrix functions $f$",
volume = "47",
publisher = pub-SPRINGER,
address = pub-SPRINGER:adr-NY,
pages = "15--24",
year = "2005",
DOI = "http://dx.doi.org/10.1007/3-540-28504-0_2",
MRclass = "65F30 (15A99)",
MRnumber = "MR2180116",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
series = "Lecture Notes in Computational Science and
Engineering",
ZMnumber = "1117.65319",
abstract = "For matrix functions $f$ we investigate how to compute
a matrix-vector product $ f(A)b $ without explicitly
computing $ f(A) $. A general method is described that
applies quadrature to the matrix version of the Cauchy
integral theorem. Methods specific to the logarithm,
based on quadrature, and fractional matrix powers,
based on solution of an ordinary differential equation
initial value problem, are also presented.",
acknowledgement = ack-nhfb,
classmath = "65F30 (Other matrix algorithms); 15A54 (Matrices over
function rings)",
keywords = "Cauchy integral theorem; fractional matrix powers;
logarithm; matrix functions; matrix-vector product;
quadrature",
}
@Article{Hargreaves:2005:EAM,
author = "Gareth I. Hargreaves and Nicholas J. Higham",
title = "Efficient algorithms for the matrix cosine and sine",
journal = j-NUMER-ALGORITHMS,
volume = "40",
number = "4",
pages = "383--400",
year = "2005",
CODEN = "NUALEG",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Higham:2005:BRS,
author = "Nicholas J. Higham",
title = "Book Review: {The SIAM 100-Digit Challenge: A Study in
High-Accuracy Numerical Computing. By Folkmar
Bornemann, Dirk Laurie, Stan Wagon, and J{\"o}rg
Waldvogel. SIAM, Philadelphia, 2004. \$57.00. xii + 306
pp., hardcover. ISBN 0-89871-561-X}",
journal = j-SIAM-REVIEW,
volume = "47",
number = "2",
pages = "382--383",
month = jun,
year = "2005",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri May 27 14:40:10 MDT 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/47/2;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97149",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Higham:2005:FPM,
author = "Nicholas J. Higham and D. Steven Mackey and Niloufer
Mackey and Fran{\c{c}}oise Tisseur",
title = "Functions Preserving Matrix Groups and Iterations for
the Matrix Square Root",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "26",
number = "3",
pages = "849--877",
month = jul,
year = "2005",
CODEN = "SJMAEL",
DOI = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/44221",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
}
@Article{Higham:2005:SSM,
author = "Nicholas J. Higham",
title = "The Scaling and Squaring Method for the Matrix
Exponential Revisited",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "26",
number = "4",
pages = "1179--1193",
month = oct,
year = "2005",
CODEN = "SJMAEL",
DOI = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/61101",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Guo:2006:SNM,
author = "Chun-Hua Guo and Nicholas J. Higham",
title = "A {Schur--Newton} Method for the Matrix {\boldmath
$p$}th Root and its Inverse",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "28",
number = "3",
pages = "788--804",
month = jan,
year = "2006",
CODEN = "SJMAEL",
DOI = "http://dx.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/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2006:CLM,
author = "Nicholas J. Higham and D. Steven Mackey and
Fran{\c{c}}oise Tisseur",
title = "The Conditioning of Linearizations of Matrix
Polynomials",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "28",
number = "4",
pages = "1005--1028",
month = jan,
year = "2006",
CODEN = "SJMAEL",
DOI = "http://dx.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/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2006: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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InCollection{Corless:2007:SAL,
author = "Robert M. Corless and Hui Ding and Nicholas J. Higham
and David J. Jeffrey",
booktitle = "{ISSAC 2007}",
title = "The solution of {$ S \exp (S) = A $} is not always the
{Lambert} {$W$} function of {$A$}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "116--121",
year = "2007",
DOI = "http://dx.doi.org/10.1145/1277548.1277565",
MRclass = "34K05 (34A05 68W30)",
MRnumber = "MR2396192 (2009e:34187)",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.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/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2007:BEP,
author = "Nicholas J. Higham and Ren-Cang Li and Fran{\c{c}}oise
Tisseur",
title = "Backward error of polynomial eigenproblems solved by
