%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author = "Nelson H. F. Beebe",
%%% version = "1.70",
%%% date = "11 December 2023",
%%% time = "12:05:19 MST",
%%% filename = "numana2010.bib",
%%% address = "University of Utah
%%% Department of Mathematics, 110 LCB
%%% 155 S 1400 E RM 233
%%% Salt Lake City, UT 84112-0090
%%% USA",
%%% telephone = "+1 801 581 5254",
%%% FAX = "+1 801 581 4148",
%%% URL = "https://www.math.utah.edu/~beebe",
%%% checksum = "22496 10970 57807 559392",
%%% email = "beebe at math.utah.edu, beebe at acm.org,
%%% beebe at computer.org (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "bibliography; BibTeX; numerical analysis",
%%% license = "public domain",
%%% supported = "yes",
%%% docstring = "This bibliography collects publications
%%% in the large field of numerical analysis
%%% from books and conference proceedings, but
%%% excluding journal articles, which are covered
%%% in separate bibliographies in the TeX User
%%% Group archive.
%%%
%%% This file includes publications for the
%%% decade 2010--2019.
%%%
%%% At version 1.70, the year coverage looked
%%% like this:
%%%
%%% 2010 ( 31) 2014 ( 23) 2018 ( 6)
%%% 2011 ( 31) 2015 ( 7) 2019 ( 1)
%%% 2012 ( 26) 2016 ( 6)
%%% 2013 ( 20) 2017 ( 9)
%%%
%%% Article: 3
%%% Book: 150
%%% Proceedings: 7
%%%
%%% Total entries: 160
%%%
%%% The initial draft of entries for 2000--2009
%%% was derived from the OCLC Proceedings
%%% database, from the MathSciNet database, from
%%% the University of California Melvyl catalog,
%%% and from the U.S. Library of Congress
%%% catalog.
%%%
%%% In this bibliography, entries are sorted
%%% first by ascending year, and within each
%%% year, alphabetically by author or editor,
%%% and then, if necessary, by the 3-letter
%%% abbreviation at the end of the BibTeX
%%% citation tag, using the bibsort -byyear
%%% utility. Year order has been chosen to
%%% make it easier to identify the most recent
%%% work.
%%%
%%% The checksum field above contains a CRC-16
%%% checksum as the first value, followed by the
%%% equivalent of the standard UNIX wc (word
%%% count) utility output of lines, words, and
%%% characters. This is produced by Robert
%%% Solovay's checksum utility.",
%%% }
%%% ====================================================================
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%%%=====================================================================
%%% Acknowledgement abbreviations:
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|https://www.math.utah.edu/~beebe/|"}
%%%=====================================================================
%%% Journal abbreviations:
@String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"}
@String{j-HIST-MATH = "Historia Mathematica"}
@String{j-SIAM-REVIEW = "SIAM Review"}
%%%=====================================================================
%%% Publishers and their addresses:
@String{pub-ACADEMIC = "Academic Press"}
@String{pub-ACADEMIC:adr = "New York, NY, USA"}
@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-BIRKHAUSER = "Birkh{\"{a}}user"}
@String{pub-BIRKHAUSER:adr = "Cambridge, MA, USA; Berlin, Germany; Basel,
Switzerland"}
@String{pub-BIRKHAUSER-BOSTON = "Birkh{\"a}user Boston Inc."}
@String{pub-BIRKHAUSER-BOSTON:adr = "Cambridge, MA, USA"}
@String{pub-CAMBRIDGE = "Cambridge University Press"}
@String{pub-CAMBRIDGE:adr = "Cambridge, UK"}
@String{pub-CHAPMAN-HALL-CRC = "Chapman and Hall/CRC"}
@String{pub-CHAPMAN-HALL-CRC:adr = "Boca Raton, FL, USA"}
@String{pub-CLARENDON = "Clarendon Press"}
@String{pub-CLARENDON:adr = "New York, NY, USA"}
@String{pub-CRC = "CRC Press"}
@String{pub-CRC:adr = "2000 N.W. Corporate Blvd., Boca Raton, FL
33431-9868, USA"}
@String{pub-DOVER = "Dover"}
@String{pub-DOVER:adr = "New York, NY, USA"}
@String{pub-ELSEVIER-ACADEMIC = "Elsevier Academic Press"}
@String{pub-ELSEVIER-ACADEMIC:adr = "Amsterdam, The Netherlands"}
@String{pub-GRUYTER = "Walter de Gruyter"}
@String{pub-GRUYTER:adr = "New York"}
@String{pub-JOHNS-HOPKINS = "The Johns Hopkins University Press"}
@String{pub-JOHNS-HOPKINS:adr = "Baltimore, MD, USA"}
@String{pub-KNOPF = "Alfred A. Knopf"}
@String{pub-KNOPF:adr = "New York, NY, USA"}
@String{pub-OLDENBOURG = "R. Oldenbourg"}
@String{pub-OLDENBOURG:adr = "M{\"u}nchen, Germany"}
@String{pub-OXFORD = "Oxford University Press"}
@String{pub-OXFORD:adr = "Walton Street, Oxford OX2 6DP, UK"}
@String{pub-PACKT = "Packt Publishing"}
@String{pub-PACKT:adr = "Birmingham, UK"}
@String{pub-PH = "Pren{\-}tice-Hall"}
@String{pub-PH:adr = "Upper Saddle River, NJ 07458, USA"}
@String{pub-PRINCETON = "Princeton University Press"}
@String{pub-PRINCETON:adr = "Princeton, NJ, USA"}
@String{pub-SIAM = "Society for Industrial and Applied
Mathematics"}
@String{pub-SIAM:adr = "Philadelphia, PA, USA"}
@String{pub-SV = "Springer-Verlag"}
@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg, Germany~/
London, UK~/ etc."}
@String{pub-WILEY = "Wiley"}
@String{pub-WILEY:adr = "New York, NY, USA"}
@String{pub-WORLD-SCI = "World Scientific Publishing Co."}
@String{pub-WORLD-SCI:adr = "Singapore; Philadelphia, PA, USA; River
Edge, NJ, USA"}
%%% ====================================================================
%%% Series abbreviations:
@String{ser-LECT-NOTES-MATH = "Lecture Notes in Mathematics"}
@String{ser-LNAI = "Lecture Notes in Artificial Intelligence"}
@String{ser-LNCS = "Lecture Notes in Computer Science"}
@String{ser-LNCSE = "Lecture Notes in Computational
Science and Engineering"}
%%%=====================================================================
%%% Bibliography entries, sorted by year, and then by citation label,
%%% with `bibsort -byyear':
@Book{Ackleh:2010:CMN,
author = "Azmy S. Ackleh and Edward James Allen and Ralph Baker
Kearfott and Padmanabhan Seshaiyer",
title = "Classical and modern numerical analysis: theory,
methods and practice",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xix + 608",
year = "2010",
ISBN = "1-4200-9157-3 (hardcover)",
ISBN-13 = "978-1-4200-9157-1 (hardcover)",
LCCN = "QA297 .C53 2010",
MRclass = "65-01",
MRnumber = "2555915",
bibdate = "Tue May 27 12:10:25 MDT 2014",
bibsource = "aubrey.tamu.edu:7090/voyager;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
note = "Theory, methods and practice",
series = "Chapman and Hall/CRC numerical analysis and scientific
computing",
abstract = "The book provides a sound foundation in numerical
analysis for more specialized topics, such as finite
element theory, advanced numerical linear algebra, and
optimization. It prepares graduate students for taking
doctoral examinations in numerical analysis. The text
covers the main areas of introductory numerical
analysis, including the solution of nonlinear
equations, numerical linear algebra, ordinary
differential equations, approximation theory, numerical
integration, and boundary value problems. Focusing on
interval computing in numerical analysis, it explains
interval arithmetic, interval computation, and interval
algorithms. The authors illustrate the concepts with
many examples as well as analytical and computational
exercises at the end of each chapter. This advanced,
graduate-level introduction to the theory and methods
of numerical analysis supplies the necessary background
in numerical methods so that students can apply the
techniques and understand the mathematical literature
in this area.",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Data processing",
xxeditor = "Azmy S. Ackleh and Padmanabhan Seshaiyer and Ralph
Baker Kearfott and Edward James Allen",
}
@Book{BaezLopez:2010:MAE,
author = "David {B{\'a}ez L{\'o}pez}",
title = "{MATLAB} with applications to engineering, physics and
finance",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xiv + 412",
year = "2010",
ISBN = "1-4398-0697-7 (hardcover)",
ISBN-13 = "978-1-4398-0697-5 (hardcover)",
LCCN = "QA297 .B28 2010",
MRclass = "65-01",
MRnumber = "2574020",
bibdate = "Tue May 27 12:31:50 MDT 2014",
bibsource = "clas.caltech.edu:210/INNOPAC;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "``A Chapman and Hall book.''.",
subject = "Numerical analysis; Data processing; MATLAB",
}
@Book{Baumgarte:2010:NRS,
author = "Thomas W. Baumgarte and Stuart L. (Stuart Louis)
Shapiro",
title = "Numerical relativity: solving {Einstein}'s equations
on the computer",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xviii + 698",
year = "2010",
ISBN = "0-521-51407-X",
ISBN-13 = "978-0-521-51407-1",
LCCN = "QC173.6 .B38 2010",
bibdate = "Fri Oct 7 08:35:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/einstein.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "General relativity (Physics); Einstein field
equations; Numerical calculations",
tableofcontents = "General relativity preliminaries \\
The $3 + 1$ decomposition of Einstein's equations \\
Constructing initial data \\
Choosing coordinates: the lapse and shift \\
Matter sources \\
Numerical methods \\
Locating black hole horizons \\
Spherically symmetric spacetimes \\
Gravitational waves \\
Collapse of collisionless clusters in axisymmetry \\
Recasting the evolution equations \\
Binary black hole initial data \\
Binary black hole evolution \\
Rotating stars \\
Binary neutron star initial data \\
Binary neutron star evolution \\
Binary black hole-neutron stars: initial data and
evolution",
}
@Book{Bockhorn:2010:MMA,
editor = "Henning Bockhorn and Dieter Mewes and Wolfgang Peukert
and Hans-Joachim Warnecke",
title = "Micro- and macromixing: analysis, simulation and
numerical calculation",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xi + 346",
year = "2010",
DOI = "https://doi.org/10.1007/978-3-642-04549-3",
ISBN = "3-642-04549-9, 3-642-04548-0",
ISBN-13 = "978-3-642-04549-3, 978-3-642-04548-6",
LCCN = "TP156.M5 M537 2010",
bibdate = "Mon Aug 23 11:05:53 MDT 2010",
bibsource = "aubrey.tamu.edu:7090/voyager;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Heat and mass transfer",
acknowledgement = ack-nhfb,
subject = "mixing; equipment and supplies; mathematical models",
}
@Book{Burden:2010:NA,
author = "Richard L. Burden and J. Douglas Faires",
title = "Numerical analysis",
publisher = "Cengage Learning",
address = "Boston, MA, USA",
edition = "Nineth",
pages = "????",
year = "2010",
ISBN = "0-538-73351-9",
ISBN-13 = "978-0-538-73351-9",
LCCN = "????",
bibdate = "Mon Aug 23 10:50:14 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
}
@Book{Christensen:2010:FSE,
author = "Ole Christensen",
title = "Functions, spaces, and expansions: mathematical tools
in physics and engineering",
publisher = pub-BIRKHAUSER-BOSTON,
address = pub-BIRKHAUSER-BOSTON:adr,
pages = "xix + 263",
year = "2010",
DOI = "https://doi.org/10.1007/978-0-8176-4980-7",
ISBN = "0-8176-4980-8",
ISBN-13 = "978-0-8176-4980-7",
LCCN = "QA331.7 .C57 2010",
bibdate = "Mon Aug 23 11:22:11 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.gbv.de:20011/gvk",
series = "Applied and numerical harmonic analysis",
acknowledgement = ack-nhfb,
subject = "computer science; engineering mathematics; Fourier
analysis; functional analysis; functions, special;
mathematical physics; mathematics",
}
@Book{Datta:2010:NLA,
author = "Biswa Nath Datta",
title = "Numerical linear algebra and applications",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Second",
pages = "xxiv + 530",
year = "2010",
DOI = "https://doi.org/10.1137/1.9780898717655",
ISBN = "0-534-17466-3 (paperback), 0-89871-685-3",
ISBN-13 = "978-0-534-17466-8 (paperback), 978-0-89871-685-6",
LCCN = "QA184.2 .D38 2010",
MRclass = "65-01 (65Fxx)",
MRnumber = "2596938",
bibdate = "Tue May 27 12:31:49 MDT 2014",
bibsource = "clas.caltech.edu:210/INNOPAC;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
prodorbis.library.yale.edu:7090/voyager;
z3950.gbv.de:20011/gvk; z3950.loc.gov:7090/Voyager",
URL = "http://www.gbv.de/dms/ilmenau/toc/603672094.PDF;
http://www.loc.gov/catdir/enhancements/fy1001/2009025104-b.html;
http://www.loc.gov/catdir/enhancements/fy1001/2009025104-d.html;
http://www.loc.gov/catdir/enhancements/fy1001/2009025104-t.html;
http://www.zentralblatt-math.org/zmath/en/search/?an=1187.65027",
acknowledgement = ack-nhfb,
subject = "Algebras, Linear; Numerical analysis",
tableofcontents = "Linear algebra problems, their importance, and
computational difficulties \\
A review of some required concepts from core linear
algebra \\
Floating point numbers and errors in computation \\
Stability of algorithms and conditioning of problems
\\
Gaussian elimination and $LU$ factorization \\
Numerical solutions of linear systems \\
$QR$ factorization, singular value decomposition, and
projections \\
Least-squares solutions to linear systems \\
Numerical matrix eigenvalue problems \\
Numerical symmetric eigenvalue problem and singular
value decomposition \\
Generalized and quadratic eigenvalue problems \\
Iterative methods for large and sparse problems: an
overview \\
Some key terms in numerical linear algebra",
}
@Book{Etter:2010:IM,
author = "Delores M. Etter",
title = "Introduction to {MATLAB}",
publisher = pub-PH,
address = pub-PH:adr,
edition = "Second",
pages = "????",
year = "2010",
ISBN = "0-13-608123-1",
ISBN-13 = "978-0-13-608123-4",
LCCN = "TA345 .E8724 2010",
bibdate = "Mon Jan 31 15:09:54 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Engineering mathematics; Data processing; MATLAB;
Numerical analysis",
}
@Book{Golub:2010:MMQ,
author = "Gene H. Golub and G{\'e}rard Meurant",
title = "Matrices, Moments and Quadrature with Applications",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xii + 363",
year = "2010",
ISBN = "0-691-14341-2",
ISBN-13 = "978-0-691-14341-5",
MRclass = "65-02 (65D30)",
MRnumber = "MR2582949",
bibdate = "Mon May 17 14:08:36 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Princeton Series in Applied Mathematics",
ZMnumber = "1217.65056",
ZMnumber = "pre05661633",
abstract = "This computationally oriented book describes and
explains the mathematical relationships among matrices,
moments, orthogonal polynomials, quadrature rules, and
the Lanczos and conjugate gradient algorithms. The book
bridges different mathematical areas to obtain
algorithms to estimate bilinear forms involving two
vectors and a function of the matrix. The first part of
the book provides the necessary mathematical background
and explains the theory. The second part describes the
applications and gives numerical examples of the
algorithms and techniques developed in the first part.
Applications addressed in the book include computing
elements of functions of matrices; obtaining estimates
of the error norm in iterative methods for solving
linear systems and computing parameters in least
squares and total least squares; and solving ill-posed
problems using Tikhonov regularization. This book will
interest researchers in numerical linear algebra and
matrix computations, as well as scientists and
engineers working on problems involving computation of
bilinear forms.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
shorttableofcontents = "Preface / xi \\
Part 1. Theory / 1 \\
1: Introduction / 3 \\
2: Orthogonal Polynomials / 8 \\
3: Properties of Tridiagonal Matrices / 24 \\
4: The Lanczos and Conjugate Gradient Algorithms / 39
\\
5: Computation of the Jacobi Matrices / 55 \\
6: Gauss Quadrature / 84 \\
7: Bounds for Bilinear Forms $u^T f(A) v$ / 112 \\
8: Extensions to Nonsymmetric Matrices / 117 \\
9: Solving Secular Equations / 122 \\
10: Examples of Gauss Quadrature Rules / 139 \\
11: Bounds and Estimates for Elements of Functions of
Matrices / 162 \\
12: Estimates of Norms of Errors in the Conjugate
Gradient Algorithm / 200 \\
13: Least Squares Problems / 227 \\
14: Total Least Squares / 256 \\
15: Discrete Ill-Posed Problems / 280 \\
Bibliography / 335 \\
Index / 361",
tableofcontents = "Preface / xi \\
Part 1. Theory / 1 \\
1: Introduction / 3 \\
2: Orthogonal Polynomials / 8 \\
2.1 Definition of Orthogonal Polynomials / 8 \\
2.2 Three-Term Recurrences / 10 \\
2.3 Properties of Zeros / 14 \\
2.4 Historical Remarks / 15 \\
2.5 Examples of Orthogonal Polynomials / 15 \\
2.6 Variable-Signed Weight Functions / 20 \\
2.7 Matrix Orthogonal Polynomials / 21 \\
3: Properties of Tridiagonal Matrices / 24 \\
3.1 Similarity / 24 \\
3.2 Cholesky Factorizations of a Tridiagonal Matrix /
25 \\
3.3 Eigenvalues and Eigenvectors / 27 \\
3.4 Elements of the Inverse / 29 \\
3.5 The $Q D$ Algorithm / 32 \\
4: The Lanczos and Conjugate Gradient Algorithms / 39
\\
4.1 The Lanczos Algorithm / 39 \\
4.2 The Nonsymmetric Lanczos Algorithm / 43 \\
4.3 The Golub--Kahan Bidiagonalization Algorithms / 45
\\
4.4 The Block Lanczos Algorithm / 47 \\
4.5 The Conjugate Gradient Algorithm / 49 \\
5: Computation of the Jacobi Matrices / 55 \\
5.1 The Stieltjes Procedure / 55 \\
5.2 Computing the Coefficients from the Moments / 56
\\
5.3 The Modified Chebyshev Algorithm / 58 \\
5.4 The Modified Chebyshev Algorithm for Indefinite
Weight Functions / 61 \\
5.5 Relations between the Lanczos and Chebyshev
Semi-Iterative Algorithms / 62 \\
5.6 Inverse Eigenvalue Problems / 66 \\
5.7 Modifications of Weight Functions / 72 \\
6: Gauss Quadrature / 84 \\
6.1 Quadrature Rules / 84 \\
6.2 The Gauss Quadrature Rules / 86 \\
6.3 The Anti-Gauss Quadrature Rule / 92 \\
6.4 The Gauss-Kronrod Quadrature Rule / 95 \\
6.5 The Nonsymmetric Gauss Quadrature Rules / 99 \\
6.6 The Block Gauss Quadrature Rules / 102 \\
7: Bounds for Bilinear Forms $u^T f(A) v$ / 112 \\
7.1 Introduction / 112 \\
7.2 The Case $u = v$ / 113 \\
7.3 The Case $u \neq v$ / 114 \\
7.4 The Block Case / 115 \\
7.5 Other Algorithms for $u \neq v$ / 115 \\
8: Extensions to Nonsymmetric Matrices / 117 \\
8.1 Rules Based on the Nonsymmetric Lanczos Algorithm /
118 \\
8.2 Rules Based on the Arnoldi Algorithm / 119 \\
9: Solving Secular Equations / 122 \\
9.1 Examples of Secular Equations / 122 \\
9.2 Secular Equation Solvers / 129 \\
9.3 Numerical Experiments / 134 \\
Part 2. Applications / 137 \\
10: Examples of Gauss Quadrature Rules / 139 \\
10.1 The Golub and Welsch Approach / 139 \\
10.2 Comparisons with Tables / 140 \\
10.3 Using the Full $Q R$ Algorithm / 141 \\
10.4 Another Implementation of $Q R$ / 143 \\
10.5 Using the $Q L$ Algorithm / 144 \\
10.6 Gauss--Radau Quadrature Rules / 144 \\
10.7 Gauss--Lobatto Quadrature Rules / 146 \\
10.8 Anti-Gauss Quadrature Rule / 148 \\
10.9 Gauss--Kronrod Quadrature Rule / 148 \\
10.10 Computation of Integrals / 149 \\
10.11 Modification Algorithms / 155 \\
10.12 Inverse Eigenvalue Problems / 156 \\
11: Bounds and Estimates for Elements of Functions of
Matrices / 162 \\
11.1 Introduction / 162 \\
11.2 Analytic Bounds for the Elements of the Inverse /
163 \\
11.3 Analytic Bounds for Elements of Other Functions /
166 \\
11.4 Computing Bounds for Elements of $f(A)$ / 167 \\
11.5 Solving $A x = c$ and Looking at $d^T x$ / 167 \\
11.6 Estimates of $\tr(A^{-1})$ and $\det(A)$ / 168 \\
11.7 Krylov Subspace Spectral Methods / 172 \\
11.8 Numerical Experiments / 173 \\
12: Estimates of Norms of Errors in the Conjugate
Gradient Algorithm / 200 \\
12.1 Estimates of Norms of Errors in Solving Linear
Systems / 200 \\
12.2 Formulas for the $A$-Norm of the Error / 202 \\
12.3 Estimates of the $A$-Norm of the Error / 203 \\
12.4 Other Approaches / 209 \\
12.5 Formulas for the $\ell_2$ Norm of the Error / 210
\\
12.6 Estimates of the $\ell_2$ Norm of the Error / 211
\\
12.7 Relation to Finite Element Problems / 212 \\
12.8 Numerical Experiments / 214 \\
13: Least Squares Problems / 227 \\
13.1 Introduction to Least Squares / 227 \\
13.2 Least Squares Data Fitting / 230 \\
13.3 Numerical Experiments / 237 \\
13.4 Numerical Experiments for the Backward Error / 253
\\
14: Total Least Squares / 256 \\
14.1 Introduction to Total Least Squares / 256 \\
14.2 Scaled Total Least Squares / 259 \\
14.3 Total Least Squares Secular Equation Solvers / 261
\\
15: Discrete Ill-Posed Problems / 280 \\
15.1 Introduction to Ill-Posed Problems / 280 \\
15.2 Iterative Methods for Ill-Posed Problems / 295 \\
15.3 Test Problems / 298 \\
15.4 Study of the GCV Function / 300 \\
15.5 Optimization of Finding the GCV Minimum / 305 \\
15.6 Study of the $L$-Curve / 313 \\
15.7 Comparison of Methods for Computing the
Regularization Parameter / 325 \\
Bibliography / 335 \\
Index / 361",
}
@Book{Griffiths:2010:NMO,
author = "David F. (David Francis) Griffiths and Desmond J.