linearization",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "29",
number = "4",
pages = "1218--1241",
year = "2007",
CODEN = "SJMAEL",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InCollection{Higham:2007:FM,
author = "Nicholas J. Higham",
title = "Functions of matrices",
crossref = "Hogben:2007:HLA",
pages = "??--??",
year = "2007",
bibdate = "Mon Aug 23 07:45:17 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Higham:2007:MFA,
author = "Nicholas J. Higham",
title = "Matrix Factorizations and Applications: Commentary",
crossref = "Chan:2007:MMC",
pages = "??--??",
year = "2007",
bibdate = "Sat Apr 07 11:25:30 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.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/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Al-Mohy:2008:CFD,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "Computing the {Fr{\'e}chet} derivative of the matrix
exponential, with an application to condition number
estimation",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "30",
number = "4",
pages = "1639--1657",
year = "2008",
CODEN = "SJMAEL",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Guo:2008:DSH,
author = "Chun-Hua Guo and Nicholas J. Higham and
Fran{\c{c}}oise Tisseur",
title = "Detecting and solving hyperbolic quadratic eigenvalue
problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "30",
number = "4",
pages = "1593--1613",
year = "2008",
CODEN = "SJMAEL",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Hale:2008:CRM,
author = "Nicholas Hale and Nicholas J. Higham and Lloyd N.
Trefethen",
title = "Computing {$ {\bf A}^\alpha, \ \log ({\bf A}) $}, and
related matrix functions by contour integrals",
journal = j-SIAM-J-NUMER-ANAL,
volume = "46",
number = "5",
pages = "2505--2523",
year = "2008",
CODEN = "SJNAAM",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Higham:2008:BEP,
author = "Nicholas J. Higham and Ren-Cang Li and Fran{\c{c}}oise
Tisseur",
title = "Backward Error of Polynomial Eigenproblems Solved by
Linearization",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "29",
number = "4",
pages = "1218--1241",
month = "????",
year = "2008",
CODEN = "SJMAEL",
DOI = "http://dx.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/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2008:CSE,
author = "Nicholas J. Higham",
title = "{Cayley}, {Sylvester}, and early matrix theory",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "428",
number = "1",
pages = "39--43",
year = "2008",
CODEN = "LAAPAW",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Book{Higham:2008:FMT,
author = "Nicholas J. Higham",
title = "Functions of Matrices: Theory and Computation",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xx + 425",
year = "2008",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/numana2000.bib",
note = "Theory and computation",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.doi.org/10.1002/nme.2076",
ISSN = "0029-5981",
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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
}
@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 = "http://dx.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/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Al-Mohy:2009:NSS,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "A new scaling and squaring algorithm for the matrix
exponential",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "3",
pages = "970--989",
year = "2009",
CODEN = "SJMAEL",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Guo:2009:DSH,
author = "Chun-Hua Guo and Nicholas J. Higham and
Fran{\c{c}}oise Tisseur",
title = "Detecting and Solving Hyperbolic Quadratic Eigenvalue
Problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "30",
number = "4",
pages = "1593--1613",
month = "????",
year = "2009",
CODEN = "SJMAEL",
DOI = "http://dx.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/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Guo:2009:IAA,
author = "Chun-Hua Guo and Nicholas J. Higham and
Fran{\c{c}}oise Tisseur",
title = "An improved arc algorithm for detecting definite
{Hermitian} pairs",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "3",
pages = "1131--1151",
year = "2009",
CODEN = "SJMAEL",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2009:CGP,
author = "Nicholas J. Higham and Christian Mehl and
Fran{\c{c}}oise Tisseur",
title = "The canonical generalized polar decomposition",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "4",
pages = "2163--2180",
year = "2009/10",
CODEN = "SJMAEL",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2009:DMP,
author = "Nicholas J. Higham and D. Steven Mackey and
Fran{\c{c}}oise Tisseur",
title = "Definite Matrix Polynomials and their Linearization by
Definite Pencils",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "2",
pages = "478--502",
month = "????",
year = "2009",
CODEN = "SJMAEL",
DOI = "http://dx.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/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2009:SSM,
author = "Nicholas J. Higham",
title = "The Scaling and Squaring Method for the Matrix
Exponential Revisited",
journal = j-SIAM-REVIEW,
volume = "51",
number = "4",
pages = "747--764",
month = "????",
year = "2009",
CODEN = "SIREAD",
DOI = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Trefethen:2009:DHP,
author = "Anne Trefethen and Nick Higham and Iain Duff and Peter
Coveney",
title = "Developing a High-Performance Computing\slash
Numerical Analysis Roadmap",
journal = j-IJHPCA,
volume = "23",
number = "4",
pages = "423--426",
month = nov,
year = "2009",
CODEN = "IHPCFL",
DOI = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://hpc.sagepub.com/content/23/4/423.full.pdf+html",
acknowledgement = ack-nhfb,
journal-URL = "http://hpc.sagepub.com/content/by/year",
}
@Article{Al-Mohy:2010:CSA,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "The complex step approximation to the {Fr{\'e}chet}
derivative of a matrix function",
journal = j-NUMER-ALGORITHMS,
volume = "53",
number = "1",
pages = "133--148",
month = jan,
year = "2010",
CODEN = "NUALEG",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=53&issue=1&spage=133",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Al-Mohy:2010:NSS,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "A New Scaling and Squaring Algorithm for the Matrix
Exponential",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "3",
pages = "970--989",
month = "????",
year = "2010",
CODEN = "SJMAEL",
DOI = "http://dx.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/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Borsdorf:2010:CNC,
author = "R{\"u}diger Borsdorf and Nicholas J. Higham and Marcos
Raydan",
title = "Computing a Nearest Correlation Matrix with Factor
Structure",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "5",
pages = "2603--2622",
month = "????",
year = "2010",
CODEN = "SJMAEL",
DOI = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Borsdorf:2010:PNA,
author = "R{\"u}diger Borsdorf and Nicholas J. Higham",
title = "A preconditioned {Newton} algorithm for the nearest
correlation matrix",
journal = j-IMA-J-NUMER-ANAL,
volume = "30",
number = "1",
pages = "94--107",
month = jan,
year = "2010",
CODEN = "IJNADH",
DOI = "http://dx.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/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://imajna.oxfordjournals.org/cgi/content/abstract/30/1/94;
http://imajna.oxfordjournals.org/cgi/reprint/30/1/94",
abstract = "Various methods have been developed for computing the
correlation matrix nearest in the Frobenius norm to a
given matrix. We focus on a quadratically convergent
Newton algorithm recently derived by Qi and Sun.
Various improvements to the efficiency and reliability
of the algorithm are introduced. Several of these
relate to the linear algebra: the Newton equations are
solved by minres instead of the conjugate gradient
method, as it more quickly satisfies the inexact Newton
condition; we apply a Jacobi preconditioner, which can
be computed efficiently even though the coefficient
matrix is not explicitly available; an efficient choice
of eigensolver is identified; and a final scaling step
is introduced to ensure that the returned matrix has
unit diagonal. Potential difficulties caused by
rounding errors in the Armijo line search are avoided
by altering the step selection strategy. These and
other improvements lead to a significant speed-up over
the original algorithm and allow the solution of
problems of dimension a few thousand in a few tens of
minutes.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Guo:2010:IAA,
author = "Chun-Hua Guo and Nicholas J. Higham and
Fran{\c{c}}oise Tisseur",
title = "An Improved Arc Algorithm for Detecting Definite
{Hermitian} Pairs",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "3",
pages = "1131--1151",
month = "????",
year = "2010",
CODEN = "SJMAEL",
DOI = "http://dx.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/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2010:CGP,
author = "Nicholas J. Higham and Christian Mehl and