(Desmond J.) Higham",
title = "Numerical methods for ordinary differential equations:
initial value problems",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiv + 271",
year = "2010",
DOI = "https://doi.org/10.1007/978-0-85729-148-6",
ISBN = "0-85729-147-5",
ISBN-13 = "978-0-85729-147-9",
LCCN = "QA371 .G72 2010",
MRclass = "65-01 (65Lxx)",
MRnumber = "2759806 (2012g:65002)",
MRreviewer = "Philip W. Sharp",
bibdate = "Tue May 27 12:31:11 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
prodorbis.library.yale.edu:7090/voyager",
note = "Initial value problems",
series = "Springer Undergraduate Mathematics Series",
acknowledgement = ack-nhfb,
subject = "Differential equations; Numerical solutions",
}
@Book{King:2010:NSM,
author = "Michael R. King and Nipa A. Mody",
title = "Numerical and statistical methods for bioengineering:
applications in {MATLAB}",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xii + 581",
year = "2010",
ISBN = "0-521-87158-1, 0-511-90984-5 (e-book)",
ISBN-13 = "978-0-521-87158-7, 978-0-511-90984-9 (e-book)",
LCCN = "R857.M34 K56 2010eb",
bibdate = "Tue May 27 12:31:06 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
prodorbis.library.yale.edu:7090/voyager;
z3950.loc.gov:7090/Voyager",
series = "Cambridge texts in biomedical engineering",
URL = "http://assets.cambridge.org/97805218/71587/cover/9780521871587.jpg;
http://site.ebrary.com//lib/yale/Doc?id=10431397",
abstract = "The first MATLAB-based numerical methods textbook for
bioengineers that uniquely integrates modelling
concepts with statistical analysis, while maintaining a
focus on enabling the user to report the error or
uncertainty in their result. Between traditional
numerical method topics of linear modelling concepts,
nonlinear root finding, and numerical integration,
chapters on hypothesis testing, data regression and
probability are interweaved. A unique feature of the
book is the inclusion of examples from clinical trials
and bioinformatics, which are not found in other
numerical methods textbooks for engineers. With a
wealth of biomedical engineering examples, case studies
on topical biomedical research, and the inclusion of
end of chapter problems, this is a perfect core text
for a one-semester undergraduate course",
acknowledgement = ack-nhfb,
subject = "Biomedical engineering; Statistical methods;
Mathematics; MATLAB; TECHNOLOGY and ENGINEERING;
Biomedical.; MEDICAL; Family and General Practice.;
Allied Health Services; Medical Technology.;
Biotechnology.; Lasers in Medicine.",
tableofcontents = "1. Types and sources of numerical error \\
2. Systems of linear equations \\
3. Statistics and probability \\
4. Hypothesis testing \\
5. Root finding techniques for nonlinear equations \\
6. Numerical quadrature \\
7. Numerical integration of ordinary differential
equations \\
8. Nonlinear data regression and optimization \\
9. Basic algorithms of bioinformatics \\
Appendix A. Introduction to MATLAB \\
Appendix B. Location of nodes for Gauss-Legendre
quadrature",
}
@Book{Kiusalaas:2010:NMEa,
author = "Jaan Kiusalaas",
title = "Numerical methods in engineering with {MATLAB\reg}",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Second",
pages = "xi + 431",
year = "2010",
ISBN = "0-521-19133-5 (hardback)",
ISBN-13 = "978-0-521-19133-3 (hardback)",
LCCN = "TA345 .K58 2010",
MRclass = "65-01",
MRnumber = "2554310",
bibdate = "Tue May 27 12:10:06 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
melvyl.cdlib.org:210/CDL90;
z3950.loc.gov:7090/Voyager",
abstract = "Numerical Methods in Engineering with MATLAB is a text
for engineering students and a reference for practicing
engineers. The choice of numerical methods was based on
their relevance to engineering problems. Every method
is discussed thoroughly and illustrated with problems
involving both hand computation and programming. MATLAB
M-files accompany each method and are available on the
book website. This code is made simple and easy to
understand by avoiding complex book-keeping schemes,
while maintaining the essential features of the method.
MATLAB was chosen as the example language because of
its ubiquitous use in engineering studies and practice.
This new edition includes the new MATLAB anonymous
functions, which allow the programmer to embed
functions into the program rather than storing them as
separate files. Other changes include the addition of
rational function interpolation in Chapter 3, the
addition of Ridder's method in place of Brent's method
in Chapter 4, and the addition of downhill simplex
method in place of the Fletcher--Reeves method of
optimization in Chapter 10.",
acknowledgement = ack-nhfb,
subject = "MATLAB; Engineering mathematics; Data processing;
Numerical analysis",
tableofcontents = "Introduction to MATLAB \\
Systems of linear algebraic equations \\
Interpolation and curve fitting \\
Roots of equations \\
Numerical differentiation \\
Numerical integration \\
Initial value problems \\
Two-point boundary value problems \\
Symmetric matrix eigenvalue problems \\
Introduction to optimization",
}
@Book{Kiusalaas:2010:NMEb,
author = "Jaan Kiusalaas",
title = "Numerical methods in engineering with {Python}",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Second",
pages = "x + 422",
year = "2010",
ISBN = "0-521-19132-7 (hardcover), 0-511-67694-8 (e-book)",
ISBN-13 = "978-0-521-19132-6 (hardcover), 978-0-511-67694-9
(e-book)",
LCCN = "TA345 .K584 2010",
bibdate = "Mon Jan 31 15:16:50 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/python.bib;
melvyl.cdlib.org:210/CDL90;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Python (computer program language); MATLAB;
engineering mathematics; data processing; numerical
analysis; Python (Computer program language);
Engineering mathematics; Data processing; Numerical
analysis; Engineering; Civil engineering; Data
processing.; Python (Computer program language)",
tableofcontents = "Cover \\
Half-title \\
Title \\
Copyright \\
Contents \\
Preface to the First Edition \\
Preface to the Second Edition \\
1 Introduction to Python \\
2 Systems of Linear Algebraic Equations \\
3 Interpolation and Curve Fitting \\
4 Roots of Equations \\
5 Numerical Differentiation \\
6 Numerical Integration \\
7 Initial Value Problems \\
8 Two-Point Boundary Value Problems \\
9 Symmetric Matrix Eigenvalue Problems \\
10 Introduction to Optimization \\
Appendices \\
List of Program Modules (by Chapter) \\
Index",
}
@Book{Kornerup:2010:FPN,
author = "Peter Kornerup and David W. Matula",
title = "Finite Precision Number Systems and Arithmetic",
volume = "133",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xv + 699",
year = "2010",
ISBN = "0-521-76135-2 (hardcover)",
ISBN-13 = "978-0-521-76135-2 (hardcover)",
LCCN = "QA248 .K627 2010",
bibdate = "Sun Jun 19 14:21:37 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Encyclopedia of mathematics and its applications",
URL = "http://assets.cambridge.org/97805217/61352/cover/9780521761352.jpg;
http://catdir.loc.gov/catdir/enhancements/fy1011/2010030521-b.html;
http://catdir.loc.gov/catdir/enhancements/fy1011/2010030521-d.html;
http://catdir.loc.gov/catdir/enhancements/fy1011/2010030521-t.html",
abstract = "Fundamental arithmetic operations support virtually
all of the engineering, scientific, and financial
computations required for practical applications, from
cryptography, to financial planning, to rocket science.
This comprehensive reference provides researchers with
the thorough understanding of number representations
that is a necessary foundation for designing efficient
arithmetic algorithms. Using the elementary foundations
of radix number systems as a basis for arithmetic, the
authors develop and compare alternative algorithms for
the fundamental operations of addition, multiplication,
division, and square root with precisely defined
roundings. Various finite precision number systems are
investigated, with the focus on comparative analysis of
practically efficient algorithms for closed arithmetic
operations over these systems. Each chapter begins with
an introduction to its contents and ends with
bibliographic notes and an extensive bibliography. The
book may also be used for graduate teaching: problems
and exercises are scattered throughout the text and a
solutions manual is available for instructors.",
acknowledgement = ack-nhfb,
subject = "Arithmetic; Foundations",
tableofcontents = "Preface / xi \\
1. Radix polynomial representations / 1 \\
2. Base and digit set conversion / 59 \\
3. Addition / \\
4. Multiplication / \\
5. Division / 275 \\
6. Square root / 398 \\
7. Floating-point number systems / 447 \\
8. Modular arithmetic and residue number systems / 528
\\
9. Rational arithmetic / 63 \\
Author index / 691 \\
Index / 693",
}
@Book{Kurzak:2010:SCM,
editor = "Jakub Kurzak and David A. Bader and J. J. Dongarra",
title = "Scientific computing with multicore and accelerators",
volume = "10",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xxxiii + 480",
year = "2010",
ISBN = "1-4398-2536-X (hardback)",
ISBN-13 = "978-1-4398-2536-5 (hardback)",
LCCN = "Q183.9 .S325 2010",
bibdate = "Fri Nov 16 06:29:59 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/super.bib;
z3950.loc.gov:7090/Voyager",
series = "Chapman and Hall/CRC computational science",
acknowledgement = ack-nhfb,
subject = "Science; Data processing; Engineering; High
performance computing; Multiprocessors; MATHEMATICS /
General; MATHEMATICS / Advanced; MATHEMATICS / Number
Systems",
}
@Book{Lange:2010:NAS,
author = "Kenneth Lange",
title = "Numerical analysis for statisticians",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xvi + 604",
year = "2010",
DOI = "https://doi.org/10.1007/978-1-4419-5945-4",
ISBN = "1-4419-5944-0 (hardcover)",
ISBN-13 = "978-1-4419-5944-7 (hardcover)",
LCCN = "QA297 .L34 2010",
bibdate = "Mon Aug 23 10:50:36 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Statistics and Computing",
acknowledgement = ack-nhfb,
subject = "mathematical statistics; statistics",
}
@Book{Magoules:2010:FGC,
editor = "F. (Fr{\'e}d{\'e}ric) Magoul{\`e}s",
title = "Fundamentals of grid computing: theory, algorithms and
technologies",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xxi + 298",
year = "2010",
ISBN = "1-4398-0367-6 (hardcover)",
ISBN-13 = "978-1-4398-0367-7 (hardcover)",
LCCN = "QA76.9.C58 F86 2010",
bibdate = "Mon Aug 23 11:06:01 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Chapman and Hall/CRC numerical analysis and scientific
computing",
acknowledgement = ack-nhfb,
subject = "computational grids (computer systems)",
}
@Book{Moin:2010:FEN,
author = "Parviz Moin",
title = "Fundamentals of engineering numerical analysis",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Second",
pages = "xiv + 241",
year = "2010",
ISBN = "0-521-88432-2 (hardcover), 0-521-71123-1",
ISBN-13 = "978-0-521-88432-7 (hardcover), 978-0-521-71123-4",
LCCN = "TA335 .M65 2010",
MRclass = "65-01",
MRnumber = "2721984 (2011j:65001)",
bibdate = "Tue May 27 11:24:21 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
abstract = "Publisher's note: Since the original publication of
this book, available computer power has increased
greatly. Today, scientific computing is playing an ever
more prominent role as a tool in scientific discovery
and engineering analysis. In this second edition, the
key addition is an introduction to the finite element
method. This is a widely used technique for solving
partial differential equations (PDEs) in complex
domains. This text introduces numerical methods and
shows how to develop, analyze, and use them. Complete
MATLAB programs for all the worked examples are now
available at www.cambridge.org/Moin, and more than 30
exercises have been added. This thorough and practical
book is intended as a first course in numerical
analysis, primarily for new graduate students in
engineering and physical science. Along with mastering
the fundamentals of numerical methods, students will
learn to write their own computer programs using
standard numerical methods.",
acknowledgement = ack-nhfb,
subject = "engineering mathematics; numerical analysis",
tableofcontents = "1. Interpolation \\
2. Numerical differentiation - finite differences \\
3. Numerical integration \\
4. Numerical solution of ordinary differential
equations \\
5. Numerical solution of partial differential equations
\\
6. Discrete transform methods \\
Appendix. A review of linear algebra",
}
@Book{Oberkampf:2010:VVS,
author = "William L. Oberkampf and Christopher J. Roy",
title = "Verification and validation in scientific computing",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "????",
year = "2010",
ISBN = "0-521-11360-1",
ISBN-13 = "978-0-521-11360-1",
LCCN = "Q183.9 .O24 2010",
bibdate = "Tue Apr 26 08:20:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://assets.cambridge.org/97805211/13601/cover/9780521113601.jpg",
abstract = "Advances in scientific computing have made modelling
and simulation an important part of the decision-making
process in engineering, science, and public policy.
This book provides a comprehensive and systematic
development of the basic concepts, principles, and
procedures for verification and validation of models
and simulations. The emphasis is placed on models that
are described by partial differential and integral
equations and the simulations that result from their
numerical solution. The methods described can be
applied to a wide range of technical fields, from the
physical sciences, engineering and technology and
industry, through to environmental regulations and
safety, product and plant safety, financial investing,
and governmental regulations. This book will be
genuinely welcomed by researchers, practitioners, and
decision makers in a broad range of fields, who seek to
improve the credibility and reliability of simulation
results. It will also be appropriate either for
university courses or for independent study",
acknowledgement = ack-nhfb,
remark = "Exchanges between the book's authors and members of
the reliable\_computing mailing list in early May 2011
discuss the extent to which this book is, or is not,
about interval arithmetic.",
subject = "Science \\
Data processing \\
Numerical calculations \\
Verification \\
Computer programs \\
Validation \\
Decision making \\
Mathematical models",
tableofcontents = "Preface \\
1. Introduction \\
Part I. Fundamental Concepts: \\
2. Fundamental concepts and terminology \\
3. Modeling and computational simulation \\
Part II. Code Verification: \\
4. Software engineering \\
5. Code verification \\
6. Exact solutions \\
Part III. Solution Verification: \\
7. Solution verification \\
8. Discretization error \\
9. Solution adaptation \\
Part IV. Model Validation and Prediction: \\
10. Model validation fundamentals \\
11. Design and execution of validation experiments \\
12. Model accuracy assessment \\
13. Predictive capability \\
Part V. Planning, Management, and Implementation
Issues: \\
14. Planning and prioritization in modeling and
simulation \\
15. Maturity assessment of modeling and simulation \\
16. Development and responsibilities for verification,
validation and uncertainty quantification \\
Appendix. Programming practices \\
Index",
}
@Book{Onate:2010:SAF,
author = "Eugenio O{\~n}ate",
title = "Structural analysis with the finite element method:
linear statistics",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxiv + 472",
year = "2010",
DOI = "https://doi.org/10.1007/978-1-4020-8733-2",
ISBN = "1-4020-8733-0",
ISBN-13 = "978-1-4020-8733-2",
LCCN = "TA347.F5 O63 2009",
bibdate = "Mon Aug 23 11:24:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Lecture notes on numerical methods in engineering and
sciences.",
acknowledgement = ack-nhfb,
remark = "Volume 1: The basis and solids. Volume 2: Beams,
plates and shells",
subject = "Finite element method; Structural analysis
(Engineering)",
}
@Book{Quarteroni:2010:SCM,
author = "Alfio Quarteroni and Fausto Saleri and Paola
Gervasio",
title = "Scientific computing with {Matlab} and {Octave}",
volume = "2",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 360",
year = "2010",
DOI = "https://doi.org/10.1007/978-3-642-12430-3",
ISBN = "3-642-12429-1",
ISBN-13 = "978-3-642-12429-7",
LCCN = "????",
MRclass = "65-01",
MRnumber = "2680972",
bibdate = "Tue May 27 11:24:21 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
note = "Third edition [of MR2253397]",
series = "Texts in Computational Science and Engineering",
acknowledgement = ack-nhfb,
}
@Book{Robert:2010:IMC,
author = "Christian P. Robert and George Casella",
title = "Introducing {Monte Carlo} methods with {R}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xix + 283",
year = "2010",
DOI = "https://doi.org/10.1007/978-1-4419-1576-4",
ISBN = "1-4419-1575-3 (paperback), 1-4419-1576-1 (ebk.)",
ISBN-13 = "978-1-4419-1575-7 (paperback), 978-1-4419-1576-4
(ebk.)",
LCCN = "QA298 .R63 2010",
MRclass = "65-01 (65C05)",
MRnumber = "2572239",
bibdate = "Tue May 27 12:31:49 MDT 2014",
bibsource = "clas.caltech.edu:210/INNOPAC;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Use R!",
acknowledgement = ack-nhfb,
subject = "Monte Carlo method; Computer programs; Mathematical
statistics; Data processing; R (Computer program
language); Markov processes; Mathematical Computing;
Monte Carlo-methode.; R (computerprogramma);
Monte-Carlo-Simulation.; R (Programm)",
}
@Book{Trappenberg:2010:FCN,
author = "Thomas P. Trappenberg",
title = "Fundamentals of computational neuroscience",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
edition = "Second",
pages = "xxv + 390",
year = "2010",
ISBN = "0-19-956841-3 (paperback)",
ISBN-13 = "978-0-19-956841-3 (paperback)",
LCCN = "QP357.5 .T746 2010",
bibdate = "Mon Jan 31 15:17:33 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
melvyl.cdlib.org:210/CDL90;
z3950.loc.gov:7090/Voyager",
abstract = "Computational neuroscience is the theoretical study of
the brain to uncover the principles and mechanisms that
guide the development, organization, information
processing, and mental functions of the nervous system.
Although not a new area, it is only recently that
enough knowledge has been gathered to establish
computational neuroscience as a scientific discipline
in its own right. Given the complexity of the field,
and its increasing importance in progressing our
understanding of how the brain works, there has long
been a need for an introductory text on what is often
assumed to be an impenetrable topic. The new edition of
Fundamentals of Computational Neuroscience build on the
success and strengths of the first edition. It
introduces the theoretical foundations of neuroscience
with a focus on the nature of information processing in
the brain. The book covers the introduction and
motivation of simplified models of neurons that are
suitable for exploring information processing in large
brain-like networks. Additionally, it introduces
several fundamental network architectures and discusses
their relevance for information processing in the
brain, giving some examples of models of higher-order
cognitive functions to demonstrate the advanced insight
that can be gained with such studies. Each chapter
starts by introducing its topic with experimental facts
and conceptual questions related to the study of brain
function. An additional feature is the inclusion of
simple Matlab programs that can be used to explore many
of the mechanisms explained in the book. An
accompanying webpage includes programs for download.