Fran{\c{c}}oise Tisseur",
title = "The Canonical Generalized Polar Decomposition",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "4",
pages = "2163--2180",
month = "????",
year = "2010",
CODEN = "SJMAEL",
DOI = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2010:CMF,
author = "Nicholas J. Higham and Awad H. Al-Mohy",
title = "Computing matrix functions",
journal = j-ACTA-NUMERICA,
volume = "19",
pages = "159--208",
year = "2010",
CODEN = "ANUMFU",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
fjournal = "Acta Numerica",
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 = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sisc/resource/1/sjoce3/v33/i2/p488_s1",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "March 01, 2011",
}
@Article{Grammont:2011:FAN,
author = "Laurence Grammont and Nicholas J. Higham and
Fran{\c{c}}oise Tisseur",
title = "A framework for analyzing nonlinear eigenproblems and
parametrized linear systems",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "435",
number = "3",
pages = "623--640",
day = "1",
month = aug,
year = "2011",
CODEN = "LAAPAW",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:2011:RSM,
author = "Nicholas J. Higham and Lijing Lin",
title = "On $p$-th roots of stochastic matrices",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "435",
number = "3",
pages = "448--463",
day = "1",
month = aug,
year = "2011",
CODEN = "LAAPAW",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:2011:SPA,
author = "Nicholas J. Higham and Lijing Lin",
title = "A {Schur--Pad{\'e}} Algorithm for Fractional Powers of
a Matrix",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "32",
number = "3",
pages = "1056--1078",
month = "????",
year = "2011",
CODEN = "SJMAEL",
DOI = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "September 29, 2011",
}
@Article{Al-Mohy:2012:IIS,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "Improved Inverse Scaling and Squaring Algorithms for
the Matrix Logarithm",
journal = j-SIAM-J-SCI-COMP,
volume = "34",
number = "4",
pages = "C153--C169",
year = "2012",
CODEN = "SJOCE3",
DOI = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2012",
}
@Article{Nakatsukasa:2012:BSI,
author = "Yuji Nakatsukasa and Nicholas J. Higham",
title = "Backward Stability of Iterations for Computing the
Polar Decomposition",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "33",
number = "2",
pages = "460--479",
month = "????",
year = "2012",
CODEN = "SJMAEL",
DOI = "http://dx.doi.org/10.1137/110857544",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Tue Oct 30 14:04:27 MDT 2012",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/33/2;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2012",
}
@Article{Al-Mohy:2013:CFD,
author = "Awad H. Al-Mohy and Nicholas J. Higham and Samuel D.
Relton",
title = "Computing the {Fr{\'e}chet} derivative of the matrix
logarithm and estimating the condition number",
journal = j-SIAM-J-SCI-COMP,
volume = "35",
number = "4",
pages = "C394--C410",
year = "2013",
CODEN = "SJOCE3",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Betcke:2013:NCN,
author = "Timo Betcke and Nicholas J. Higham and Volker Mehrmann
and Christian Schr{\"o}der and Fran{\c{c}}oise
Tisseur",
title = "{NLEVP}: a collection of nonlinear eigenvalue
problems",
journal = j-TOMS,
volume = "39",
number = "2",
pages = "Art. 7, 28",
year = "2013",
CODEN = "ACMSCU",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=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:??",
month = jul,
year = "2013",
CODEN = "ACMSCU",
DOI = "http://dx.doi.org/10.1145/2491491.2491494",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Jul 19 17:20:56 MDT 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "It is a widespread but little-noticed phenomenon that
the normwise relative error $ || x - y || / || x || $
of vectors $x$ and $y$ of floating point numbers of the
same precision, where $y$ is an approximation to x, can
be many orders of magnitude smaller than the unit
roundoff. We analyze this phenomenon and show that in
the $ \infty $-norm it happens precisely when $x$ has
components of widely varying magnitude and every
component of $x$ of largest magnitude agrees with the
corresponding component of $y$. Performance profiles
are a popular way to compare competing algorithms
according to particular measures of performance. We
show that performance profiles based on normwise
relative errors can give a misleading impression due to
the influence of zero or tiny normwise relative errors.
We propose a transformation that reduces the influence
of these extreme errors in a controlled manner, while
preserving the monotonicity of the underlying data and
leaving the performance profile unchanged at its left
end-point. Numerical examples with both artificial and
genuine data illustrate the benefits of the
transformation.",
acknowledgement = ack-nhfb,
articleno = "24",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "http://portal.acm.org/toc.cfm?idx=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",
year = "2013",
CODEN = "SJMAEL",
DOI = "http://dx.doi.org/10.1137/130906118",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F60 (15A16)",
MRnumber = "3102571",
bibdate = "Thu Mar 6 09:16:29 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{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 = "http://dx.doi.org/10.1137/120876605",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Fri Jul 19 07:43:53 MDT 2013",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/35/3;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2013",
}
@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 = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/ijsa.bib;
http://www.math.utah.edu/pub/tex/bib/pvm.bib",
URL = "http://hpc.sagepub.com/content/28/1/97.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "International Journal of High Performance Computing
Applications",
journal-URL = "http://hpc.sagepub.com/content/by/year",
onlinedate = "July 11, 2013",
}
@Article{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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
}
%%% ====================================================================
%%% 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",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Mar 22 15:39:54 MST 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
http://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://doi.acm.org/10.1145/77626.77627;
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://portal.acm.org/toc.cfm?idx=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 = "http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
http://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://portal.acm.org/toc.cfm?idx=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 = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "The Eighth EPSRC Numerical Analysis Summer School was
held at the University of Leicester from the 5th to the
17th of July, 1998.",
series = "Springer series in computational mathematics",
acknowledgement = ack-nhfb,
keywords = "numerical analysis",
}
@Proceedings{Higham:1998:NAP,
editor = "D. J. (Desmond J.) Higham and G. A. Watson and D. F.
(David Francis) Griffiths",
booktitle = "{Numerical analysis 1997: Proceedings of the 17th
Dundee Biennial Conference, June 24--27, 1997}",
title = "{Numerical analysis 1997: proceedings of the 17th
Dundee Biennial Conference, June 24--27, 1997}",
volume = "380",
publisher = pub-LONGMAN-ST,
address = pub-LONGMAN-ST:adr,
pages = "254",
year = "1998",
ISBN = "0-582-31261-2 (paperback)",
ISBN-13 = "978-0-582-31261-6 (paperback)",
ISSN = "0269-3674",
LCCN = "QA297 .D85 1997",
bibdate = "Tue Jan 3 15:19:05 MST 2006",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
melvyl.cdlib.org:210/CDL90",
series = "Pitman Research Notes in Mathematics",
acknowledgement = ack-nhfb,
meetingname = "Dundee Conference on Numerical Analysis (17th: 1997)",
subject = "Numerical analysis; Congresses",
}
@Proceedings{Higham:2001:PEC,
editor = "Nicholas J. Higham and Roger Horn and Thomas J.
Laffey",
booktitle = "Proceedings of the {Eighth Conference of the
International Linear Algebra Society}",
title = "Proceedings of the {Eighth Conference of the
International Linear Algebra Society}",
publisher = pub-ELS,
address = pub-ELS:adr,
pages = "x--xii + 1--609",
year = "2001",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
MRclass = "00B25 (15-06)",
MRnumber = "MR1839422",
bibdate = "Sat Apr 16 17:55:00 2005",
bibsource = "http://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,
}
@Book{Chan:2007:MMC,
editor = "Raymond H. Chan and Chen Greif and Dianne P. O'Leary",
booktitle = "Milestones in matrix computation: the selected works
of {Gene H. Golub} with commentaries",
title = "Milestones in matrix computation: the selected works
of {Gene H. Golub} with commentaries",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xi + 565",
year = "2007",
ISBN = "0-19-920681-3",
ISBN-13 = "978-0-19-920681-0",
LCCN = "????",
bibdate = "Sat Apr 07 10:23:33 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
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 = "Gene H. Golub\\
Biography, Chen Greif\\
Publications of Gene H. Golub\\
Major Awards\\
Students of Gene H. Golub\\
Iterative Methods for Linear Systems\\
Commentary, Anne Greenbaum\\
References\\
Chebyshev semi-iterative methods, successive
over-relaxation iterative methods, and second-order
Richardson iterative methods, Parts I. and II, G. Golub
and R. S. Varga\\
A generalized conjugate gradient method for
non-symmetric systems of linear equations, P. Concus
and G. Golub\\
A generalized conjugate gradient method for the
numerical solution of elliptic partial differential
equations, P. Concus, G. Golub, D. O'Leary\\
Hermitian and Skew-Hermitian splitting methods for
non-Hermitian positive definite linear systems, Z.-Z.