The book is aimed at those within the brain and
cognitive sciences, from graduate level and upwards.",
acknowledgement = ack-nhfb,
subject = "Computational neuroscience; Neurons; physiology;
Brain; Computational Biology; methods; Models,
Neurological; Nerve Net; Neurosciences",
tableofcontents = "Introduction \\
Basic Nuerons \\
Neurons and conductance-based models \\
Simplified neuron and population models \\
Associators and synaptic plasticity \\
Basic Networks \\
Cortical organizations and simple networks \\
Feed-forward mapping networks \\
Cortical feature maps and competitive population coding
\\
Recurrent associative networks and episodic memory \\
System-Level Models \\
Modular networks, motor control, and reinforcement
learning \\
The cognitive brain \\
Some useful mathematics \\
Numerical calculus \\
Basic probability theory \\
Basic information theory \\
A brief introduction to MATLAB",
}
@Book{Tveito:2010:ESC,
author = "Aslak Tveito and Hans Petter Langtangen and Bj{\o}rn
Frederik Nielsen and Xing Cai",
title = "Elements of scientific computing: with 88 figures and
18 tables",
volume = "7",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xii + 459",
year = "2010",
DOI = "https://doi.org/10.1007/978-3-642-11299-7",
ISBN = "3-642-11298-6",
ISBN-13 = "978-3-642-11298-0, 978-3-642-11299-7 (eISBN)",
ISSN = "1611-0994",
LCCN = "Q183.9 .E446 2010",
MRclass = "65-01",
MRnumber = "2723363",
bibdate = "Tue May 27 12:08:24 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Texts in Computational Science and Engineering",
acknowledgement = ack-nhfb,
subject = "Science; Data processing; Numerical analysis",
tableofcontents = "Computing integrals \\
Differential equations: the first steps \\
Systems of ordinary differential equations \\
Nonlinear algebraic equations \\
Method of least squares \\
About scientific software \\
Diffusion equation \\
Analysis of the diffusion equation \\
Parameter estimation and inverse problems \\
Glimpse of parallel computing",
}
@Book{VanLoan:2010:ITC,
author = "Charles F. {Van Loan} and K.-Y. Daisy Fan",
title = "Insight through computing: a {MATLAB} introduction to
computational science and engineering",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xviii + 434",
year = "2010",
ISBN = "0-89871-691-8",
ISBN-13 = "978-0-89871-691-7",
LCCN = "QA297 .V25 2010",
bibdate = "Fri Nov 16 10:03:00 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/java2010.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy1007/2009030277-b.html;
http://www.loc.gov/catdir/enhancements/fy1007/2009030277-d.html;
http://www.loc.gov/catdir/enhancements/fy1007/2009030277-t.html",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Data processing; Science; Computer
simulation; Engineering mathematics; MATLAB",
tableofcontents = "Preface \\
MATLAB glossary \\
Programming topics \\
Software \\
1. From formula to program \\
2. Limits and error \\
3. Approximation with fractions \\
4. The discrete versus the continuous \\
5. Abstraction \\
6. Randomness \\
7. The second dimension \\
8. Reordering \\
9. Search \\
10. Points, polygons and circles \\
11. Text file processing \\
12. The matrix: part II \\
13. Acoustic file processing \\
14. Divide and conquer \\
15. Optimization \\
Appendix A. Refined graphics \\
Appendix B. Mathematical facts \\
Appendix C. MATLAB, Java, and C \\
Appendix D. Exit interview \\
Index",
}
@Book{Watkins:2010:FMC,
author = "David S. Watkins",
title = "Fundamentals of Matrix Computations",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Third",
pages = "xvi + 644",
year = "2010",
ISBN = "0-470-52833-8 (hardcover)",
ISBN-13 = "978-0-470-52833-4 (hardcover)",
LCCN = "QA188 .W38 2010",
MRclass = "65-01 (65Fxx)",
MRnumber = "2778339 (2012a:65002)",
bibdate = "Tue May 27 12:31:46 MDT 2014",
bibsource = "clas.caltech.edu:210/INNOPAC;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Pure and applied mathematics.",
acknowledgement = ack-nhfb,
subject = "Matrices",
}
@Book{Ascher:2011:FCN,
author = "Uri M. (Uri M.) Ascher and Chen Greif",
title = "A first course in numerical methods",
volume = "7",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxii + 552",
year = "2011",
DOI = "https://doi.org/10.1137/1.9780898719987",
ISBN = "0-89871-997-6",
ISBN-13 = "978-0-89871-997-0",
LCCN = "QA297 .A748 2011",
MRclass = "65-01",
MRnumber = "2839122",
bibdate = "Tue May 27 12:30:46 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
prodorbis.library.yale.edu:7090/voyager;
z3950.gbv.de:20011/gvk; z3950.loc.gov:7090/Voyager",
series = "Computational science and engineering",
URL = "http://www.loc.gov/catdir/enhancements/fy1111/2011007041-b.html;
http://www.loc.gov/catdir/enhancements/fy1111/2011007041-d.html;
http://www.loc.gov/catdir/enhancements/fy1111/2011007041-t.html",
acknowledgement = ack-nhfb,
subject = "Numerical calculations; Data processing; Numerical
analysis; Algorithms",
tableofcontents = "Numerical algorithms \\
Roundoff errors \\
Nonlinear equations in one variable \\
Linear algebra background \\
Linear systems: direct methods \\
Linear least squares problems \\
Linear systems: iterative methods \\
Eigenvalues and singular values \\
Nonlinear systems and optimization \\
Polynomial interpolation \\
Piecewise polynomial interpolation \\
Best approximation \\
Fourier transform \\
Numerical differentiation \\
Numerical integration \\
Differential equations",
}
@Book{Babuska:2011:FEI,
author = "Ivo Babu{\v{s}}ka and J. R. (John Robert) Whiteman and
Theofanis Strouboulis",
title = "Finite elements: an introduction to the method and
error estimation",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xii + 323",
year = "2011",
ISBN = "0-19-850670-8",
ISBN-13 = "978-0-19-850670-6",
LCCN = "QA276.8 .B33X 2011",
bibdate = "Tue May 27 12:30:44 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
prodorbis.library.yale.edu:7090/voyager;
z3950.loc.gov:7090/Voyager",
note = "An introduction to the method and error estimation",
URL = "http://www.loc.gov/catdir/enhancements/fy1108/2010033235-b.html;
http://www.loc.gov/catdir/enhancements/fy1108/2010033235-d.html;
http://www.loc.gov/catdir/enhancements/fy1108/2010033235-t.html",
acknowledgement = ack-nhfb,
subject = "Finite element method; Estimation theory; Error
analysis (Mathematics)",
}
@Book{Bailey:2011:PTS,
editor = "David H. Bailey and Robert F. Lucas and Samuel Watkins
Williams",
title = "Performance tuning of scientific applications",
volume = "11",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "????",
year = "2011",
ISBN = "1-4398-1569-0 (hardback)",
ISBN-13 = "978-1-4398-1569-4 (hardback)",
LCCN = "Q183.9 .P47 2011",
bibdate = "Thu Nov 15 17:15:34 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/super.bib;
z3950.loc.gov:7090/Voyager",
series = "Chapman and Hall/CRC computational science",
abstract = "This book presents an overview of recent research and
applications in computer system performance for
scientific and high performance computing. After a
brief introduction to the field of scientific computer
performance, the text provides comprehensive coverage
of performance measurement and tools, performance
modeling, and automatic performance tuning. It also
includes performance tools and techniques for
real-world scientific applications. Various chapters
address such topics as performance benchmarks, hardware
performance counters, the PMaC modeling system, source
code-based performance modeling, climate modeling
codes, automatic tuning with ATLAS, and much more.",
acknowledgement = ack-nhfb,
subject = "Science; Data processing; Evaluation; Electronic
digital computers; System design; Computer programs;
COMPUTERS / Computer Engineering; MATHEMATICS /
Advanced; MATHEMATICS / Number Systems",
}
@Book{Banerjee:2011:LAM,
author = "Sudipto Banerjee and Anindya Roy",
title = "Linear Algebra and Matrix Analysis for Statistics",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xvii + 565",
year = "2011",
ISBN = "1-4200-9538-2 (hardback)",
ISBN-13 = "978-1-4200-9538-8 (hardback)",
LCCN = "QA184.2 .B36 2014",
bibdate = "Mon Sep 15 18:16:29 MDT 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Chapman and Hall/CRC texts in statistical science
series",
URL = "http://images.tandf.co.uk/common/jackets/websmall/978142009/9781420095388.jpg",
abstract = "Linear algebra and the study of matrix algorithms have
become fundamental to the development of statistical
models. Using a vector-space approach, this book
provides an understanding of the major concepts that
underlie linear algebra and matrix analysis. Each
chapter introduces a key topic, such as
infinite-dimensional spaces, and provides illustrative
examples. The authors examine recent developments in
diverse fields such as spatial statistics, machine
learning, data mining, and social network analysis.
Complete in its coverage and accessible to students
without prior knowledge of linear algebra, the text
also includes results that are useful for traditional
statistical applications.",
acknowledgement = ack-nhfb,
subject = "Algebras, Linear; Matrices; Mathematical statistics;
MATHEMATICS / Algebra / General.; MATHEMATICS /
Probability and Statistics / General.; Algebras,
Linear.; Mathematical statistics.; Matrices.",
}
@Book{Borwein:2011:IMM,
author = "Jonathan M. Borwein and Matthew P. Skerritt",
title = "An introduction to modern mathematical computing",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 216",
year = "2011",
DOI = "https://doi.org/10.1007/978-1-4614-0122-3",
ISBN = "1-4614-0121-6",
ISBN-13 = "978-1-4614-0121-6",
MRclass = "65-01 (15-01 26-01 68-01)",
MRnumber = "2808248",
bibdate = "Tue May 27 11:24:21 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
note = "With Maple$ {^{}{\rm {T}}M} $",
series = "Springer Undergraduate Texts in Mathematics and
Technology",
acknowledgement = ack-nhfb,
}
@Book{Chen:2011:FEM,
author = "Zhangxin Chen",
title = "The finite element method: its fundamentals and
applications in engineering",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xxi + 326",
year = "2011",
ISBN = "981-4350-56-7 (hardcover), 981-4350-57-5 (paperback)",
ISBN-13 = "978-981-4350-56-3 (hardcover), 978-981-4350-57-0
(paperback)",
LCCN = "TA347.F5 C467 2011",
MRclass = "65-01 (65M60 65N30)",
MRnumber = "2985965",
MRreviewer = "Tsu-Fen Chen",
bibdate = "Tue May 27 12:31:40 MDT 2014",
bibsource = "clas.caltech.edu:210/INNOPAC;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
note = "Its fundamentals and applications in engineering",
acknowledgement = ack-nhfb,
subject = "Finite element method; Problems, exercises, etc;
Engineering mathematics; Finite-Elemente-Methode.",
}
@Book{Cohen:2011:NAM,
author = "Harold Cohen",
title = "Numerical approximation methods",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiv + 485",
year = "2011",
DOI = "https://doi.org/10.1007/978-1-4419-9837-8",
ISBN = "1-4419-9836-5",
ISBN-13 = "978-1-4419-9836-1",
MRclass = "65-01",
MRnumber = "2883150",
bibdate = "Tue May 27 11:24:21 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
acknowledgement = ack-nhfb,
}
@Book{Davies:2011:FEM,
author = "Alan J. Davies",
title = "The finite element method: an introduction with
partial differential equations",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
edition = "Second",
pages = "ix + 297",
year = "2011",
ISBN = "0-19-960913-6",
ISBN-13 = "978-0-19-960913-0",
LCCN = "TA347.F5 D38 2011",
MRclass = "65-01 (65M60 65N30)",
MRnumber = "3087393",
bibdate = "Tue May 27 12:31:39 MDT 2014",
bibsource = "clas.caltech.edu:210/INNOPAC;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
note = "An introduction with partial differential equations",
URL = "http://www.loc.gov/catdir/enhancements/fy1211/2011022386-b.html;
http://www.loc.gov/catdir/enhancements/fy1211/2011022386-d.html;
http://www.loc.gov/catdir/enhancements/fy1211/2011022386-t.html",
acknowledgement = ack-nhfb,
subject = "Finite element method",
}
@Book{Davis:2011:MP,
author = "Timothy A. Davis",
title = "{MATLAB} primer",
publisher = pub-CRC,
address = pub-CRC:adr,
edition = "Eighth",
pages = "xvi + 232",
year = "2011",
ISBN = "1-4398-2862-8",
ISBN-13 = "978-1-4398-2862-5",
LCCN = "QA297 .D38 2011",
bibdate = "Mon Jan 31 14:24:46 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "MATLAB; Numerical analysis; Data processing",
}
@Book{Deuflhard:2011:NM,
author = "Peter Deuflhard and Martin Weiser",
title = "{Numerische Mathematik 3} ({German}) [{Numerical}
mathematics 3]",
publisher = pub-GRUYTER,
address = pub-GRUYTER:adr,
pages = "x + 432",
year = "2011",
ISBN = "3-11-021802-X",
ISBN-13 = "978-3-11-021802-2",
MRclass = "65-01 (65M06 65M50 65M60 65N06 65N30 65N50)",
MRnumber = "2779847 (2012a:65001)",
MRreviewer = "Othmar Koch",
bibdate = "Tue May 27 11:24:21 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
note = "Adaptive L{\"o}sung partieller
Differentialgleichungen. [Adaptive solutions of partial
differential equations]",
series = "de Gruyter Lehrbuch [de Gruyter Textbook]",
acknowledgement = ack-nhfb,
language = "German",
}
@Book{Fiedler:2011:MGG,
author = "Miroslav Fiedler",
title = "Matrices and Graphs in Geometry",
volume = "139",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "viii + 197",
year = "2011",
ISBN = "0-521-46193-6",
ISBN-13 = "978-0-521-46193-1",
LCCN = "QA447 .F45 2011",
bibdate = "Tue Feb 7 16:22:53 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/linala2010.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Encyclopedia of Mathematics and its Applications",
URL = "http://assets.cambridge.org/97805214/61931/cover/9780521461931.jpg;
http://catdir.loc.gov/catdir/enhancements/fy1101/2010046601-b.html;
http://catdir.loc.gov/catdir/enhancements/fy1101/2010046601-d.html;
http://catdir.loc.gov/catdir/enhancements/fy1101/2010046601-t.html",
abstract = "Simplex geometry is a topic generalizing geometry of
the triangle and tetrahedron. The appropriate tool for
its study is matrix theory, but applications usually
involve solving huge systems of linear equations or
eigenvalue problems, and geometry can help in
visualizing the behaviour of the problem. In many
cases, solving such systems may depend more on the
distribution of non-zero coefficients than on their
values, so graph theory is also useful. The author has
discovered a method that in many (symmetric) cases
helps to split huge systems into smaller parts. Many
readers will welcome this book, from undergraduates to
specialists in mathematics, as well as non-specialists
who only use mathematics occasionally, and anyone who
enjoys geometric theorems. It acquaints the reader with
basic matrix theory, graph theory and elementary
Euclidean geometry so that they too can appreciate the
underlying connections between these various areas of
mathematics and computer science.\par
This book comprises, in addition to auxiliary material,
the research on which I have worked for the past more
than 50 years. Some of the results appear here for the
first time. The impetus for writing the book came from
the late Victor Klee, after my talk in Minneapolis in
1991. The main subject is simplex geometry, a topic
which fascinated me from my student times, caused, in
fact, by the richness of triangle and tetrahedron
geometry on one side and matrix theory on the other
side. A large part of the content is concerned with
qualitative properties of a simplex. This can be
understood as studying not just relations of equalities
but also inequalities. It seems that this direction is
starting to have important consequences in practical
(and important) applications, such as finite element
methods.",
acknowledgement = ack-nhfb,
subject = "Geometry; Matrices; Graphic methods",
tableofcontents = "Matricial approach to Euclidean geometry \\
Simplex geometry \\
Qualitative properties of the angles in a simplex ---
Special simplexes \\
Further geometric objects \\
Applications",
}
@Book{Galvis:2011:IAN,
author = "Juan Galvis and Henrique Versieux",
title = "Introdu{\c{c}}{\~a}o {\`a} aproxima{\c{c}}{\~a}o
num{\'e}rica de equa{\c{c}}{\~o}es diferenciais
parciais via o m{\'e}todo de elementos finitos.
({Portuguese}) [{Introduction} to numerical
approximation of partial differential equations via the
finite-element method]",
publisher = "Instituto Nacional de Matem\'atica Pura e Aplicada
(IMPA)",
address = "Rio de Janeiro, Brasil",
pages = "91",
year = "2011",
ISBN = "85-244-0325-X",
ISBN-13 = "978-85-244-0325-5",
MRclass = "65-01 (65M60 65N30)",
MRnumber = "2816863 (2012f:65001)",
MRreviewer = "Carlos V{\'a}zquez Cend{\'o}n",
bibdate = "Tue May 27 11:24:21 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
note = "28$ {^{}{\rm {o}}} $ Col{\'o}quio Brasileiro de
Matem{\'a}tica. [28th Brazilian Mathematics
Colloquium]",
series = "Publica\c c\~oes Matem\'aticas do IMPA. [IMPA
Mathematical Publications]",
acknowledgement = ack-nhfb,
language = "Portuguese",
}
@Book{Gustafsson:2011:FSC,
author = "Bertil Gustafsson",
title = "Fundamentals of scientific computing",
volume = "8",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiv + 316",
year = "2011",
DOI = "https://doi.org/10.1007/978-3-642-19495-5",
ISBN = "3-642-19494-X",
ISBN-13 = "978-3-642-19494-8",
MRclass = "65-01",
MRnumber = "2808067",
bibdate = "Tue May 27 11:24:21 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Texts in Computational Science and Engineering",
acknowledgement = ack-nhfb,
}
@Book{Gautschi:2011:ACH,
editor = "Walter Gautschi and Giuseppe Mastroianni and
Themistocles M. Rassias",
booktitle = "Approximation and Computation: In Honor of {Gradimir
V. Milovanovi{\'c}}",
title = "Approximation and Computation: In Honor of {Gradimir
V. Milovanovi{\'c}}",
volume = "42",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xviii + 482",
year = "2011",
DOI = "https://doi.org/10.1007/978-1-4419-6594-3",
ISBN = "1-4419-6593-9 (paperback), 1-4419-6594-7 (e-book),
1-4419-6595-5, 1-4614-2703-7",
ISBN-13 = "978-1-4419-6593-6 (paperback), 978-1-4419-6594-3
(e-book), 978-1-4419-6595-0, 978-1-4614-2703-2",
LCCN = "QA39.2 .A67 2011; QA221 .A6345 2011",
bibdate = "Thu Jan 9 18:51:01 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Springer Optimization and Its Applications",
abstract = "Approximation theory and numerical analysis are
central to the creation of accurate computer
simulations and mathematical models. Research in these
areas can influence the computational techniques used
in a variety of mathematical and computational
sciences. This collection of contributed chapters,
dedicated to the renowned mathematician Gradimir V.
Milovanovi{\'c}, represent the recent work of experts
in the fields of approximation theory and numerical
analysis. These invited contributions describe new
trends in these important areas of research including
theoretic developments, new computational algorithms,
and multidisciplinary applications. Special features of
this volume: --- Presents results and approximation
methods in various computational settings including
polynomial and orthogonal systems, analytic functions,
and differential equations. --- Provides a historical
overview of approximation theory and many of its
subdisciplines. --- Contains new results from diverse
areas of research spanning mathematics, engineering,
and the computational sciences.
``\booktitle{Approximation and Computation}'' is
intended for mathematicians and researchers focusing on
approximation theory and numerical analysis, but can
also be a valuable resource to students and researchers
in engineering and other computational and applied
sciences.",
acknowledgement = ack-nhfb,
subject = "Inform{\`a}tica; Matem{\`a}tica; Models
estoc{\`a}stics",
tableofcontents = "Cont{\'e}: Part I Introduction. \\
The Scientific Work of Gradimir V. Milovanovi{\'c}
(Aleksandar Ivi{\'c}) \\
My Collaboration with Gradimir V. Milovanovi{\'c}
(Walter Gautschi) \\
On Some Major Trends in Mathematics (Themistocles M.
Rassias) \\
Part II Polynomials and Orthogonal Systems \\
An Application of Sobolev Orthogonal Polynomials to the
Computation of a Special Hankel Determinant (Paul
Barry, Predrag M. Rajkovi{\'c} and Marko D.
Petkovi{\'c}) \\
Extremal Problems for Polynomials in the Complex Plane
(Borislav Bojanov) \\
Energy of Graphs and Orthogonal Matrices (V.
Bo{\v{z}}in and M. Mateljevi{\'c}) \\
Interlacing Property of Zeros of Shifted Jacobi
Polynomials (Aleksandar S. Cvetkovi{\'c}) \\
Trigonometric Orthogonal Systems (Aleksandar S.
Cvetkovi{\'c} and Marija P. Stani{\'c}) \\
Experimental Mathematics Involving Orthogonal
Polynomials (Walter Gautschi) \\
Compatibility of Continued Fraction Convergents with
Pad{\'e} Approximants (Jacek Gilewicz and Rados{\l}aw
Jedynak) \\
Orthogonal Decomposition of Fractal Sets (Ljubi{\v{s}}a
M. Koci{\'c}, Sonja Gegovska Zajkova, Elena
Baba{\v{c}}e) \\
Positive Trigonometric Sums and Starlike Functions
(Stamatis Koumandos) \\
Part III Quadrature Formulae. \\
Quadrature Rules for Unbounded Intervals and Their
Application to Integral Equations (G. Monegato, L.
Scuderi) \\
Gauss-Type Quadrature Formulae for Parabolic Splines
with Equidistant Knots (Geno Nikolov and Corina Simian)
\\
Approximation of the Hilbert Transform on the Real Line
Using Freud Weights (Incoronata Notarangelo) \\
The Remainder Term of Gauss--Tu\'ran Quadratures for
Analytic Functions (Miodrag M. Spalevi{\'c} and
Miroslav S. Prani{\'c}) \\
Towards a General Error Theory of the Trapezoidal Rule
(J{\"o}rg Waldvogel) \\
Part IV Differential Equations \\
Finite Difference Method for a Parabolic Problem with
Concentrated Capacity and Time-Dependent Operator
(Dejan R. Bojovi{\'c} and Bo{\v{s}}ko S. Jovanovi{\'c})
\\
Adaptive Finite Element Approximation of the
Francfort--Marigo Model of Brittle Fracture (Siobhan
Burke, Christoph Ortner and Endre S{\"u}li) \\
A Nystr{\"o}m Method for Solving a Boundary Value
Problems on $[0, \infty)$ (Carmelina Frammartino) \\
Finite Difference Approximation of a Hyperbolic
Transmission Problem (Bo{\v{s}}ko S. Jovanovi{\'c}) \\
Homeomorphisms and Fredholm Theory for Perturbations of
Nonlinear Fredholm Maps of Index Zero and of AProper
Maps with Applications (P. S. Milojevi{\'c}) \\
Singular Support and FLq Continuity of
Pseudodifferential Operators (Stevan Pilipovi{\'c},
Nenad Teofanov and Joachim Toft) \\
On a Class of Matrix Differential Equations with
Polynomial Coefficients (Boro M. Piperevski) \\
Part V Applications \\
Optimized Algorithm for Petviashvili?s Method for
Finding Solitons in Photonic Lattices (Raka
Jovanovi{\'c} and Milan Tuba) \\
Explicit Method for the Numerical Solution of the
Fokker--Planck Equation of Filtered Phase Noise (Dejan
Mili{\'c}) \\
Numerical Method for Computer Study of Liquid Phase
Sintering: Densification Due to Gravity-Induced
Skeletal Settling (Zoran S. Nikoli{\'c}) \\
Computer Algebra and Line Search (Predrag
Stanimirovi{\'c}, Marko Miladinovi{\'c} and Ivan M.
Jovanovi{\'c}) \\
Roots of AG bands (Neboj{\v{s}}a Stevanovi{\'c} and
Petar V. Proti{\'c}) \\
Context Hidden Markov Model for Named Entity
Recognition (Branimir T. Todorovi{\'c}, Svetozar R.
Ran{\v{c}}i{\'c}, Edin H. Mulali{\'c}) \\
On the Interpolating Quadratic Spline (Zlatko Udovi\v
ci{\'c}) \\
Visualization of Infinitesimal Bending of Curves
(Ljubica S. Velimirovi{\'c}, Svetozar R.
Ran{\v{c}}i{\'c}, Milan Lj. Zlatanovi{\'c})",
}
@Book{Hermann:2011:NM,
author = "Martin Hermann",
title = "Numerische {Mathematik}",
publisher = pub-OLDENBOURG,
address = pub-OLDENBOURG:adr,
edition = "Expanded",
pages = "xiv + 563",
year = "2011",
ISBN = "3-486-70820-1",
ISBN-13 = "978-3-486-70820-2",
MRclass = "65-01",
MRnumber = "2933531",
bibdate = "Tue May 27 11:24:21 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
acknowledgement = ack-nhfb,
}
@Book{Johnson:2011:EMS,
author = "Richard K. Johnson",
title = "The elements of {MATLAB} style",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "????",
year = "2011",
ISBN = "0-521-73258-1",
ISBN-13 = "978-0-521-73258-1",
LCCN = "QA76.73.M296 J64 2011",
bibdate = "Mon Jan 31 14:25:07 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
abstract = "A guide for MATLAB programmers that offers a
collection of standards and guidelines for creating
MATLAB code that will be easy to understand, enhance,
and maintain. Avoid doing things that would be an
unpleasant surprise to other software developers. The
interfaces and the behavior exhibited by your software
must be predictable and consistent. If they are not,
the documentation must clearly identify and justify any
unusual instances of use or behavior.",
acknowledgement = ack-nhfb,
subject = "MATLAB; Computer programming; Computer software;
Quality control; Numerical analysis; Data processing",
tableofcontents = "1. General principles \\
2. Formatting \\
3. Naming \\
4. Documentation \\
5. Programming \\
6. Files and organization \\
7. Development",
}
@Book{Kepner:2011:GAL,
author = "Jeremy V. Kepner and J. R. (John R.) Gilbert",
title = "Graph algorithms in the language of linear algebra",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxvii + 361",
year = "2011",
ISBN = "0-89871-990-9 (hardcover)",
ISBN-13 = "978-0-89871-990-1 (hardcover)",
LCCN = "QA166.245 .K47 2011",
bibdate = "Fri Nov 16 09:38:48 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Software, environments, and tools",
URL = "http://www.loc.gov/catdir/enhancements/fy1113/2011003774-b.html;
http://www.loc.gov/catdir/enhancements/fy1113/2011003774-d.html;
http://www.loc.gov/catdir/enhancements/fy1113/2011003774-t.html",
acknowledgement = ack-nhfb,
subject = "Graph algorithms; Algebras, Linear",
}
@Book{King:2011:NSM,
author = "Michael R. King and Nipa A. Mody",
title = "Numerical and statistical methods for bioengineering:
applications in {MATLAB}",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xii + 581",
year = "2011",
ISBN = "0-521-87158-1 (hardback)",
ISBN-13 = "978-0-521-87158-7 (hardback)",
LCCN = "R857.M34 K56 2011; R857.M34 K56X 2011 (LC)",
MRclass = "65-01 (62-01 62P10 92B05)",
MRnumber = "2767120",
bibdate = "Tue May 27 12:31:06 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
prodorbis.library.yale.edu:7090/voyager",
note = "Applications in MATLAB",
series = "Cambridge Texts in Biomedical Engineering",
abstract = "The first MATLAB-based numerical methods textbook for
bioengineers that uniquely integrates modelling
concepts with statistical analysis, while maintaining a
focus on enabling the user to report the error or
uncertainty in their result. Between traditional
numerical method topics of linear modelling concepts,
nonlinear root finding, and numerical integration,
chapters on hypothesis testing, data regression and
probability are interweaved. A unique feature of the
book is the inclusion of examples from clinical trials
and bioinformatics, which are not found in other
numerical methods textbooks for engineers. With a
wealth of biomedical engineering examples, case studies
on topical biomedical research, and the inclusion of
end of chapter problems, this is a perfect core text
for a one-semester undergraduate course.\par
Cambridge Texts in Biomedical Engineering provides a
forum for high-quality accessible textbooks targeted at
undergraduate and graduate courses in biomedical
engineering. It will cover a broad range of biomedical
engineering topics from introductory texts to advanced
topics including, but not limited to, biomechanics,
physiology, biomedical instrumentation, imaging,
signals and systems, cell engineering, and
bioinformatics. The series will blend theory and
practice, aimed primarily at biomedical engineering
students but will be suitable for broader courses in
engineering, the life sciences and medicine",
acknowledgement = ack-nhfb,
subject = "Biomedical engineering; Statistical methods;
Mathematics; MATLAB",
tableofcontents = "1. Types and sources of numerical error \\
2. Systems of linear equations \\
3. Probability and statistics \\
4. Hypothesis testing \\
5. Root-finding techniques for nonlinear equations \\
6. Numerical quadrature \\
7. Numerical integration of ordinary differential
equations \\
8. Nonlinear data regression and optimization \\
9. Basic algorithms of bioinformatics \\
Appendix A. Introduction to MATLAB \\
Appendix B. Location of nodes for Gauss-Legendre
quadrature",
}
@Book{Klee:2011:SDS,
author = "Harold Klee and Randal Allen",
title = "Simulation of dynamic systems with {MATLAB\reg} and
{Simulink\reg}",
publisher = pub-CRC,
address = pub-CRC:adr,
edition = "Second",
pages = "xix + 795",
year = "2011",
ISBN = "1-4398-3673-6 (hardback)",
ISBN-13 = "978-1-4398-3673-6 (hardback)",
LCCN = "QA76.9.C65 K585 2011",
MRclass = "65-01 (34-04 65Lxx 93-04)",
MRnumber = "2768103 (2011m:65001)",
bibdate = "Tue May 27 12:31:45 MDT 2014",
bibsource = "clas.caltech.edu:210/INNOPAC;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
note = "With a foreword by Chris Bauer and Chris Schwarz",
abstract = "``Employing the widely adopted MATLAB and Simulink
software packages, this book offers the scientific and
engineering communities integrated coverage of
continuous simulation and the essential prerequisites
in one resource. It also provides a complete
introduction to the Real-Time Workshop. The text takes
the reader through the process of converting a
mathematical model of a continuous or discrete system
into a simulation model and source code implementation,
which can be explored to better understand the dynamic
behavior of the system. The second edition addresses
common nonlinearities, expands coverage of the Kalman
filter, and features extensive treatment of numerical
parameters. \par
In the first article of SIMULATION magazine in Fall
1963, the editor John McLeod proclaimed simulation to
mean ``the act of representing some aspects of the real
world by numbers or symbols which may be easily
manipulated to facilitate their study.'' Two years
later, it was modified to ``the development and use of
models for the study of the dynamics of existing or
hypothesized systems.'' More than forty years later,
the simulation community has yet to converge upon a
universally accepted definition",
acknowledgement = ack-nhfb,
subject = "Computer simulation; SIMULINK; MATLAB",
}
@Book{Monahan:2011:NMS,
author = "John F. Monahan",
title = "Numerical methods of statistics",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Second",
pages = "xvi + 447",
year = "2011",
DOI = "https://doi.org/10.1017/CBO9780511977176",
ISBN = "0-521-13951-1 (paperback), 0-521-19158-0",
ISBN-13 = "978-0-521-13951-9 (paperback), 978-0-521-19158-6",
LCCN = "QA276.4 .M65 2011 (LC); QA276.4 .M65 2011",
MRclass = "65-01 (60-04 62-04 65C60)",
MRnumber = "2791641",
bibdate = "Tue May 27 12:30:59 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "Cambridge Series in Statistical and Probabilistic
Mathematics",
acknowledgement = ack-nhfb,
subject = "Mathematical statistics; Data processing",
}
@Book{Nahin:2011:NCT,
author = "Paul J. Nahin",
title = "Number-crunching: taming unruly computational problems
from mathematical physics to science fiction",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xxvi + 376",
year = "2011",
ISBN = "0-691-14425-7 (hardcover), 1-4008-3958-0 (e-book)",
ISBN-13 = "978-0-691-14425-2 (hardcover), 978-1-4008-3958-2
(e-book)",
LCCN = "QC20.7.E4 N34 2011",
bibdate = "Wed Oct 22 08:11:12 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.jstor.org/stable/10.2307/j.ctt7rk7v",
abstract = "How do technicians repair broken communications cables
at the bottom of the ocean without actually seeing
them? What's the likelihood of plucking a needle out of
a haystack the size of the Earth? And is it possible to
use computers to create a universal library of
everything ever written or every photo ever taken?
These are just some of the intriguing questions that
best-selling popular math writer Paul Nahin tackles in
Number-Crunching. Through brilliant math ideas and
entertaining stories, Nahin demonstrates how odd and
unusual math problems can be solved by bringing
together basic physics ideas and today's powerful
computers. Some of the outcomes discussed are so
counterintuitive they will leave readers astonished.
Nahin looks at how the art of number-crunching has
changed since the advent of computers, and how
high-speed technology helps to solve fascinating
conundrums such as the three-body, Monte Carlo,
leapfrog, and gambler's ruin problems. Along the way,
Nahin traverses topics that include algebra,
trigonometry, geometry, calculus, number theory,
differential equations, Fourier series, electronics,
and computers in science fiction. He gives historical
background for the problems presented, offers many
examples and numerous challenges, supplies MATLAB codes
for all the theories discussed, and includes detailed
and complete solutions.",
acknowledgement = ack-nhfb,
remark = "A collection of challenging problems in mathematical
physics that roar like lions when attacked
analytically, but which purr like kittens when
confronted by a high-speed electronic computer and its
powerful scientific software (plus some speculations
for the future from science fiction).",
subject = "Mathematical physics; Data processing; Problems,
exercises, etc",
tableofcontents = "Feynman meets Fermat \\
Just for fun: two quick number-crunching problems \\
Computers and mathematical physics \\
The astonishing problem of the hanging masses \\
The three-body problem and computers \\
Electrical circuit analysis and computers \\
The leapfrog problem \\
Science fiction: when computers become like us \\
A cautionary epilogue",
}
@Book{Naumann:2011:ADC,
author = "Uwe Naumann",
title = "The art of differentiating computer programs: an
introduction to algorithmic differentiation",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xviii + 340",
year = "2011",
ISBN = "1-61197-206-X",
ISBN-13 = "978-1-61197-206-1",
LCCN = "QA76.76.A98 N38 2011",
bibdate = "Fri Nov 16 09:54:38 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Software, environments, and tools",
URL = "http://www.loc.gov/catdir/enhancements/fy1201/2011032262-b.html;
http://www.loc.gov/catdir/enhancements/fy1201/2011032262-d.html;
http://www.loc.gov/catdir/enhancements/fy1201/2011032262-t.html",
acknowledgement = ack-nhfb,
subject = "Computer programs; Automatic differentiations;
Sensitivity theory (Mathematics)",
}
@Book{Razavy:2011:HQM,
author = "Mohsen Razavy",
title = "{Heisenberg}'s quantum mechanics",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xix + 657",
year = "2011",
ISBN = "981-4304-11-5 (paperback), 981-4304-10-7",
ISBN-13 = "978-981-4304-11-5 (paperback), 978-981-4304-10-8",
LCCN = "QC174.12 .R39 2011",
bibdate = "Mon Nov 28 08:38:47 MST 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.gbv.de:20011/gvk",
abstract = "This book provides a detailed account of quantum
theory with a much greater emphasis on the Heisenberg
equations of motion and the matrix method. The book
features a deeper treatment of the fundamental concepts
such as the rules of constructing quantum mechanical
operators and the classical-quantal correspondence; the
exact and approximate methods based on the Heisenberg
equations; the determinantal approach to the scattering
theory and the LSZ reduction formalism where the latter
method is used to obtain the transition matrix. The
uncertainty relations for a number of different
observables are derived and discussed. A comprehensive
chapter on the quantization of systems with
nonlocalized interaction is included. Exact solvable
models, and approximate techniques for solution of
realistic many-body problems are also considered. The
book takes a unified look in the final chapter,
examining the question of measurement in quantum
theory, with an introduction to the Bell's
inequalities.",
acknowledgement = ack-nhfb,
tableofcontents = "1.1: The Lagrangian and the Hamilton Principle \\
1.2: Noether's Theorem \\
1.3: The Hamiltonian Formulation \\
1.4: Canonical Transformation \\
1.5: Action-Angle Variables \\
1.6: Poisson Brackets \\
1.7: Time Development of Dynamical Variables and
Poisson Brackets \\
1.8: Infinitesimal Canonical Transformation \\
1.9: Action Principle with Variable End Points \\
1.10: Symmetry and Degeneracy in Classical Dynamics \\
1.11: Closed Orbits and Accidental Degeneracy \\
1.12: Time-Dependent Exact Invariants \\
2.1: Equivalence of Wave and Matrix Mechanics \\
3.1: Vectors and Vector Spaces \\
3.2: Special Types of Operators \\
3.3: Vector Calculus for the Operators \\
3.4: Construction of Hermitian and Self-Adjoint
Operators \\
3.5: Symmetrization Rule \\
3.6: Weyl's Rule \\
3.7: Dirac's Rule \\
3.8: Von Neumann's Rules \\
3.9: Self-Adjoint Operators \\
3.10: Momentum Operator in a Curvilinear Coordinates
\\
3.11: Summation Over Normal Modes \\
4.1: The Uncertainty Principle \\
4.2: Application of the Uncertainty Principle for
Calculating Bound State Energies \\
4.3: Time-Energy Uncertainty Relation \\
4.4: Uncertainty Relations for Angular Momentum-Angle
Variables \\
4.5: Local Heisenberg Inequalities \\
4.6: The Correspondence Principle \\
4.7: Determination of the State of a System \\
5.1: Schwinger's Action Principle and Heisenberg's
equations of Motion \\
5.2: Nonuniqueness of the Commutation Relations \\
5.3: First Integrals of Motion \\
6.1: Galilean Invariance \\
6.2: Wave Equation and the Galilean Transformation \\
6.3: Decay Problem in Nonrelativistic Quantum Mechanics
and Mass Superselection Rule \\
6.4: Time-Reversal Invariance \\
6.5: Parity of a State \\
6.6: Permutation Symmetry \\
6.7: Lattice Translation \\
6.8: Classical and Quantum Integrability \\
6.9: Classical and Quantum Mechanical Degeneracies \\
7.1: Klein's Method \\
7.2: The Anharmonic Oscillator \\
7.3: The Double-Well Potential \\
7.4: Chasman's Method \\
7.5: Heisenberg's Equations of Motion for Impulsive
Forces \\
7.6: Motion of a Wave Packet \\
7.7: Heisenberg's and Newton's Equations of Motion \\
8.1: Energy Spectrum of the Two-Dimensional Harmonic
Oscillator \\
8.2: Exactly Solvable Potentials Obtained from
Heisenberg's Equation \\
8.3: Creation and Annihilation Operators \\
8.4: Determination of the Eigenvalues by Factorization
Method \\
8.5: A General Method for Factorization \\
8.6: Supersymmetry and Superpotential \\
8.7: Shape Invariant Potentials \\
8.8: Solvable Examples of Periodic Potentials \\
9.1: The Angular Momentum Operator \\
9.2: Determination of the Angular Momentum Eigenvalues
\\
9.3: Matrix Elements of Scalars and Vectors and the
Selection Rules \\
9.4: Spin Angular Momentum \\
9.5: Angular Momentum Eigenvalues Determined from the
Eigenvalues of Two Uncoupled Oscillators \\
9.6: Rotations in Coordinate Space and in Spin Space
\\
9.7: Motion of a Particle Inside a Sphere \\
Almost Degenerate Perturbation Theory \\
9.8: The Hydrogen Atom \\
9.9: Calculation of the Energy Eigenvalues Using the
Runge[-]Lenz Vector \\
9.10: Classical Limit of Hydrogen Atom \\
9.11: Self-Adjoint Ladder Operator \\
9.12: Self-Adjoint Ladder Operator tiff Angular
Momentum \\
9.13: Generalized Spin Operators \\
9.14: The Ladder Operator \\
10.1: Discrete-Time Formulation of the Heisenberg's
Equations of Motion \\
10.2: Quantum Tunneling Using Discrete-Time Formulation
\\
10.3: Determination of Eigenvalues from
Finite-Difference Equations \\
10.4: Systems with Several Degrees of Freedom \\
10.5: Weyl-Ordered Polynomials and Bender[-]Dunne
Algebra \\
10.6: Integration of the Operator Differential
Equations \\
10.7: Iterative Solution for Polynomial Potentials \\
10.8: Another Numerical Method for the Integration of
the Equations of Motion \\
10.9: Motion of a Wave Packet \\
11.1: Perturbation Theory Applied to the Problem of a
Quartic Oscillator \\
11.2: Degenerate Perturbation Theory \\
11.3: Almost Degenerate Perturbation Theory \\
11.4: van der Waals Interaction \\
11.5: Time-Dependent Perturbation Theory \\
11.6: The Adiabatic Approximation \\
11.7: Transition Probability to the First Order \\
12.1: WKB Approximation for Bound States \\
12.2: Approximate Determination of the Eigenvalues for
Nonpolynomial Potentials \\
12.3: Generalization of the Semiclassical Approximation
to Systems with N Degrees of Freedom \\
12.4: A Variational Method Based on Heisenberg's
Equation of Motion \\
12.5: Raleigh--Ritz Variational Principle \\
12.6: Tight-Binding Approximation \\
12.7: Heisenberg's Correspondence Principle \\
12.8: Bohr and Heisenberg Correspondence and the
Frequencies and Intensities of the Emitted Radiation
\\
13.1: Equations of Motion of Finite Order \\
13.2: Equation of Motion of Infinite Order \\
13.3: Classical Expression for the Energy \\
13.4: Energy Eigenvalues when the Equation of Motion is
of Infinite Order \\
14.1: Determinantal Method in Potential Scattering
14.2: Two Solvable Problems \\
14.3: Time-Dependent Scattering Theory \\
14.4: The Scattering Matrix \\
14.5: The Lippmann[-]Schwinger Equation \\
14.6: Analytical Properties of the Radial Wave Function
\\
14.7: The Jost Function \\
14.8: Zeros of the Jost Function and Bound Sates \\
14.9: Dispersion Relation \\
14.10: Central Local Potentials having Identical Phase
Shifts and Bound States \\
14.11: The Levinson Theorem \\
14.12: Number of Bound States for a Given Partial Wave
\\
14.13: Analyticity of the S-Matrix and the Principle of
Casuality \\
14.14: Resonance Scattering \\
14.15: The Born Series \\
14.16: Impact Parameter Representation of the
Scattering Amplitude \\
14.17: Determination of the Impact Parameter Phase
Shift from the Differential Cross Section \\
14.18: Elastic Scattering of Identical Particles \\
14.19: Transition Probability \\
14.20: Transition Probabilities for Forced Harmonic
Oscillator \\
15.1: Diffraction in Time \\
15.2: High Energy Scattering from an Absorptive Target
\\
16.1: The Aharonov--Bohm Effect \\
16.2: Time-Dependent Interaction \\
16.3: Harmonic Oscillator with Time-Dependent Frequency
\\
16.4: Heisenberg's Equations for Harmonic Oscillator
with Time-Dependent Frequency \\
16.5: Neutron Interferometry \\
16.6: Gravity-Induced Quantum Interference \\
16.7: Quantum Beats in Waveguides with Time-Dependent
Boundaries \\
16.8: Spin Magnetic Moment \\
16.9: Stern--Gerlach Experiment \\
16.10: Precession of Spin Magnetic Moment in a Constant
Magnetic Field \\
16.11: Spin Resonance \\
16.12: A Simple Model of Atomic Clock \\
16.13: Berry's Phase \\
17.1: Ground State of Two-Electron Atom \\
17.2: Hartree and Hartree-Fock Approximations \\
17.3: Second Quantization \\
17.4: Second-Quantized Formulation of the Many-Boson
Problem \\
17.5: Many-Fermion Problem \\
17.6: Pair Correlations Between Fermions \\
17.7: Uncertainty Relations for a Many-Fermion System
\\
17.8: Pair Correlation Function for Noninteracting
Bosons \\
17.9: Bogoliubov Transformation for a Many-Boson System
\\
17.10: Scattering of Two Quasi-Particles \\
17.11: Bogoliubov Transformation for Fermions
Interacting through Pairing Forces \\
17.12: Damped Harmonic Oscillator \\
18.1: Coherent State of the Radiation Field \\
18.2: Casimir Force \\
18.3: Casimir Force Between Parallel Conductors \\
18.4: Casimir Force in a Cavity with Conducting Walls
\\
19.1: Theory of Natural Line Width \\
19.2: The Lamb Shift \\
19.3: Heisenberg's Equations for Interaction of an Atom
with Radiation \\
20.1: EPR Experiment with Particles \\
20.2: Classical and Quantum Mechanical Operational
Concepts of Measurement \\
20.3: Collapse of the Wave Function \\
20.4: Quantum versus Classical Correlations",
}
@Book{Scott:2011:NA,
author = "L. Ridgway Scott",
title = "Numerical analysis",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xiv + 325",
year = "2011",
ISBN = "0-691-14686-1 (hardcover)",
ISBN-13 = "978-0-691-14686-7 (hardcover)",
LCCN = "QA297 .S38 2011; QA297 .S393 2011",
MRclass = "65-01 (41A05 41A10)",
MRnumber = "2796928",
bibdate = "Tue May 27 12:30:57 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
prodorbis.library.yale.edu:7090/voyager;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Numerical analysis",
tableofcontents = "Ch. 1. Numerical algorithms \\
Ch. 2. Nonlinear equations \\
Ch. 3. Linear systems \\
Ch. 4. Direct solvers \\
Ch. 5. Vector spaces \\
Ch. 6. Operators \\
Ch. 7. Nonlinear systems \\
Ch. 8. Iterative methods \\
Ch. 9. Conjugate gradients \\
Ch. 10. Polynominal interpolation \\
Ch. 11. Chebyshev and Hermite interpolation \\
Ch. 12. Approximation theory \\
Ch. 13. Numerical quadrature \\
Ch. 14. Eigenvalue problems \\
Ch. 15. Eigenvalue algorithms \\
Ch. 16. Ordinary differential equations \\
Ch. 17. Higher-order ODE discretization methods \\
Ch. 18. Floating point \\
Ch. 19. Notation",
}
@Book{Stenger:2011:HSN,
author = "Frank Stenger",
title = "Handbook of Sinc Numerical Methods",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xx + 463",
year = "2011",