Bai, G. Golub, M. K. Ng\\
Solution of Least Squares Problems\\
Commentary, {\AA}ke Bj{\"o}rck\\
References\\
Numerical methods for solving linear least squares
problems, G. Golub\\
Singular value decomposition and least squares
solutions, G. Golub and C. Reinsch\\
The differentiation of pseudo-inverses and non-linear
least squares problems whose variables separate, G.
Golub and V. Pereyra\\
Generalized cross-validation as a method for choosing a
good ridge parameter, G. Golub, M. Heath, G. Wahba\\
An analysis of the total least squares problem, G.
Golub and C. Van Loan\\
Matrix Factorizations and Applications\\
Commentary, Nicholas Higham\\
References\\
Calculating the singular values and pseudo-inverse of a
matrix, G. Golub and W. Kahan\\
The simplex method of linear programming using LU
decomposition, R. Bartels and G. Golub\\
On direct methods for solving Poisson's equation, B. L.
Buzbee, G. Golub, C. W. Nielson\\
Numerical methods for computing angles between linear
subspaces, {\AA}. Bj{\"o}rck, G. Golub\\
Methods for modifying matrix factorizations, P. Gill,
G. Golub, W. Murray, M. Saunders\\
Orthogonal Polynomials and Quadrature\\
Commentary, Walter Gautschi\\
References\\
Calculation of Gauss quadrature rules, G. Golub, J.
Welsch\\
Matrices, moments and quadrature, G. Golub, G.
Meurant\\
Computation of Gauss--Kronrod quadrature rules, D.
Calvetti, G. Golub, W. Gragg, L. Reichel\\
Eigenvalue Problems\\
Commentary, G. W. Stewart\\
References\\
Some modified matrix eigenvalue problems, G. Golub\\
Ill-conditioned eigensystems and the computation of the
Jordan canonical form, G. Golub, J. Wilkinson\\
The block Lanczos method for computing eigenvalues, G.
Golub, R. Underwood\\
The numerically stable reconstruction of a Jacobi
matrix from spectral data, C. de Boor, G. Golub",
}
@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 = "????",
year = "2007",
ISBN = "1-58488-510-6",
ISBN-13 = "978-1-58488-510-8",
LCCN = "QA184.2 .H36 2007",
bibdate = "Sun Aug 22 10:30:50 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
z3950.loc.gov:7090/Voyager",
series = "Discrete mathematics and its applications",
URL = "http://www.loc.gov/catdir/enhancements/fy0647/2006045491-d.html",
acknowledgement = ack-nhfb,
keywords = "Maple",
remark = "Associate editors: Richard Brualdi, Anne Greenbaum,
and Roy Mathias.",
subject = "Algebras, Linear",
tableofcontents = "I. Linear algebra \\
Vectors, matrices and systems of linear equations /
Jane Day \\
Linear independence, span, and bases / Mark Mills \\
Linear transformations / Francesco Barioli \\
Determinants and eigenvalues / Luz M. DeAlba \\
Inner product spaces, orthogonal projection, least
squares and singular value decomposition / Lixing Han
and Michael Neumann \\
Canonical forms / Leslie Hogben \\
Unitary similarity, normal matrices, and spectral
theory / Helene Shapiro \\
Hermitian and positive definite matrices / Wayne
Barrett \\
Nonnegative and stochastic matrices / Uriel G. Rothblum
\\
Partitioned matrices / Robert Reams \\
Functions of matrices / Nicholas J. Higham \\
Quadratic, bilinear and sesquilinear forms / Raphael
Loewy \\
Multilinear algebra / J.A. Dias de Silva and Armando
Machado \\
Matrix equalities and inequalities / Michael
Tsatsomeros \\
Matrix perturbation theory / Ren-Cang Li \\
Pseudospectra / Mark Embree \\
Singular values and singular value inequalities / Roy
Mathias \\
Numerical range / Chi-Kwong Li \\
Matrix stability and inertia / Daniel Hershkowitz \\