ISBN = "1-4398-2158-5 (hardback), 1-4398-2159-3 (e-book)",
ISBN-13 = "978-1-4398-2158-9 (hardback), 978-1-4398-2159-6
(e-book)",
LCCN = "QA372 .S8195 2010",
bibdate = "Mon Apr 21 17:35:42 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Chapman and Hall/CRC numerical analysis and scientific
computation series",
URL = "http://www.crcpress.com/product/isbn/9781439821589",
ZMnumber = "Zbl 1208.65143",
abstract = "This handbook is essential for solving numerical
problems in mathematics, computer science, and
engineering. The methods presented are similar to
finite elements but more adept at solving analytic
problems with singularities over irregularly shaped yet
analytically described regions. The author makes sinc
methods accessible to potential users by limiting
details as to how or why these methods work. From
calculus to partial differential and integral
equations, the book can be used to approximate almost
every type of operation. It includes more than 470
MATLAB programs, along with a CD-ROM containing these
programs for ease of use",
acknowledgement = ack-nhfb,
subject = "Galerkin methods; Differential equations; Numerical
solutions; mathematics / applied; mathematics /
differential equations; mathematics / number systems",
tableofcontents = "One-Dimensional Sinc Theory \\
Introduction and Summary \\
Sampling over the Real Line \\
More General Sinc Approximation on $R$ \\
Sinc, Wavelets, Trigonometric and Algebraic Polynomials
and Quadratures \\
Sinc Methods on $\Gamma$ \\
Rational Approximation at Sinc Points \\
Polynomial Methods at Sinc Points \\
\\
Sinc Convolution-BIE Methods for PDE and IE \\
Introduction and Summary \\
Some Properties of Green's Functions \\
Free-Space Green's Functions for PDE \\
Laplace Transforms of Green's Functions \\
Multi-Dimensional Convolution Based on Sinc \\
Theory of Separation of Variables \\
\\
Explicit 1-d Program Solutions via Sinc-Pack \\
Introduction and Summary \\
Sinc Interpolation \\
Approximation of Derivatives \\
Sinc Quadrature \\
Sinc Indefinite Integration \\
Sinc Indefinite Convolution \\
Laplace Transform Inversion \\
Hilbert and Cauchy Transforms \\
Sinc Solution of ODE \\
Wavelet Examples \\
\\
Explicit Program Solutions of PDE via Sinc-Pack \\
Introduction and Summary \\
Elliptic PDE \\
Hyperbolic PDE \\
Parabolic PDE \\
Performance Comparisons \\
\\
Directory of Programs \\
Wavelet Formulas \\
One Dimensional Sinc Programs \\
Multi-Dimensional Laplace Transform Programs \\
\\
Bibliography \\
\\
Index",
}
@Book{Tucker:2011:VNS,
author = "Warwick Tucker",
title = "Validated numerics: a short introduction to rigorous
computations",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "????",
year = "2011",
ISBN = "0-691-14781-7 (hardcover)",
ISBN-13 = "978-0-691-14781-9 (hardcover)",
LCCN = "QA76.95 .T83 2011",
bibdate = "Mon May 16 19:10:17 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
acknowledgement = ack-nhfb,
subject = "Numerical calculations; Verification; Science; Data
processing",
}
@Article{Watkins:2011:FA,
author = "David S. Watkins",
title = "{Francis}'s Algorithm",
journal = j-AMER-MATH-MONTHLY,
volume = "118",
number = "5",
pages = "387--403",
month = may,
year = "2011",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Thu May 26 16:28:05 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
URL = "http://www.jstor.org/stable/info/10.4169/amer.math.monthly.118.05.387",
abstract = "John Francis's implicitly shifted QR algorithm turned
the problem of matrix eigenvalue computation from
difficult to routine almost overnight about fifty years
ago. It was named one of the top ten algorithms of the
twentieth century by Dongarra and Sullivan, and it
deserves to be more widely known and understood by the
general mathematical community. This article provides
an efficient introduction to Francis's algorithm that
follows a novel path. Efficiency is gained by omitting
the traditional but wholly unnecessary detour through
the basic QR algorithm. A brief history of the
algorithm is also included. It was not a one-man show;
some other important names are Rutishauser, Wilkinson,
and Kublanovskaya. Francis was never a specialist in
matrix computations. He was employed in the early
computer industry, spent some time on the problem of
eigenvalue computation and did amazing work, and then
moved on to other things. He never looked back, and he
remained unaware of the huge impact of his work until
many years later.",
acknowledgement = ack-nhfb,
}
@Book{Zhang:2011:MTB,
author = "Fuzhen Zhang",
title = "Matrix Theory: Basic Results and Techniques",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xviii + 399",
year = "2011",
DOI = "https://doi.org/10.1007/978-1-4614-1099-7",
ISBN = "1-4614-1098-3 (paperback), 1-4614-1099-1 (e-book)",
ISBN-13 = "978-1-4614-1098-0 (paperback), 978-1-4614-1099-7
(e-book)",
LCCN = "QA188 .Z47 2011",
MRclass = "15-02 (15A09 15A15 15A18 15A45 15A54 15A60)",
MRnumber = "2857760 (2012h:15001)",
MRreviewer = "Mohammad Sal Moslehian",
bibdate = "Fri Nov 21 06:49:56 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Universitext",
URL = "http://www.loc.gov/catdir/enhancements/fy1406/2011935372-b.html;
http://www.loc.gov/catdir/enhancements/fy1406/2011935372-d.html;
http://www.loc.gov/catdir/enhancements/fy1406/2011935372-t.html",
abstract = "The aim of this book is to concisely present
fundamental ideas, results, and techniques in linear
algebra and mainly matrix theory. The book contains ten
chapters covering various topics ranging from
similarity and special types of matrices to Schur
complements and matrix normality. This book can be used
as a textbook or a supplement for a linear algebra and
matrix theory class or a seminar for senior
undergraduate or graduate students. The book can also
serve as a reference for instructors and researchers in
the fields of algebra, matrix analysis, operator
theory, statistics, computer science, engineering,
operations research, economics, and other fields.
Major changes in this revised and expanded second
edition: * Expansion of topics such as matrix
functions, nonnegative matrices, and (unitarily
invariant) matrix norms; * A new chapter, Chapter 4,
with updated material on numerical ranges and radii,
matrix norms, and special operations such as the
Kronecker and Hadamard products and compound matrices;
* A new chapter, Chapter 10, on matrix inequalities,
which presents a variety of inequalities on the
eigenvalues and singular values of matrices and
unitarily invariant norms.",
acknowledgement = ack-nhfb # " and " # ack-rah,
tableofcontents = "Preface to the Second Edition \\
Preface \\
Frequently Used Notation and Terminology \\
Frequently Used Terms \\
1 Elementary Linear Algebra Review \\
2 Partitioned Matrices, Rank, and Eigenvalues \\
3 Matrix Polynomials and Canonical Forms \\
4 Numerical Ranges, Matrix Norms, and Special
Operations \\
5 Special Types of Matrices \\
6 Unitary Matrices and Contractions \\
7 Positive Semidefinite Matrices \\
8 Hermitian Matrices \\
9 Normal Matrices \\
10 Majorization and Matrix Inequalities \\
References \\
Notation \\
Index",
}
@Book{Altman:2012:USM,
author = "Yair M. Altman",
title = "Undocumented secrets of {MATLAB--Java} programming",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xxi + 663 + 16",
year = "2012",
ISBN = "1-4398-6904-9 (electronic bk.), 1-4398-6903-0
(hardback), 1-4398-6903-0",
ISBN-13 = "978-1-4398-6904-8 (electronic bk.), 978-1-4398-6903-1
(hardback), 978-1-4398-6903-1",
LCCN = "QA297 .A544 2012",
bibdate = "Fri Nov 16 08:10:20 MST 2012",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
acknowledgement = ack-nhfb,
subject = "MATLAB; Numerical analysis; Data processing; Java
(Computer program language); COMPUTERS / Programming /
Algorithms; COMPUTERS / Computer Engineering;
MATHEMATICS / Number Systems. MATHEMATICS / Numerical
Analysis",
tableofcontents = "1.: Introduction to Java in MATLAB \\
2.: Using non-GUI Java libraries in MATLAB \\
3.: Rich GUI using Java Swing \\
4.: Uitools \\
5.: Built-in MATLAB widgets and Java classes \\
6.: Customizing MATLAB controls \\
7.: The Java frame \\
8.: The MATLAB desktop \\
9.: Using MATLAB from within Java \\
10.: Putting it all together \\
Appendix A.: What Is Java? \\
Appendix B.: UDD \\
Appendix C.: Open questions",
}
@Book{Antia:2012:NMS,
author = "H. M. Antia",
title = "Numerical methods for scientists and engineers",
volume = "2",
publisher = "Hindustan Book Agency, New Delhi",
address = "New Delhi",
edition = "Third",
pages = "xxxii + 855",
year = "2012",
ISBN = "93-80250-40-1 (hardcover)",
ISBN-13 = "978-93-80250-40-3 (hardcover)",
LCCN = "TA335 .A58 2012",
MRclass = "65-01",
MRnumber = "3025059",
bibdate = "Tue May 27 12:31:37 MDT 2014",
bibsource = "clas.caltech.edu:210/INNOPAC;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "Texts and Readings in Physical Sciences",
acknowledgement = ack-nhfb,
remark = "Previous ed.: Basel: Birkh{\"a}user, 2002.",
subject = "Numerical analysis; Engineering mathematics",
}
@Book{Atkinson:2012:SHA,
author = "Kendall Atkinson and Weimin Han",
title = "Spherical Harmonics and Approximations on the Unit
Sphere: an Introduction",
volume = "2044",
publisher = pub-SV,
address = pub-SV:adr,
pages = "ix + 244",
year = "2012",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/978-3-642-25983-8",
ISBN = "3-642-25982-0 (print), 3-642-25983-9 (e-book)",
ISBN-13 = "978-3-642-25982-1 (print), 978-3-642-25983-8
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
LCCN = "QA3 .L28 no. 2044; QA406 .A85 2012",
MRclass = "41A30 (65N30 65R20); 41-02 (33C55 41A30 41A63 42A10)",
MRnumber = "2934227",
MRreviewer = "Feng Dai",
bibdate = "Tue May 6 14:56:41 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/lnm2010.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = ser-LECT-NOTES-MATH,
URL = "http://link.springer.com/book/10.1007/978-3-642-25983-8;
http://www.springerlink.com/content/978-3-642-25983-8;
http://www.springerlink.com/content/u58550t8417n/",
abstract = "These notes provide an introduction to the theory of
spherical harmonics in an arbitrary dimension as well
asan overview of classical and recent results on some
aspects of the approximation of functions by spherical
polynomials and numerical integration over the unit
sphere. The notes are intended for graduate students in
the mathematical sciences and researchers who are
interested in solving problems involving partial
differential and integral equations on the unit sphere,
especially on the unit sphere in three-dimensional
Euclidean space. Some related work for approximation on
the unit disk in the plane is also briefly discussed,
with results being generalizable to the unit ball in
more dimensions.",
acknowledgement = ack-nhfb,
series-URL = "http://link.springer.com/bookseries/304",
tableofcontents = "1. Preliminaries \\
2. Spherical harmonics \\
3. Differentiation and integration over the sphere \\
4. Approximation theory \\
5. Numerical quadrature \\
6. Applications: spectral methods",
}
@Book{Attaway:2012:MPI,
author = "Stormy Attaway",
title = "{MATLAB}: a practical introduction to programming and
problem solving",
publisher = "Butterworth-Heinemann",
address = "Waltham, MA, USA",
edition = "Second",
pages = "xx + 518",
year = "2012",
ISBN = "0-12-385081-9",
ISBN-13 = "978-0-12-385081-2",
LCCN = "QA297 .A87 2012",
bibdate = "Thu May 3 08:07:25 MDT 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Data processing; MATLAB; Computer
programming",
}
@Book{Chaitin-Chatelin:2012:EM,
author = "Fran{\c{c}}oise Chaitin-Chatelin and Mario Ahu{\'e}s
and Walter Ledermann",
title = "Eigenvalues of matrices",
volume = "71",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Revised",
pages = "xxx + 410",
year = "2012",
ISBN = "1-61197-245-0",
ISBN-13 = "978-1-61197-245-0",
LCCN = "QA188 .C44 2012",
bibdate = "Tue Aug 12 15:33:32 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Classics in applied mathematics",
URL = "http://www.loc.gov/catdir/enhancements/fy1305/2012033049-d.html;
http://www.loc.gov/catdir/enhancements/fy1305/2012033049-t.html;
http://www.loc.gov/catdir/enhancements/fy1307/2012033049-b.html",
acknowledgement = ack-nhfb,
remark = "Translated from the original French.",
subject = "Matrices; Eigenvalues",
tableofcontents = "Supplements from linear algebra \\
Elements of spectral theory \\
Why compute eigenvalues? \\
Error analysis \\
Foundations of methods for computing eigenvalues \\
Numerical methods for large matrices \\
Chebyshev's iterative methods \\
Polymorphic information processing with matrices",
}
@Book{Davis:2012:LAP,
author = "Ernest Davis",
title = "Linear algebra and probability for computer science
applications",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xviii + 413",
year = "2012",
ISBN = "1-4665-0155-3 (hardcover)",
ISBN-13 = "978-1-4665-0155-3 (hardcover)",
LCCN = "QA76.9.M35 D38 2012",
bibdate = "Tue May 5 16:14:05 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
abstract = "Taking a computer scientist's point of view, this
classroom-tested text gives an introduction to linear
algebra and probability theory, including some basic
aspects of statistics. It discusses examples of
applications from a wide range of areas of computer
science, including computer graphics, computer vision,
robotics, natural language processing, web search,
machine learning, statistical analysis, game playing,
graph theory, scientific computing, decision theory,
coding, cryptography, network analysis, data
compression, and signal processing. It includes an
extensive discussion of MATLAB, and includes numerous
MATLAB exercises and programming assignments.",
acknowledgement = ack-nhfb,
subject = "Computer science; Mathematics; Algebras, Linear;
Probabilities",
}
@Book{Eubank:2012:SCC,
author = "Randall L. Eubank and Ana Kupresanin",
title = "Statistical computing in {C++} and {R}",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xv + 540",
year = "2012",
ISBN = "1-4200-6650-1 (hardcover)",
ISBN-13 = "978-1-4200-6650-0 (hardcover)",
LCCN = "QA276.4 .E87 2012",
bibdate = "Thu Jul 10 13:05:53 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/s-plus.bib;
z3950.loc.gov:7090/Voyager",
series = "Chapman and Hall/CRC the R series",
abstract = "When one looks at a book with `statistical computing'
in the title, the expectation is most likely for a
treatment of the topic that has close ties to numerical
analysis. There are many texts written from this
perspective that provide valuable resources for those
who are actively involved in the solution of computing
problems that arise in statistics. The presentation in
the present text represents a departure from this
classical emphasis in that it concentrates on the
writing of code rather than the development and study
of algorithms, per se. The goal is to provide a
treatment of statistical computing that lays a
foundation for original code development in a research
environment. The advancement of statistical methodology
is now inextricably linked to the use of computers. New
methodological ideas must be translated into usable
code and then numerically evaluated relative to
competing procedures. As a result, many statisticians
expend significant amounts of their creative energy
while sitting in front of a computer monitor. The end
products from the vast majority of these efforts are
unlikely to be reflected in changes to core aspects of
numerical methods or computer hardware. Nonetheless,
they are modern statisticians that are (often very)
involved in computing. This book is written with that
particular audience in mind. What does a modern
statistician need to know about computing? Our belief
is that they need to understand at least the basic
principles of algorithmic thinking. The translation of
a mathematical problem into its computational analog
(or analogs) is a skill that must be learned, like any
other, by actively solving relevant problems.",
acknowledgement = ack-nhfb,
author-dates = "1952--",
subject = "Statistics; Data processing; C++ (Computer program
language); R (Computer program language); MATHEMATICS /
Probability and Statistics / General.",
tableofcontents = "1.1. Programming paradigms \\
1.2. Object-oriented programming \\
1.3. What lies ahead \\
2.1. Introduction \\
2.2. Storage in C++ \\
2.3. Integers \\
2.4. Floating-point representation \\
2.5. Errors \\
2.6. Computing a sample variance \\
2.7. Storage in R \\
2.8. Exercises \\
3.1. Introduction \\
3.2. Variables and scope \\
3.3. Arithmetic and logical operators \\
3.4. Control structures \\
3.5. Using arrays and pointers \\
3.6. Functions \\
3.7. Classes, objects and methods \\
3.8. Miscellaneous topics \\
3.8.1. Structs \\
3.8.2. The this pointer \\
3.8.3.const correctness \\
3.8.4. Forward references \\
3.8.5. Strings \\
3.8.6. Namespaces \\
3.8.7. Handling errors \\
3.8.8. Timing a program \\
3.9. Matrix and vector classes \\
3.10. Input, output and templates \\
3.11. Function templates \\
3.12. Exercises \\
4.1. Introduction \\
4.2. Congruential methods \\
4.3. Lehmer type generators in C++ \\
4.4. An FM2 class \\
4.5. Other generation methods \\
4.6. Nonuniform generation \\
4.7. Generating random normals \\
4.8. Generating random numbers in R \\
4.9. Using the R Standalone Math Library \\
4.10. Exercises \\
5.1. Introduction \\
5.2. File input and output \\
5.3. Classes, methods and namespaces \\
5.4. Writing R functions \\
5.5. Avoiding loops in R \\
5.6. An example \\
5.7. Using C/C++ code in R \\
5.8. Exercises \\
6.1. Introduction \\
6.2. Creating a new class \\
6.3. Generic methods \\
6.4. An example \\
6.5. Exercises \\
7.1. Introduction \\
7.2. Solving linear equations \\
7.2.1. Solving triangular systems \\
7.2.2. Gaussian elimination \\
7.2.3. Cholesky decomposition \\
7.2.4. Banded matrices \\
7.2.5. An application: linear smoothing splines \\
7.2.6. Banded matrices via inheritance \\
7.3. Eigenvalues and eigenvectors \\
7.4. Singular value decomposition \\
7.5. Least squares \\
7.6. The Template Numerical Toolkit \\
7.7. Exercises \\
8.1. Introduction \\
8.2. Function objects \\
8.3. Golden section \\
8.3.1. Dealing with multiple minima \\
8.3.2. An application: linear smoothing splines
revisited \\
8.4. Newton's method \\
8.5. Maximum likelihood \\
8.6. Random search \\
8.7. Exercises \\
9.1. Introduction \\
9.2. ADT dictionary \\
9.2.1. Dynamic arrays and quicksort \\
9.2.2. Linked lists and mergesort \\
9.2.3. Stacks and queues \\
9.2.4. Hash tables \\
9.3. ADT priority queue \\
9.3.1. Heaps \\
9.3.2. A simple heap in C++ \\
9.4. ADT ordered set \\
9.4.1. A simple C++ binary search tree \\
9.4.2. Balancing binary trees \\
9.5. Pointer arithmetic, aerators and templates \\
9.5.1. Iterators \\
9.5.2. A linked list template class \\
9.6. Exercises \\
10.1. Introduction \\
10.2. Container basics \\
10.3. Vector and deque \\
10.3.1. Streaming data \\
10.3.2. Flexible data input \\
10.3.3. Guess5 revisited \\
10.4. The C++ list container \\
10.4.1. An example \\
10.4.2. A chaining hash table \\
10.5. Queues \\
10.6. The map and set containers \\
10.7. Algorithm basics \\
10.8. Exercises \\
11.1. Introduction \\
11.2. OpenMP \\
11.3. Basic MPI commands for C++ \\
11.4. Parallel processing in R \\
11.5. Parallel random number generation \\
11.6. Exercises \\
A.1. Getting around and finding things \\
A.2. Seeing what's there \\
A.3. Creating and destroying things \\
A.4. Things that are running and how to stop them \\
B.1. R as a calculator \\
B.2. R as a graphics engine \\
B.3. R for statistical analysis \\
C.1. Pseudo-random numbers \\
C.2. Hash tables \\
C.3. Tuples",
}
@Article{Gander:2012:ERG,
author = "Martin J. Gander and Gerhard Wanner",
title = "From {Euler}, {Ritz}, and {Galerkin} to Modern
Computing",
journal = j-SIAM-REVIEW,
volume = "54",
number = "4",
pages = "627--666",
month = "????",
year = "2012",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/100804036",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "http://epubs.siam.org/toc/siread/54/4;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 2012",
}
@Book{Griffiths:2012:TWA,
author = "Graham W. Griffiths and W. E. Schiesser",
title = "Traveling wave analysis of partial differential
equations: numerical and analytical methods with
{MATLAB} and {Maple}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xiii + 447",
year = "2012",
ISBN = "0-12-384652-8 (hardcover)",
ISBN-13 = "978-0-12-384652-5 (hardcover)",
LCCN = "QA374 .G75 2012",
bibdate = "Tue Jun 19 15:02:49 MDT 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Differential equations, Partial; Numerical analysis;
Computer programs; MATLAB; Maple (Computer file)",
tableofcontents = "Introduction to traveling wave analysis \\
Linear advection equation \\
Linear diffusion equation \\
A linear convection diffusion reaction equation \\
Diffusion equation with nonlinear source terms \\
Burgers-Huxley equation \\
Burgers-Fisher equation \\
Fisher-Kolmogorov equation \\
Fitzhugh-Nagumo equation \\
Kolmogorov-Petrovskii-Piskunov equation \\
Kuramoto-Sivashinsky equation \\
Kawahara equation \\
Regularized long wave equation \\
Extended Bernoulli equation \\
Hyperbolic Liouville equation \\
Sine-Gordon equation \\
Mth-Oder Klein-Gordon equation \\
Boussinesq equation \\
Modified wave equation \\
Appendix: Analytical solution methods for traveling
wave problems",
}
@Book{Hamming:2012:IAN,
author = "R. W. (Richard Wesley) Hamming",
title = "Introduction to Applied Numerical Analysis",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "x + 331",
year = "2012",
ISBN = "0-486-48590-0 (paperback)",
ISBN-13 = "978-0-486-48590-4 (paperback)",
LCCN = "QA297 .H275 2012",
bibdate = "Mon Aug 6 08:42:33 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Dover books on mathematics",
abstract = "This book is appropriate for an applied numerical
analysis course for upper-level undergraduate and
graduate students as well as computer science students.
Actual programming is not covered, but an extensive
range of topics includes round-off and function
evaluation, real zeros of a function, integration,
ordinary differential equations, optimization,
orthogonal functions, Fourier series, and much more.",
acknowledgement = ack-nhfb,
author-dates = "1915--1998",
remark = "Originally published as \cite{Hamming:1989:IAN}.",
subject = "Numerical analysis; Data processing",
tableofcontents = "Preface \\
1. Roundoff and Function Evaluation \\
2. Real Zeros of a Function \\
3. Complex Zeros \\
4. Zeros of Polynomials \\
5. Simultaneous Linear Equations and Matrices \\
6. Interpolation and Roundoff Estimation \\
7. Integration \\
8. Ordinary Differential Equations \\
9. Optimization \\
10. Least Squares \\
11. Orthogonal Functions \\
12. Fourier Series \\
13. Chebyshev Approximation \\
14. Random Processes \\
15. Design of a Library \\
Index",
}
@Book{Horn:2012:MA,
author = "Roger A. Horn and Charles R. (Charles Royal) Johnson",
title = "Matrix Analysis",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Second",
pages = "xviii + 643",
year = "2012",
DOI = "https://doi.org/10.1017/CBO9781139020411",
ISBN = "0-521-83940-8 (hardcover), 0-521-54823-3 (paperback),
1-283-74139-3, 1-139-77904-4, 1-139-77600-2 (e-book),
1-139-02041-2 (e-book)",
ISBN-13 = "978-0-521-83940-2 (hardcover), 978-0-521-54823-6
(paperback), 978-1-283-74139-2, 978-1-139-77904-3,
978-1-139-77600-4 (e-book), 978-1-139-02041-1
(e-book)",
LCCN = "QA188 .H66 2012",
bibdate = "Thu Nov 20 09:13:05 MST 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/linala2010.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
abstract = "The thoroughly revised and updated second edition of
this acclaimed text has several new and expanded
sections and more than 1,100 exercises.",
acknowledgement = ack-nhfb,
subject = "Matrices; MATHEMATICS; Algebra; Abstract; Matrices",
tableofcontents = "Frontmatter / i--vi \\
Contents / vii--x \\
Preface to the Second Edition / xi--xiv \\
Preface to the First Edition / xv--xviii \\
0. Review and Miscellanea / 1--42 \\
1. Eigenvalues, Eigenvectors, and Similarity / 43--82
\\
2. Unitary Similarity and Unitary Equivalence / 83--162
\\
3. Canonical Forms for Similarity and Triangular
Factorizations / 163--224 \\
4. Hermitian Matrices, Symmetric Matrices, and
Congruences / 225--312 \\
5. Norms for Vectors and Matrices / 313--386 \\
6. Location and Perturbation of Eigenvalues / 387--424
\\
7. Positive Definite and Semidefinite Matrices /
425--516 \\
8. Positive and Nonnegative Matrices / 517--554 \\
Appendix A. Complex Numbers / 555--556 \\
Appendix B. Convex Sets and Functions / 557--560 \\
Appendix C. The Fundamental Theorem of Algebra /
561--562 \\
Appendix D. Continuity of Polynomial Zeroes and Matrix
Eigenvalues / 563--564 \\
Appendix E. Continuity, Compactness, and Weierstrass's
Theorem / 565--566 \\
Appendix F. Canonical Pairs / 567--570 \\
References / 571--574 \\
Notation / 575--578 \\
Hints for Problems / 579--606 \\
Index / 607--643",
}
@Book{Kharab:2012:INM,
author = "Abdelwahab Kharab and Ronald B. Guenther",
title = "An introduction to numerical methods: a {MATLAB}
approach",
publisher = pub-CHAPMAN-HALL-CRC,
address = pub-CHAPMAN-HALL-CRC:adr,
edition = "Third",
pages = "14 + 567",
year = "2012",
ISBN = "1-4398-6899-9 (hardback), 1-4398-6900-6 (e-book)",
ISBN-13 = "978-1-4398-6899-7 (hardback), 978-1-4398-6900-0
(e-book)",
LCCN = "QA297 .K52 2012",
bibdate = "Fri Nov 16 06:29:40 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Data processing; MATLAB",
tableofcontents = "Introduction \\
Number system and errors \\
Roots of equations \\
System of linear equations \\
Interpolation \\
Interpolation with spline functions \\
The method of least-squares \\
Numerical optimization \\
Numerical differentiation \\
Numerical integration \\
Numerical methods for linear integral equations \\
Numerical methods for differential equations \\
Boundary-value problems \\
Eigenvalues and eigenvectors \\
Partial differential equations",
}
@Book{Kugler:2012:AMB,
author = "Philipp K{\"u}gler and Wolfgang Windsteiger",
title = "Algorithmische {Methoden}. {Band} 2",
publisher = "Birkh{\"a}user/Springer Basel AG, Basel",
pages = "viii + 159",
year = "2012",
DOI = "https://doi.org/10.1007/978-3-7643-8516-3",
ISBN = "3-7643-8515-4; 3-7643-8516-2",
ISBN-13 = "978-3-7643-8515-6; 978-3-7643-8516-3",
MRclass = "65-01 (68-01)",
MRnumber = "3086486",
bibdate = "Tue May 27 11:24:21 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
note = "Funktionen, Matrizen, multivariate Polynome.
[Functions, matrices, multivariate polynomials]",
series = "Mathematik Kompakt. [Compact Mathematics]",
acknowledgement = ack-nhfb,
}
@Book{Langtangen:2012:PSP,
author = "Hans Petter Langtangen",
title = "A primer on scientific programming with {Python}",
volume = "6",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Third",
year = "2012",
DOI = "https://doi.org/10.1007/978-3-642-30293-0",
ISBN = "3-642-30292-0, 3-642-30293-9 (e-book)",
ISBN-13 = "978-3-642-30292-3, 978-3-642-30293-0 (e-book)",
ISSN = "1611-0994",
LCCN = "QA76.73.P98 L36 2012",
bibdate = "Fri Nov 29 07:00:01 MST 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/python.bib",
series = "Texts in computational science and engineering",
URL = "http://site.ebrary.com/id/10650410",
abstract = "The book serves as a first introduction to computer
programming of scientific applications, using the
high-level Python language. The exposition is example-
and problem-oriented, where the applications are taken
from mathematics, numerical calculus, statistics,
physics, biology, and finance. The book teaches
``Matlab-style'' and procedural programming as well as
object-oriented programming. High school mathematics is
a required background, and it is advantageous to study
classical and numerical one-variable calculus in
parallel with reading this book. Besides learning how
to program computers.",
acknowledgement = ack-nhfb,
subject = "Python (Computer program language); Computer
programming; Science; Data processing",
tableofcontents = "Computing with Formulas \\
Loops and Lists \\
Functions and Branching \\
Input Data and Error Handling \\
Array Computing and Curve Plotting \\
Files, Strings, and Dictionaries \\
Introduction to Classes \\
Random Numbers and Simple Games \\
Object-Oriented Programming",
}
@Book{Laub:2012:CMA,
author = "Alan J. Laub",
title = "Computational matrix analysis",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xiii + 154",
year = "2012",
ISBN = "1-61197-220-5 (paperback), 1-61197-221-3 (e-book)",
ISBN-13 = "978-1-61197-220-7 (paperback), 978-1-61197-221-4
(e-book)",
LCCN = "QA274.2 .L38 2012",
MRclass = "65-01 (65Fxx)",
MRnumber = "2934576",
MRreviewer = "Petko Petkov",
bibdate = "Tue May 27 12:02:28 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Other titles in applied mathematics",
URL = "http://www.loc.gov/catdir/enhancements/fy1211/2011050702-b.html;
http://www.loc.gov/catdir/enhancements/fy1211/2011050702-d.html;
http://www.loc.gov/catdir/enhancements/fy1211/2011050702-t.html",
acknowledgement = ack-nhfb,
subject = "Matrix analytic methods; Data processing",
}
@Book{Layton:2012:ADM,
author = "William J. Layton and Leo G. Rebholz",
title = "Approximate Deconvolution Models of Turbulence:
Analysis, Phenomenology and Numerical Analysis",
volume = "2042",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 184",
year = "2012",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/978-3-642-24409-4",
ISBN = "3-642-24408-4 (print), 3-642-24409-2 (e-book)",
ISBN-13 = "978-3-642-24408-7 (print), 978-3-642-24409-4
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
LCCN = "QA3 .L28 no. 2042",
MRclass = "76-02 (76D03 76D05 76F65)",
MRnumber = "2934085",
MRreviewer = "Peter Bernard Weichman",
bibdate = "Tue May 6 14:56:41 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/lnm2010.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = ser-LECT-NOTES-MATH,
URL = "http://link.springer.com/book/10.1007/978-3-642-24409-4;
http://www.springerlink.com/content/978-3-642-24409-4",
acknowledgement = ack-nhfb,
series-URL = "http://link.springer.com/bookseries/304",
}
@Book{Molitierno:2012:ACM,
author = "Jason J. Molitierno",
title = "Applications of combinatorial matrix theory to
{Laplacian} matrices of graphs",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "405",
year = "2012",
ISBN = "1-4398-6337-7 (hardcover)",
ISBN-13 = "978-1-4398-6337-4 (hardcover)",
LCCN = "QA166.243 .M65 2012",
bibdate = "Tue May 5 16:13:52 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Discrete mathematics and its applications",
abstract = "On the surface, matrix theory and graph theory are
seemingly very different branches of
mathematics. However, these two branches of mathematics
interact since it is often convenient to represent a
graph as a matrix. Adjacency, Laplacian, and incidence
matrices are commonly used to represent graphs. In
1973, Fiedler published his first paper on Laplacian
matrices of graphs and showed how many properties of
the Laplacian matrix, especially the eigenvalues, can
give us useful information about the structure of the
graph. Since then, many papers have been published on
Laplacian matrices. This book is a compilation of many
of the exciting results concerning Laplacian matrices
that have been developed since the mid 1970's. Papers
written by well-known mathematicians such as
(alphabetically) Fallat, Fiedler, Grone, Kirkland,
Merris, Mohar, Neumann, Shader, Sunder, and several
others are consolidated here. Each theorem is
referenced to its appropriate paper so that the reader
can easily do more in-depth research on any topic of
interest. However, the style of presentation in this
book is not meant to be that of a journal but rather a
reference textbook. Therefore, more examples and more
detailed calculations are presented in this book than
would be in a journal article. Additionally, most
sections are followed by exercises to aid the reader in
gaining a deeper understanding of the material. Some
exercises are routine calculations that involve
applying the theorems presented in the section. Other
exercises require a more in-depth analysis of the
theorems and require the reader to prove theorems that
go beyond what was presented in the section. Many of
these exercises are taken from relevant papers and they
are referenced accordingly.",
acknowledgement = ack-nhfb,
subject = "Graph connectivity; Laplacian matrices; COMPUTERS /
Operating Systems / General.; COMPUTERS / Programming /
Algorithms.; MATHEMATICS / Combinatorics.",
}
@Book{Pont:2012:DDW,
author = "Jean-Claude Pont and Christophe Rossel",
title = "Le destin douloureux de {Walther Ritz} (1878--1909),
physicien th{\'e}oricien de g{\'e}nie",
volume = "24",
publisher = "Archives de l'{\'e}tat du Valais",
address = "Vallesia, France",
pages = "264 + 41",
year = "2012",
ISBN = "2-9700636-5-4 (hardcover)",
ISBN-13 = "978-2-9700636-5-0 (hardcover)",
LCCN = "????",
bibdate = "Mon Apr 21 12:49:54 MDT 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/histmath.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Cahiers de Vallesia",
acknowledgement = ack-nhfb,
author-dates = "(1941--\ldots{}.).",
remark = "Contributions en fran{\c{c}}ais et en anglais.",
subject = "Ritz, Walther; Biographies.; Physique
math{\'e}matique; Histoire.; Sciences",
subject-dates = "(1878--1909)",
tableofcontents = "Aspects de la vie et de l'oeuvre de Walther Ritz,
physicien th{\'e}oricien valaisan / Jean-Claude Pont
\\
Walther Ritz et ses correspondants / Jean-Claude Pont
\\
Walther Ritz, quelques dates / Jean-Claude Pont \\
Sion au temps de Walther Ritz / Patrice Tschopp \\
Ritz face {\`a} la physique de son temps / Jan Lacki
\\
Walther Ritz exp{\'e}rimentateur / Nicolas Produit \\
Walther Ritz's theoretical work in spectroscopy,
focussing on series formulas / Klaus Hentschel \\
From Euler, Ritz and Galerkin to modern computing /
Martin J. Gander and Gerhard Wanner \\
Electrodynamics in the physics of Walther Ritz /
Olivier Darrigol \\
Manifestations {\`a} l'occasion du centenaire de la
mort de Walther Ritz, Sion, 17--19 septembre 2009 \\
Bibliographie des {\'e}crits de Walther Ritz /
Jean-Claude Pont and Nicolas Produit",
}
@Book{Rebaza:2012:FCA,
author = "Jorge Rebaza",
title = "A first course in applied mathematics",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xvi + 439",
year = "2012",
ISBN = "1-118-22962-2",
ISBN-13 = "978-1-118-22962-0",
LCCN = "TA342 .R43 2012",
bibdate = "Tue May 5 16:13:00 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy1201/2011043340-d.html;
http://www.loc.gov/catdir/enhancements/fy1201/2011043340-t.html;
http://www.loc.gov/catdir/enhancements/fy1210/2011043340-b.html",
abstract = "This book details how applied mathematics involves
predictions, interpretations, analysis, and
mathematical modeling to solve real-world problems. Due
to the broad range of applications, mathematical
concepts and techniques and reviewed throughout,
especially those in linear algebra, matrix analysis,
and differential equations. Some classical definitions
and results from analysis are also discussed and used.
Some applications (postscript fonts, information
retrieval, etc.) are presented at the end of a chapter
as an immediate application of the theory just covered,
while those applications that are discussed in more
detail (ranking web pages, compression, etc.) are
presented in dedicated chapters. A collection of
mathematical models of a slightly different nature,
such as basic discrete mathematics and optimization, is
also provided. Clear proofs of the main theorems
ultimately help to make the statements of the theorems
more understandable, and a multitude of examples follow
important theorems and concepts. In addition, the
author builds material from scratch and thoroughly
covers the theory needed to explain the applications in
full detail, while not overwhelming readers with
unnecessary topics or discussions. In terms of
exercises, the author continuously refers to the real
numbers and results in calculus when introducing a new
topic so readers can grasp the concept of the otherwise
intimidating expressions. By doing this, the author is
able to focus on the concepts rather than the rigor.
The quality, quantity, and varying level of difficulty
of the exercises provides instructors more classroom
flexibility. Topical coverage includes linear algebra;
ranking web pages; matrix factorizations; least
squares; image compression; ordinary differential
equations; dynamical systems; and mathematical
models.",
acknowledgement = ack-nhfb,
author-dates = "1962--",
subject = "Mathematical models; Computer simulation; Mathematics
/ Applied",
tableofcontents = "Preface / xi \\
1. Basics of Linear Algebra / 1 \\
1.1 Notation and Terminology / 1 \\
1.2 Vector and Matrix Norms / 4 \\
1.3 Dot Product and Orthogonality / 8 \\
1.4 Special Matrices / 9 \\
1.5 Vector Spaces / 21 \\
1.6 Linear Independence and Basis / 24 \\
1.7 Orthogonalization and Direct Sums / 30 \\
1.8 Column Space, Row Space and Null Space / 34 \\
1.9 Orthogonal Projections / 43 \\
1.10 Eigenvalues and Eigenvectors / 47 \\
1.11 Similarity / 56 \\
1.12 Bezier Curves Postscripts Fonts / 59 \\
1.13 Final Remarks and Further Reading / 68 \\
2. Ranking Web Pages / 79 \\
2.1 The Power Method / 80 \\
2.2 Stochastic, Irreducible and Primitive Matrices / 84
\\
2.3 Google's PageRank Algorithm / 92 \\
2.4 Alternatives to Power Method / 106 \\
2.5 Final Remarks and Further Reading / 120 \\
3. Matrix Factorizations / 131 \\
3.1 LU Factorization / 132 \\
3.2 QR Factorization / 142 \\
3.3 Singular Value Decomposition (SVD) / 155 \\
3.4 Schur Factorization / 166 \\
3.5 Information Retrieval / 186 \\
3.6 Partition of Simple Substitution Cryptograms / 194
\\
3.7 Final Remarks and Further Reading / 203 \\
4. Least Squares / 215 \\
4.1 Projections and Normal Equations / 215 \\
4.2 Least Squares and QR Factorization / 224 \\
4.3 Lagrange Multipliers / 228 \\
4.4 Final Remarks and Further Reading / 231 \\
5. Image Compression / 235 \\
5.1 Compressing with Discrete Cosine Transform / 236
\\
5.2 Huffman Coding / 260 \\
5.3 Compression with SVD / 267 \\
5.4 Final Remarks and Further Reading / 271 \\
6. Ordinary Differential Equations / 277 \\
6.1 One-Dimensional Differential Equations / 278 \\
6.2 Linear Systems of Differential Equations / 307 \\
6.3 Solutions via Eigenvalues and Eigenvectors / 308
\\
6.4 Fundamentals Matrix Solution / 312 \\
6.5 Final Remarks and Further Reading / 316 \\
7. Dynamical Systems / 325 \\
7.1 Linear Dynamical Systems / 326 \\
7.2 Nonlinear Dynamical Systems / 340 \\
7.3 Predator--Prey Models with Harvesting / 374 \\
7.4 Final Remarks and Further Reading / 385 \\
8. Mathematical Models / 395 \\
8.1 Optimization of a Waste Management System / 396 \\
8.2 Grouping Problem in Networks / 404 \\
8.3 American Cutaneous Leishmaniasis / 410 \\
8.4 Variable Population Interactions / 420 \\
References / 431 \\
Index / 435",
}
@Book{Rizopoulos:2012:JML,
author = "Dimitris Rizopoulos",
title = "Joint models for longitudinal and time-to-event data:
with applications in {R}",
volume = "6",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xiv + 261",
year = "2012",
ISBN = "1-4398-7286-4 (hardcover)",
ISBN-13 = "978-1-4398-7286-4 (hardcover)",
LCCN = "QA279 .R59 2012",
bibdate = "Thu Jul 21 05:59:33 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/s-plus.bib;
z3950.loc.gov:7090/Voyager",
series = "Chapman and Hall/CRC biostatistics series",
abstract = "Joint models for longitudinal and time-to-event data
have become a valuable tool in the analysis of
follow-up data. These models are applicable mainly in
two settings: First, when focus is in the survival
outcome and we wish to account for the effect of an
endogenous time-dependent covariate measured with
error, and second, when focus is in the longitudinal
outcome and we wish to correct for nonrandom dropout.
Due to their capability to provide valid inferences in
settings where simpler statistical tools fail to do so,
and their wide range of applications, the last 25 years
have seen many advances in the joint modeling field.
Even though interest and developments in joint models
have been widespread, information about them has been
equally scattered in articles, presenting recent
advances in the field, and in book chapters in a few
texts dedicated either to longitudinal or survival data
analysis. However, no single monograph or text
dedicated to this type of models seems to be available.