Inverse eigenvalue problems / Alberto Borobia \\
Totally positive and totally negative matrices / Shaun
M. Fallat \\
Linear preserver problems / Peter Semrl \\
Matrices over integral domains / Shmuel Friedland \\
Similarities of families of matrices / Shmuel Friedland
\\
Max-plus algebra / Marianne Akian, Ravindra Bapat,
St{\'e}phane Gaubert \\
Matrices leaving a cone invariant / Bit-Shun Tam and
Hans Schneider \\
II. Combinatorial matrix theory and graphs \\
Combinatorial matrix theory / Richard A. Brualdi \\
Matrices and graphs / Willem H. Haemers \\
Digraphs and matrices / Jeffrey L. Stuart \\
Bipartite graphs and matrices / Bryan L. Shader \\
Permanents / Ian M. Wanless \\
D-optimal designs / Michael G. Neubauer and William
Watkins \\
Sign pattern matrices / Frank J. Hall and Zhongshan Li
\\
Multiplicity lists for the eigenvalues of symmetric
matrices with a given graph / Charles R. Johnson, Anto
nio Leal Duarte, and Carlos M. Saiago \\
Matrix completion problems / Leslie Hogben and Amy
Wangsness \\
Algebraic connectivity / Steve Kirkland \\
III. Numerical methods \\
Vector and matrix norms, error analysis, efficiency and
stability / Ralph Byers and Biswa Nath Datta \\
Matrix factorizations, and direct solution of linear
systems / Christopher Beattie \\
Least squares solution of linear systems / Per
Christian Hansen and Hans Bruun Nielsen \\
Sparse matrix methods / Esmond G. Ng \\
Iterative solution methods for linear systems / Anne
Greenbaum \\
Symmetric matrix eigenvalue techniques / Ivan Slapnicar
\\
Unsymmetric matrix eigenvalue techniques / David S.
Watkins \\
The implicitly restarted Arnoldi method / D.C. Sorensen
\\
Computation of the singular value decomposition / Alan
Kaylor Cline and Inderjit S. Dhillon \\
Computing eigenvalues and singular values to high
relative accuracy / Zlatko Drmac \\
Fast matrix multiplication / Dario A. Bini \\
Structured matrix computations / Michael Ng \\
Large-scale matrix computations / Roland W. Freund \\
IV. Applications \\
Linear programming / Leonid S. Vaserstein \\
Semidefinite programming / Henry Wolkowicz \\
Random vectors and linear statistical models / Simo
Puntanen and George P.H. Styan \\
Multivariate statistical analysis / Simo Puntanen,
George A.F. Seber, and George P.H. Styan \\
Markov chains / Beatrice Meini \\
Differential equations and stability / Volker Mehrmann
and Tatjana Stykel \\
Dynamical systems and linear algebra / Fritz Colonius
and Wolfgang Kliemann \\
Control theory / Peter Benner \\
Fourier analysis / Kenneth Howell \\
Linear algebra and mathematical physics / Lorenzo Sadun
\\
Linear algebra in biomolecular modeling / Zhijun Wu \\
Coding theory / Joachim Rosenthal and Paul Weiner \\
Quantum computation / Zijian Diao \\
Information retrieval and web search / Amy Langville
and Carl Meyer \\
Signal processing / Michael Stewart \\
Geometry / Mark Hunacek \\
Some applications of matrices and graphs in Euclidean
geometry / Miroslav Fiedler \\
Matrix groups / Peter J. Cameron \\
Group representations / Randall Holmes and T.Y. Tam \\
Nonassociative algebras / Murray R. Bremner, Lucia I.
Muakami and Ivan P. Shestakov \\
Lie algebras / Robert Wilson \\
V. Computational software \\
MATLAB / Steven J. Leon \\
Linear algebra in Maple / David J. Jeffrey and Robert
M. Corless \\
Mathematica / Heikki Ruskeep{\"a}{\"a} \\
BLAS / Jack Dongarra, Victor Eijkhout, and Julien
Langou \\
LAPACK / Zhaojun Bai \\
Use of ARPACK and EIGS / D.C. Sorensen",
}
%%% Last MathSciNet search: Thu Mar 6 09:20:03 2014