The purpose in writing this book, therefore, is to
provide an overview of the theory and application of
joint models for longitudinal and survival data. In the
literature two main frameworks have been proposed,
namely the random effects joint model that uses latent
variables to capture the associations between the two
outcomes (Tsiatis and Davidian, 2004), and the marginal
structural joint models based on G estimators (Robins
et al., 1999, 2000). In this book we focus in the
former. Both subfields of joint modeling, i.e.,
handling of endogenous time-varying covariates and
nonrandom dropout, are equally covered and presented in
real datasets.",
acknowledgement = ack-nhfb,
shorttableofcontents = "1. Introduction \\
2. Longitudinal data analysis \\
3. Analysis of event time data \\
4. Joint models for longitudinal and time-to-event data
\\
5. Extensions of the standard joint model \\
6. Joint model diagnostics \\
7. Prediction and accuracy in joint models",
subject = "Numerical analysis; Data processing; R (Computer
program language); MATHEMATICS / Probability and
Statistics / General; MEDICAL / Epidemiology",
tableofcontents = "Preface \\
1: Introduction \\
1.1: Goals \\
1.2: Motivating Studies \\
1.2.1: Primary Biliary Cirrhosis Data \\
1.2.2: AIDS Data \\
1.2.3: Liver Cirrhosis Data \\
1.2.4: Aortic Valve Data \\
1.2.5: Other Applications \\
1.3: Inferential Objectives in Longitudinal Studies \\
1.3.1: Effect of Covariates on a Single Outcome \\
1.3.2: Association between Outcomes \\
1.3.3: Complex Hypothesis Testing \\
1.3.4: Prediction \\
1.3.5: Statistical Analysis with Implicit Outcomes \\
1.4: Overview \\
2: Longitudinal Data Analysis \\
2.1: Features of Longitudinal Data \\
2.2: Linear Mixed-Effects Models \\
2.2.1: Estimation \\
2.2.2: Implementation in R \\
2.3: Missing Data in Longitudinal Studies \\
2.3.1: Missing Data Mechanisms \\
2.3.2: Missing Not at Random Model Families \\
2.4: Further Reading \\
3: Analysis of Event Time Data \\
3.1: Features of Event Time Data \\
3.2: Basic Functions in Survival Analysis \\
3.2.1: Likelihood Construction for Censored Data \\
3.3: Relative Risk Regression Models \\
3.3.1: Implementation in R \\
3.4: Time-Dependent Covariates \\
3.5: Extended Cox Model \\
3.6: Further Reading \\
4: Joint Models for Longitudinal and Time-to-Event Data
\\
4.1: The Basic Joint Model \\
4.1.1: The Survival Submodel \\
4.1.2: The Longitudinal Submodel \\
4.2: Joint Modeling in R: A Comparison with the
Extended Cox Model \\
4.3: Estimation of Joint Models \\
4.3.1: Two-Stage Approaches \\
4.3.2: Joint Likelihood Formulation \\
4.3.3: Standard Errors with an Unspecified Baseline
Risk Function \\
4.3.4: Optimization Control in JM \\
4.3.5: Numerical Integration \\
4.3.6: Numerical Integration Control in JM \\
4.3.7: Convergence Problems \\
4.4: Asymptotic Inference for Joint Models \\
4.4.1: Hypothesis Testing \\
4.4.2: Confidence Intervals \\
4.4.3: Design Considerations \\
4.5: Estimation of the Random Effects \\
4.6: Connection with the Missing Data Framework \\
4.7: Sensitivity Analysis under Joint Models \\
5: Extensions of the Standard Joint Model \\
5.1: Parameterizations \\
5.1.1: Interaction Effects \\
5.1.2: Lagged Effects \\
5.1.3: Time-Dependent Slopes Parameterization \\
5.1.4: Cumulative Effects Parameterization \\
5.1.5: Random-Effects Parameterization \\
5.2: Handling Exogenous Time-Dependent Covariates \\
5.3: Stratified Relative Risk Models \\
5.4: Latent Class Joint Models \\
5.5: Multiple Failure Times \\
5.5.1: Competing Risks \\
5.5.2: Recurrent Events \\
5.6: Accelerated Failure Time Models \\
5.7: Joint Models for Categorical Longitudinal Outcomes
\\
5.7.1: The Generalized Linear Mixed Model (GLMM) \\
5.7.2: Combining Discrete Repeated Measures with
Survival \\
5.8: Joint Models for Multiple Longitudinal Outcomes
\\
6: Joint Model Diagnostics \\
6.1: Residuals for Joint Models \\
6.1.1: Residuals for the Longitudinal Part \\
6.1.2: Residuals for the Survival Part \\
6.2: Dropout and Residuals \\
6.3: Multiple Imputation Residuals \\
6.3.1: Fixed Visit Times \\
6.3.2: Random Visit Times \\
6.4: Random-Effects Distribution \\
7: Prediction and Accuracy in Joint Models \\
7.1: Dynamic Predictions of Survival Probabilities \\
7.1.1: Definition \\
7.1.2: Estimation \\
7.1.3: Implementation in R \\
7.2: Dynamic Predictions for the Longitudinal Outcome
\\
7.3: Effect of Parameterization on Predictions \\
7.4: Prospective Accuracy for Joint Models \\
7.4.1: Discrimination Measures for Binary Outcomes \\
7.4.2: Discrimination Measures for Survival Outcomes
\\
7.4.3: Prediction Rules for Longitudinal Markers \\
7.4.4: Discrimination Indices \\
7.4.5: Estimation under the Joint Modeling Framework
\\
7.4.6: Implementation in R \\
A: A Brief Introduction to R \\
A.1: Obtaining and Installing R and R Packages \\
A.2: Simple Manipulations \\
A.2.1: Basic R Objects \\
A.2.2: Indexing \\
A.3: Import and Manipulate Data Frames \\
A.4: The Formula Interface \\
B: The EM Algorithm for Joint Models \\
B.1: A Short Description of the EM Algorithm \\
B.2: The E-step for Joint Models \\
B.3: The M-step for Joint Models \\
C: Structure of the JM Package \\
C.1: Methods for Standard Generic Functions \\
C.2: Additional Functions \\
References \\
Index",
}
@Book{Shapira:2012:SPC,
author = "Yair Shapira",
title = "Solving {PDEs} in {C++}: numerical methods in a
unified object-oriented approach",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Second",
pages = "xxxii + 776",
year = "2012",
DOI = "https://doi.org/10.1137/9781611972177",
ISBN = "1-61197-216-7 (paperback)",
ISBN-13 = "978-1-61197-216-0 (paperback)",
LCCN = "QA377 .S466 2012",
bibdate = "Thu Aug 28 08:20:59 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Computational science and engineering series",
acknowledgement = ack-nhfb,
author-dates = "1960--",
subject = "Differential equations, Partial; C++ (Computer program
language); Object-oriented programming (Computer
science)",
tableofcontents = "Part I. Elementary background in programming \\
1. Concise introduction to C \\
2. Concise introduction to C++ \\
3. Data structures used in the present algorithms \\
Part II. Object-oriented programming \\
4. From Wittgenstein--Lacan's theory to the
object-oriented implementation of graphs and matrices
\\
5. FFT and other algorithms in numerics and
cryptography \\
6. Object-oriented analysis of nonlinear ordinary
differential equations \\
Part III. Partial differential equations and their
discretization \\
7. The convection--diffusion equation \\
8. Some stability analysis \\
9. About nonlinear conservation laws \\
10. Application in image processing \\
Part IV. Finite elements \\
11. About the weak formulation \\
12. Some background in linear finite elements \\
13. Unstructured finite-element meshes \\
14. Adaptive mesh refinement \\
15. Towards high-order finite elements\\
Part V. The numerical solution of large sparse linear
systems of algebraic equations \\
16. Sparse matrices and their object-oriented
implementation \\
17. Iterative methods for the numerical solution of
large sparse linear systems of algebraic equations \\
18. Towards parallelism\\
Part VI. Applications in two spatial dimensions \\
19. Diffusion equations \\
20. The linear elasticity equations \\
21. The Stokes equations \\
22. Application in electromagnetic waves \\
23. Multigrid for nonlinear equations and for the
fusion problem in image processing \\
Part VII. Applications in three spatial dimensions \\
24. Polynomials in three independent variables \\
25. The Helmholtz equation : error estimate \\
26. Adaptive finite elements in three spatial
dimensions \\
27. Application in nonlinear optics : the nonlinear
Helmholtz equation in three spatial dimensions \\
28. High-order finite elements in three spatial
dimensions \\
29. Application in the nonlinear Maxwell equations \\
30. Towards inverse problems \\
31. Application in the Navier--Stokes equations \\
Appendix A. Solutions to selected exercises \\
Bibliography \\
Index",
}
@Book{Sirca:2012:CMP,
author = "Simon {\v{S}}irca and Martin Horvat",
title = "Computational methods for physicists",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xx + 715",
year = "2012",
DOI = "https://doi.org/10.1007/978-3-642-32478-9",
ISBN = "3-642-32477-0; 3-642-32478-9",
ISBN-13 = "978-3-642-32477-2; 978-3-642-32478-9",
MRclass = "65-01",
MRnumber = "3013260",
bibdate = "Tue May 27 11:24:21 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
note = "Compendium for students",
series = "Graduate Texts in Physics",
acknowledgement = ack-nhfb,
}
@Book{Soetaert:2012:SDE,
author = "Karline Soetaert and Jeff Cash and Francesca Mazzia",
title = "Solving differential equations in {R}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 248",
year = "2012",
DOI = "https://doi.org/10.1007/978-3-642-28070-2",
ISBN = "3-642-28069-2 (hardcover), 3-642-28070-6 (e-book)",
ISBN-13 = "978-3-642-28069-6 (hardcover), 978-3-642-28070-2
(e-book)",
LCCN = "QA371.5.D37 S64 2012",
MRclass = "68N15 65Lxx",
bibdate = "Tue Mar 13 16:56:48 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/s-plus.bib;
z3950.loc.gov:7090/Voyager",
series = "Use R!",
abstract = "Mathematics plays an important role in many scientific
and engineering disciplines. This book deals with the
numerical solution of differential equations, a very
important branch of mathematics. Our aim is to give a
practical and theoretical account of how to solve a
large variety of differential equations, comprising
ordinary differential equations, initial value problems
and boundary value problems, differential algebraic
equations, partial differential equations and delay
differential equations. The solution of differential
equations using R is the main focus of this book. It is
therefore intended for the practitioner, the student
and the scientist, who wants to know how to use R for
solving differential equations. However, it has been
our goal that non-mathematicians should at least
understand the basics of the methods, while obtaining
entrance into the relevant literature that provides
more mathematical background. Therefore, each chapter
that deals with R examples is preceded by a chapter
where the theory behind the numerical methods being
used is introduced. In the sections that deal with the
use of R for solving differential equations, we have
taken examples from a variety of disciplines, including
biology, chemistry, physics, pharmacokinetics. Many
examples are well-known test examples, used frequently
in the field of numerical analysis.",
acknowledgement = ack-nhfb,
subject = "Statistics; Computer simulation; Differential
equations; Differential equations, Partial; Computer
science; Mathematics; Mathematical statistics;
Statistics and Computing/Statistics Programs; Ordinary
Differential Equations; Partial Differential Equations;
Computational Mathematics and Numerical Analysis;
Simulation and Modeling; Mathematics.; Computer
simulation.; Differential equations.; Differential
equations, Partial.; Mathematical statistics.;
Statistics.",
tableofcontents = "1 Differential Equations / 1 \\
1.1 Basic Theory of Ordinary Differential Equations / 1
\\
1.1.1 First Order Differential Equations / 1 \\
1.1.2 Analytic and Numerical Solutions / 2 \\
1.1.3 Higher Order Ordinary Differential Equations / 3
\\
1.1.4 Initial and Boundary Values / 4 \\
1.1.5 Existence and Uniqueness of Analytic Solutions /
5 \\
1.2 Numerical Methods / 6 \\
1.2.1 The Euler Method / 6 \\
1.2.2 Implicit Methods / 7 \\
1.2.3 Accuracy and Convergence of Numerical Methods / 8
\\
1.2.4 Stability and Conditioning / 9 \\
1.3 Other Types of Differential Equations / 11 \\
1.3.1 Partial Differential Equations / 11 \\
1.3.2 Differential Algebraic Equations / 12 \\
1.3.3 Delay Differential Equations / 13 \\
References / 13 \\
2 Initial Value Problems / 15 \\
2.1 Runge--Kutta Methods / 15 \\
2.1.1 Explicit Runge--Kutta Formulae / 15 \\
2.1.2 Deriving a Runge--Kutta Formula / 17 \\
2.1.3 Implicit Runge--Kutta Formulae / 22 \\
2.2 Linear Multistep methods / 22 \\
2.2.1 Convergence, Stability and Consistency / 23 \\
2.2.2 Adams Methods / 25 \\
2.2.3 Backward Differentiation Formulae / 27 \\
2.2.4 Variable Order--Variable Coefficient Formulae for
Linear Multistep Methods / 29 \\
2.3 Boundary Value Methods / 30 \\
2.4 Modified Extended Backward Differentiation Formulae
/ 31 \\
2.5 Stiff Problems / 32 \\
2.5.1 Stiffness Detection / 33 \\
2.5.2 Non-stiffness Test / 34 \\
2.6 Implementing Implicit Methods / 34 \\
2.6.1 Fixed-Point Iteration to Convergence / 34 \\
2.6.2 Chord Iteration / 35 \\
2.6.3 Predictor--Corrector Methods / 36 \\
2.6.4 Newton Iteration for Implicit Runge--Kutta
Methods / 36 \\
2.7 Codes to Solve Initial Value Problems / 37 \\
2.7.1 Codes to Solve Non-stiff Problems / 38 \\
2.7.2 Codes to Solve Stiff Problems / 38 \\
2.7.3 Codes that Switch Between Stiff and Non-stiff
Solvers / 38 \\
References / 39 \\
3 Solving Ordinary Differential Equations in R / 41 \\
3.1 Implementing Initial Value Problems in R / 41 \\
3.1.1 A Differential Equation Comprising One Variable /
42 \\
3.1.2 Multiple Variables: The Lorenz Model / 44 \\
3.2 Runge--Kutta Methods / 45 \\
3.2.1 Rigid Body Equations / 47 \\
3.2.2 Arenstorf Orbits / 49 \\
3.3 Linear Multistep Methods / 51 \\
3.3.1 Seven Moving Stars / 52 \\
3.3.2 A Stiff Chemical Example / 56 \\
3.4 Discontinuous Equations, Events / 59 \\
3.4.1 Pharmacokinetic Models / 60 \\
3.4.2 A Bouncing Ball / 64 \\
3.4.3 Temperature in a Climate-Controlled Room / 66 \\
3.5 Method Selection / 68 \\
3.5.1 The van der Pol Equation / 70 \\
3.6 Exercises / 75 \\
3.6.1 Getting Started with IVP / 75 \\
3.6.2 The Robertson Problem / 76 \\
3.6.3 Displaying Results in a Phase-Plane Graph / 76
\\
3.6.4 Events and Roots / 78 \\
3.6.5 Stiff Problems / 79 \\
References / 79 \\
4 Differential Algebraic Equations / 81 \\
4.1 Introduction / 81 \\
4.1.1 The Index of a DAE / 82 \\
4.1.2 A Simple Example / 83 \\
4.1.3 DAEs in Hessenberg Form / 84 \\
4.1.4 Hidden Constraints and the Initial Conditions /
85 \\
4.1.5 The Pendulum Problem / 86 \\
4.2 Solving DAEs / 87 \\
4.2.1 Semi-implicit DAEs of Index 1 / 87 \\
4.2.2 General Implicit DAEs of Index 1 / 88 \\
4.2.3 Discretization Algorithms / 89 \\
4.2.4 DAEs of Higher Index / 90 \\
4.2.5 Index of a DAE Variable / 93 \\
References / 94 \\
5 Solving Differential Algebraic Equations in R / 95
\\
5.1 Differential Algebraic Equation Solvers in R / 95
\\
5.2 A Simple DAE of Index 2 / 96 \\
5.2.1 Solving the DAEs in General Implicit Form / 97
\\
5.2.2 Solving the DAEs in Linearly Implicit Form / 98
\\
5.3 A Nonlinear Implicit ODE / 98 \\
5.4 A DAE of Index 3: The Pendulum Problem / 100 \\
5.5 Multibody Systems / 101 \\
5.5.1 The Car Axis Problem / 102 \\
5.6 Electrical Circuit Models / 106 \\
5.6.1 The Transistor Amplifier / 107 \\
5.7 Exercises / 111 \\
5.7.1 A Simple DAE / 111 \\
5.7.2 The Robertson Problem / 111 \\
5.7.3 The Pendulum Problem Revisited / 111 \\
5.7.4 The Akzo Nobel Problem / 112 \\
References / 115 \\
6 Delay Differential Equations / 117 \\
6.1 Delay Differential Equations / 117 \\
6.1.1 DDEs with Delays of the Dependent Variables / 118
\\
6.1.2 DDEs with Delays of the Derivatives / 118 \\
6.2 Difficulties when Solving DDEs / 119 \\
6.2.1 Discontinuities in DDEs / 119 \\
6.2.2 Small and Vanishing Delays / 120 \\
6.3 Numerical Methods for Solving DDEs / 121 \\
References / 121 \\
7 Solving Delay Differential Equations in R / 123 \\
,7.1 Delay Differential Equation Solvers in R / 123 \\
7.2 Two Simple Examples / 124 \\
7.2.1 DDEs Involving Solution Delay Terms / 124 \\
7.2.2 DDEs Involving Derivative Delay Terms / 124 \\
7.3 Chaotic Production of White Blood Cells / 125 \\
7.4 A DDE Involving a Root Function / 127 \\
7.5 Vanishing Time Delays / 128 \\
7.6 Predator--Prey Dynamics with Harvesting / 130 \\
7.7 Exercises / 132 \\
7.7.1 The Lemming Model / 132 \\
7.7.2 Oberle and Pesch / 132 \\
7.7.3 An Epidemiological Model / 133 \\
7.7.4 A Neutral DDE / 134 \\
7.7.5 Delayed Cellular Neural Networks With Impulses /
134 \\
References / 135 \\
8 Partial Differential Equations / 137 \\
8.1 Partial Differential Equations / 137 \\
8.1.1 Alternative Formulations / 138 \\
8.1.2 Polar, Cylindrical and Spherical Coordinates /
140 \\
8.1.3 Boundary Conditions / 141 \\
8.2 Solving PDEs / 142 \\
8.3 Discretising Derivatives / 143 \\
8.3.1 Basic Diffusion Schemes / 144 \\
8.3.2 Basic Advection Schemes / 145 \\
8.3.3 Flux-Conservative Discretisations / 147 \\
8.3.4 More Complex Advection Schemes / 148 \\
8.4 The Method Of Lines / 152 \\
8.5 The Finite Difference Method / 153 \\
References / 153 \\
9 Solving Partial Differential Equations in R / 157 \\
9.1 Methods for Solving PDEs in R / 157 \\
9.1.1 Numerical Approximations / 157 \\
9.1.2 Solution Methods / 159 \\
9.2 Solving Parabolic, Elliptic and Hyperbolic PDEs in
R / 160 \\
9.2.1 The Heat Equation / 160 \\
9.2.2 The Wave Equation / 163 \\
9.2.3 Poisson and Laplace's Equation / 166 \\
9.2.4 The Advection Equation / 168 \\
9.3 More Complex Examples / 170 \\
9.3.1 The Brusselator in One Dimension / 170 \\
9.3.2 The Brusselator in Two Dimensions / 173 \\
9.3.3 Laplace Equation in Polar Coordinates / 174 \\
9.3.4 The Time-Dependent 2-D Sine-Gordon Equation / 176
\\
9.3.5 The Nonlinear Schr{\"o}dinger Equation / 179 \\
9.4 Exercises / 181 \\
9.4.1 The Gray--Scott Equation / 181 \\
9.4.2 A Macroscopic Model of Traffic / 182 \\
9.4.3 A Vibrating String / 183 \\
9.4.4 A Pebble in a Bucket of Water / 184 \\
9.4.5 Combustion in 2-D / 184 \\
References / 185 \\
10 Boundary Value Problems / 187 \\
10.1 Two-Point Boundary Value Problems / 187 \\
10.2 Characteristics of Boundary Value Problems / 188
\\
10.2.1 Uniqueness of Solutions / 188 \\
10.2.2 Isolation of Solutions / 189 \\
10.2.3 Stiffness of Boundary Value Problems and
Dichotomy / 189 \\
10.2.4 Conditioning of Boundary Value Problems / 190
\\
10.2.5 Singular Problems / 191 \\
10.3 Boundary Conditions / 192 \\
10.3.1 Separated Boundary Conditions / 192 \\
10.3.2 Defining Good Boundary Conditions / 193 \\
10.3.3 Problems Defined on an Infinite Interval / 193
\\
10.4 Methods of Solution / 194 \\
10.5 Shooting Methods for Two-Point BVPs / 194 \\
10.5.1 The Linear Case / 194 \\
10.5.2 The Nonlinear Case / 195 \\
10.5.3 Multiple Shooting / 196 \\
10.6 Finite Difference Methods / 197 \\
10.6.1 A Low Order Method for Second Order Equations /
197 \\
10.6.2 Other Low Order Methods / 198 \\
10.6.3 Higher Order Methods Based on Collocation
Runge--Kutta Schemes / 199 \\
10.6.4 Higher Order Methods Based on Mono Implicit
Runge--Kutta Formulae / 200 \\
10.6.5 Higher Order Methods Based on Linear Multistep
Formulae / 201 \\
10.6.6 Deferred Correction / 202 \\
10.7 Codes for the Numerical Solution of Boundary Value
Problems / 203 \\
References / 203 \\
11 Solving Boundary Value Problems in R / 207 \\
11.1 Boundary Value Problem Solvers in R / 207 \\
11.2 A Simple BVP Example / 208 \\
11.2.1 Implementing the BVP in First Order Form / 208
\\
11.2.2 Implementing the BVP in Second Order Form / 209
\\
11.3 A More Complex BVP Example / 210 \\
11.4 More Complex Initial or End Conditions / 214 \\
11.5 Solving a Boundary Value Problem Using
Continuation / 216 \\
11.5.1 Manual Continuation / 216 \\
11.5.2 Automatic Continuation / 219 \\
11.6 BVPs with Unknown Constants / 220 \\
11.6.1 The Elastica Problem / 221 \\
11.6.2 Non-separated Boundary Conditions / 222 \\
11.6.3 An Unknown Integration Interval / 225 \\
11.7 Integral Constraints / 228 \\
11.8 Sturm--Liouville Problems / 229 \\
11.9 A Reaction Transport Problem / 230 \\
11.10 Exercises / 233 \\
11.10.1 A Stiff Boundary Value Problem / 233 \\
11.10.2 The Mathieu Equation / 234 \\
11.10.3 Another Swirling Flow Problem / 234 \\
11.10.4 Another Reaction Transport Problem / 236 \\
References / 237 \\
A Appendix / 239 \\
A. 1 Butcher Tableaux for Some Runge--Kutta Methods : /
239 \\
A.2 Coefficients for Some Linear Multistep Formulae /
239 \\
A.3 Implemented Integration Methods for Solving Initial
Value Problems in R / 241 \\
A.4 Other Integration Methods in R / 242 \\
References / 242 \\
Index / 245",
}
@Book{Wulf:2012:CVR,
author = "Andrea Wulf",
title = "Chasing {Venus}: the race to measure the heavens",
publisher = pub-KNOPF,
address = pub-KNOPF:adr,
pages = "xxvi + 304",
year = "2012",
ISBN = "0-307-70017-8 (hardcover), 0-307-95861-2 (e-book)",
ISBN-13 = "978-0-307-70017-9 (hardcover), 978-0-307-95861-7
(e-book)",
LCCN = "QB205.A2 W85 2012",
bibdate = "Mon Jun 18 14:33:26 MDT 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
abstract = "The author of the highly acclaimed Founding Gardeners
now gives us an enlightening chronicle of the first
truly international scientific endeavor --- the
eighteenth-century quest to observe the transit of
Venus and measure the solar system. On June 6, 1761,
the world paused to observe a momentous occasion: the
first transit of Venus between the earth and the sun in
more than a century. Through that observation,
astronomers could calculate the size of the solar
system --- but only if the transit could be viewed at
the same time from many locations. Overcoming
incredible odds and political strife, astronomers from
Britain, France, Russia, Germany, Sweden, and the
American colonies set up observatories in remote
corners of the world only to have their efforts
thwarted by unpredictable weather and warring armies.
Fortunately, transits of Venus occur in pairs: eight
years later, the scientists were given a second chance
to get it right. Chasing Venus brings to life this
extraordinary endeavor: the personalities of
eighteenth-century astronomy, the collaborations,
discoveries, personal rivalries, volatile international
politics, and the race to be first to measure the
distances between the planets.\par
On June 6, 1761, the world paused to observe a
momentous occasion: the first transit of Venus between
the Earth and the sun in more than a century. Through
that observation, astronomers could calculate the size
of the solar system --- but only if the transit could
be viewed at the same time from many locations.
Overcoming incredible odds and political strife,
astronomers from Britain, France, Russia, Germany,
Sweden, and the American colonies set up observatories
in remote corners of the world only to have their
efforts thwarted by unpredictable weather and warring
armies. Fortunately, transits of Venus occur in pairs:
eight years later, the scientists were given a second
chance to get it right. Chasing Venus brings to life
this extraordinary endeavor: the personalities of
eighteenth-century astronomy, the collaborations,
discoveries, personal rivalries, volatile international
politics, and the race to be first to measure the
distances between the planets.",
acknowledgement = ack-nhfb,
remark = "The Venus solar transit of Tuesday 5 June 2012 was
expected to be visible in Salt Lake City, which
normally enjoys clear skies during much of the year.
Alas, heavy clouds hung low in the valley on that
single day, obscuring the event. Only near sundown was
the final part of the six-hour transit partly visible
through the clouds, by which time, most observers
(including me) had given up.",
subject = "geodetic astronomy; history; 18th century; astronomy;
Venus (planet); transit",
tableofcontents = "The gauntlet \\
Transit 1761. Call to action; The French are first;
Britain enters the race; To Siberia; Getting ready for
Venus; Day of transit, 6 June 1761; How far to the sun?
\\
Transit 1769. A second change; Russia enters the race;
The most daring voyage of all; Scandinavia, or, The
Land of the Midnight Sun; The North American continent;
Racing to the four corners of the globe; Day of
transit, 3 June 1769; After the transit \\
A new dawn \\
List of observers, 1761 \\
List of observers, 1769",
}
@Book{Bailey:2013:CAM,
editor = "David H. Bailey and Heinz H. Bauschke and Peter
Borwein and Frank Garvan and Michel Th{\'e}ra and Jon
D. Vanderwerff and Henry Wolkowicz",
booktitle = "Computational and analytical mathematics: in honor of
{Jonathan Borwein}'s 60th Birthday",
title = "Computational and analytical mathematics: in honor of
{Jonathan Borwein}'s 60th Birthday",
volume = "50",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xv + 701",
year = "2013",
DOI = "https://doi.org/10.1007/978-1-4614-7621-4",
ISBN = "1-4614-7620-8, 1-4614-7621-6 (e-book)",
ISBN-13 = "978-1-4614-7620-7, 978-1-4614-7621-4 (e-book)",
ISSN = "2194-1009",
LCCN = "QA241",
bibdate = "Thu Aug 11 13:32:34 MDT 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
series = "Springer proceedings in mathematics and statistics",
URL = "http://public.eblib.com/choice/publicfullrecord.aspx?p=1466708;
http://swb.eblib.com/patron/FullRecord.aspx?p=1466708;
http://www.myilibrary.com?id=547562",
abstract = "The research of Jonathan Borwein has had a profound
impact on optimization, functional analysis, operations
research, mathematical programming, number theory, and
experimental mathematics. Having authored more than a
dozen books and more than 300 publications, Dr. Borwein
is one of the most productive Canadian mathematicians
ever. His research spans pure, applied, and
computational mathematics as well as high performance
computing, and continues to have an enormous impact:
MathSciNet lists more than 2500 citations by more than
1250 authors, and Borwein is one of the 250 most cited
mathematicians of the period 1980--1999. He has served
the Canadian Mathematics Community through his
presidency (2000--2002) as well as his 15 years of
editing the CMS book series. Jonathan Borwein's vision
and initiative have been crucial in initiating and
developing several institutions that provide support
for researchers with a wide range of scientific
interests. A few notable examples include the Centre
for Experimental and Constructive Mathematics and the
IRMACS Centre at Simon Fraser University, the Dalhousie
Distributed Research Institute at Dalhousie University,
the Western Canada Research Grid, and the Centre for
Computer Assisted Research Mathematics and its
Applications, University of Newcastle. The workshops
that were held over the years in Dr. Borwein's honor
attracted high-caliber scientists from a wide range of
mathematical fields. This present volume is an
outgrowth of the workshop entitled Computational and
Analytical Mathematics, held in May 2011 in celebration
of Jonathan Borwein's 60th Birthday. The collection
contains various state-of-the-art research manuscripts
and surveys presenting contributions that have risen
from the conference, and is an excellent opportunity to
survey state-of-the-art research and discuss promising
research directions and approaches.",
acknowledgement = ack-nhfb,
subject = "Number theory; Mathematical analysis; Mathematics;
Functional Analysis; Operator Theory; Operations
Research, Management Science; Algebra; Intermediate.;
Mathematical analysis.; Number theory.",
tableofcontents = "Normal Numbers and Pseudorandom Generators / David
H. Bailey and Jonathan M. Borwein / 1--18 \\
New Demiclosedness Principles for (Firmly) Nonexpansive
Operators / Heinz H. Bauschke / 19--28 \\
Champernowne's Number, Strong Normality, and the X
Chromosome / Adrian Belshaw and Peter B. Borwein /
29--44 \\
Optimality Conditions for Semivectorial Bilevel Convex
Optimal Control Problems / Henri Bonnel and Jacqueline
Morgan / 45--78 \\
Monotone Operators Without Enlargements / Jonathan M.
Borwein and Regina S. Burachik / 79--103 \\
A Br{\o}ndsted--Rockafellar Theorem for Diagonal
Subdifferential Operators / Radu Ioan Bo{\c{t}} and
Ern{\"o} Robert Csetnek / 105--112 \\
A $q$-Analog of Euler's Reduction Formula for the
Double Zeta Function / David M. Bradley and Xia Zhou /
113--126 \\
Fast Computation of Bernoulli, Tangent and Secant
Numbers / Richard P. Brent and David Harvey / 127--142
\\
Monotone Operator Methods for Nash Equilibria in
Non-potential Games / Luis M. Brice{\"a}no-Arias and
Patrick L. Combettes / 143--159 \\
Compactness, Optimality, and Risk / B. Cascales, J.
Orihuela and M. Ruiz Gal{\'a}n / 161--218 \\
Logarithmic and Complex Constant Term Identities / Tom
Chappell, Alain Lascoux and S. Ole Warnaar /
219--250\\
Preprocessing and Regularization for Degenerate
Semidefinite Programs / Yuen-Lam Cheung, Simon Schurr
and Henry Wolkowicz / 251--303 \\
The Largest Roots of the Mandelbrot Polynomials /
Robert M. Corless and Piers W. Lawrence / 305--324 \\
On the Fractal Distribution of Brain Synapses / Richard
Crandall / 325--348 \\
Visible Points in Convex Sets and Best Approximation /
Frank Deutsch, Hein Hundal and Ludmil Zikatanov /
349--364 \\
On Derivative Criteria for Metric Regularity / Asen L.
Dontchev and H{\'e}l{\`e}ne Frankowska / 365--374 \\
Five Classes of Monotone Linear Relations and Operators
/ Mclean R. Edwards / 375--400 \\
Upper Semicontinuity of Duality and Preduality Mappings
/ J. R. Giles / 401--410 \\
Convexity and Variational Analysis / A. D. Ioffe /
411--444 \\
Generic Existence of Solutions and Generic
Well-Posedness of Optimization Problems / P. S.
Kenderov and J. P. Revalski / 445--453 \\
Legendre Functions Whose Gradients Map Convex Sets to
Convex Sets / Alexander Knecht and Jon Vanderwerff /
455--462\\
On the Convergence of Iteration Processes for
Semigroups of Nonlinear Mappings in Banach Spaces / W.
M. Kozlowski and Brailey Sims / 463--484 \\
Techniques and Open Questions in Computational Convex
Analysis / Yves Lucet / 485--500 \\
Existence and Approximation of Fixed Points of Right
Bregman Nonexpansive Operators / Victoria
Mart{\'i}n-M{\'a}rquez and Simeon Reich / 501--520 \\
Primal Lower Nice Functions and Their Moreau Envelopes
/ Marc Mazade and Lionel Thibault / 521--553 \\
Bundle Method for Non-Convex Minimization with Inexact
Subgradients and Function Values / Dominikus Noll /
555--592 \\
Convergence of Linesearch and Trust-Region Methods
Using the Kurdyka--{\L}ojasiewicz Inequality /
Dominikus Noll and Aude Rondepierre / 593--611 \\
Strong Duality in Conic Linear Programming: Facial
Reduction and Extended Duals / G{\'a}bor Pataki /
613--634 \\
Towards a New Era in Subdifferential Analysis? /
Jean-Paul Penot /635--665 \\
Modular Equations and Lattice Sums / Mathew Rogers and
Boonrod Yuttanan / 667--680 \\
An Epigraph-Based Approach to Sensitivity Analysis in
Set-Valued Optimization / Douglas E. Ward and Stephen
E. Wright / 681--701",
}
@Book{Corless:2013:GIN,
author = "Robert M. Corless and Nicolas Fillion",
title = "A Graduate Introduction to Numerical Methods: from the
Viewpoint of Backward Error Analysis",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxxix + 868",
year = "2013",
ISBN = "1-4614-8452-9 (hardcover), 1-4614-8453-7 (e-book)",
ISBN-13 = "978-1-4614-8452-3 (hardcover), 978-1-4614-8453-0
(e-book)",
LCCN = "QA297 .C665 2013",
bibdate = "Sat Oct 6 08:53:42 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Textbooks; Error analysis
(Mathematics); Mathematics; Methodology; Study and
teaching (Graduate)",
tableofcontents = "Computer Arithmetic and Fundamental Concepts of
Computation \\
Polynomials and Series \\
Rootfinding and Function Evaluation \\
Solving $ A x = b$ \\
Solving $A x = \lambda x$ \\
Structured Linear Systems \\
Iterative Methods \\
Polynomial and Rational Interpolation \\
The Discrete Fourier Transform \\
Numerical Integration \\
Numerical Differentiation and Finite Differences \\
Numerical Solution of ODEs \\
Numerical Methods for ODEs \\
Numerical Solutions of Boundary Value Problems \\
Numerical Solution of Delay DEs \\
Numerical Solution of PDEs",
}
@Book{Dennis:2013:RSC,
author = "Brian Dennis",
title = "The {R} student companion",
publisher = "CRC Press, Taylor and Francis Group",
address = "Boca Raton, FL, USA",
pages = "xvii + 339",
year = "2013",
ISBN = "1-4398-7540-5 (paperback)",
ISBN-13 = "978-1-4398-7540-7 (paperback)",
LCCN = "QA276.45.R3 D46 2013",
bibdate = "Thu Jul 10 12:58:52 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/s-plus.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://jacketsearch.tandf.co.uk/common/jackets/covers/websmall/978143987/9781439875407.jpg",
abstract = "R is a computer package for scientific graphs and
calculations. It is written and maintained by
statisticians and scientists, for scientists to use in
their work. It is easy to use, yet is extraordinarily
powerful. R is spreading rapidly throughout the science
and technology world, and it is setting the standards
for graphical data displays in science publications. R
is free. It is an open-source product that is easy to
install on most computers. It is available for Windows,
Mac, and Unix/Linux operating systems. One simply
downloads and installs it from the R website (http://
www.r-project.org/). This book is for high school and
college students, and anyone else, who wants to learn
to use R. With this book, you can put your computer to
work in powerful fashion, in any subject that uses
applied mathematics. In particular, physics, life
sciences, chemistry, earth science, economics,
engineering, and business involve much analysis,
modeling, simulation, statistics, and graphing. These
quantitative applications become remarkably
straightforward and understandable when performed with
R. Difficult concepts in mathematics and statistics
become clear when illustrated with R. The book starts
from the beginning and assumes the reader has no
computer programming background. The mathematical
material in the book requires only a moderate amount of
high school algebra. R makes graphing calculators seem
awkward and obsolete. The calculators are hard to
learn, cumbersome to use for anything but tiny
problems, and the graphs are small and have poor
resolution. Calculating in R by comparison is
intuitive, even fun. Fantastic, publication-quality
graphs of data, equations, or both can be produced with
little effort.",
acknowledgement = ack-nhfb,
author-dates = "1952--",
subject = "R (Computer program language); Probabilities;
Mathematical statistics; Data processing; MATHEMATICS /
General.; MATHEMATICS / Probability and Statistics /
General.",
tableofcontents = "1. Introduction: Getting started with R \\
2. R scripts \\
3. Functions \\
4. Basic graphs \\
5. Data input and output \\
6. Loops \\
7. Logic and control \\
8. Quadratic functions \\
9. Trigonometric functions \\
10. Exponential and logarithmic functions \\
11. Matrix arithmetic \\
12. Systems of linear equations \\
13. Advanced graphs \\
14. Probability and simulation \\
15. Fitting models to data \\
16. Conclusion: It doesn't take a rocket scientist \\
Appendix A Installing R \\
Appendix B: Getting help \\
Appendix C: Common R expressions",
}
@Book{Golub:2013:MC,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Matrix Computations",
publisher = pub-JOHNS-HOPKINS,
address = pub-JOHNS-HOPKINS:adr,
edition = "Fourth",
pages = "xxi + 756",
year = "2013",
ISBN = "1-4214-0794-9 (hardcover), 1-4214-0859-7 (e-book)",
ISBN-13 = "978-1-4214-0794-4 (hardcover), 978-1-4214-0859-0
(e-book)",
LCCN = "QA188 .G65 2013",
bibdate = "Fri Nov 21 06:49:56 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Johns Hopkins Studies in the Mathematical Sciences",
URL = "https://jhupbooks.press.jhu.edu/title/matrix-computations",
abstract = "This revised edition provides the mathematical
background and algorithmic skills required for the
production of numerical software. It includes rewritten
and clarified proofs and derivations, as well as new
topics such as Arnoldi iteration, and domain
decomposition methods.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
shorttableofcontents = "1: Matrix multiplication \\
2: Matrix analysis \\
3: General linear systems \\
4: Special linear systems \\
5: Orthogonalization and least squares \\
6: Modified least squares problems and methods \\
7: Unsymmetric eigenvalue problems \\
8: Symmetric eigenvalue problems \\
9: Functions of matrices \\
10: Large sparse eigenvalue problems \\
11: Large sparse linear system problems \\
12: Special topics",
subject = "Matrices; Data processing; Data processing.; Matrix.;
Matrizenrechnung.; Matrizentheorie.; Numerische
Mathematik.",
tableofcontents = "Preface \\
Global References \\
Other Books \\
Useful URLs \\
Common Notation \\
1: Matrix Multiplication \\
1.1 Basic Algorithms and Notation \\
1.2 Structure and Efficiency \\
1.3 Block Matrices and Algorithms \\
1.4 Fast Matrix--Vector Products \\
1.5 Vectorization and Locality \\
1.6 Parallel Matrix Multiplication \\
2: Matrix Analysis \\
2.1 Basic Ideas from Linear Algebra \\
2.2 Vector Norms \\
2.3 Matrix Norms \\
2.4 The Singular Value Decomposition \\
2.5 Subspace Metrics \\
2.6 The Sensitivity of Square Systems \\
2.7 Finite Precision Matrix Computations \\
3: General Linear Systems \\
3.1 Triangular Systems \\
3.2 The $L U$ Factorization \\
3.3 Roundoff Error in Gaussian Elimination \\
3.4 Pivoting \\
3.5 Improving and Estimating Accuracy \\
3.6 Parallel $L U$ \\
4: Special Linear Systems \\
4.1 Diagonal Dominance and Symmetry \\
4.2 Positive Definite Systems \\
4.3 Banded Systems \\
4.4 Symmetric Indefinite Systems \\
4.5 Block Tridiagonal Systems \\
4.6 Vandermonde Systems \\
4.7 Classical Methods for Toeplitz Systems \\
4.8 Circulant and Discrete Poisson Systems \\
5: Orthogonalization and Least Squares \\
5.1 Householder and Givens Transformations \\
5.2 The $Q R$ Factorization \\
5.3 The Full-Rank Least Squares Problem \\
5.4 Other Orthogonal Factorizations \\
5.5 The Rank-Deficient Least Squares Problem \\
5.6 Square and Underdetermined Systems \\
6: Modified Least Squares Problems and Methods \\
6.1 Weighting and Regularization \\
6.2 Constrained Least Squares \\
6.3 Total Least Squares \\
6.4 Subspace Computations with the SVD \\
6.5 Updating Matrix Factorizations \\
7: Unsymmetric Eigenvalue Problems \\
7.1 Properties and Decompositions \\
7.2 Perturbation Theory \\
7.3 Power Iterations \\
7.4 The Hessenberg and Real Schur Forms \\
7.5 The Practical $Q R$ Algorithm \\
7.6 Invariant Subspace Computations \\
7.7 The Generalized Eigenvalue Problem \\
7.8 Hamiltonian and Product Eigenvalue Problems \\
7.9 Pseudospectra \\
8: Symmetric Eigenvalue Problems \\
8.1 Properties and Decompositions \\
8.2 Power Iterations \\
8.3 The Symmetric $Q R$ Algorithm \\
8.4 More Methods for Tridiagonal Problems \\
8.5 Jacobi Methods \\
8.6 Computing the SVD \\
8.7 Generalized Eigenvalue Problems with Symmetry \\
9: Functions of Matrices \\
9.1 Eigenvalue Methods \\
9.2 Approximation Methods \\
9.3 The Matrix Exponential \\
9.4 The Sign, Square Root, and Log of a Matrix \\
10: Large Sparse Eigenvalue Problems \\
10.1 The Symmetric Lanczos Process \\
10.2 Lanczos, Quadrature, and Approximation \\
10.3 Practical Lanczos Procedures \\
10.4 Large Sparse SVD Frameworks \\
10.5 Krylov Methods for Unsymmetric Problems \\
10.6 Jacobi--Davidson and Related Methods \\
11: Large Sparse Linear System Problems \\
11.1 Direct Methods \\
11.2 The Classical Iterations \\
11.3 The Conjugate Gradient Method \\
11.4 Other Krylov Methods \\
11.5 Preconditioning \\
11.6 The Multigrid Framework \\
12: Special Topics \\
12.1 Linear Systems with Displacement Structure \\
12.2 Structured-Rank Problems \\
12.3 Kronecker Product Computations \\
12.4 Tensor Unfoldings and Contractions \\
12.5 Tensor Decompositions and Iterations \\
Index",
}
@Book{Graham:2013:SSM,
author = "C. (Carl) Graham and D. (Denis) Talay",
title = "Stochastic Simulation and {Monte Carlo} Methods:
Mathematical Foundations of Stochastic Simulation",
volume = "68",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 260 + 4",
year = "2013",
DOI = "https://doi.org/10.1007/978-3-642-39363-1",
ISBN = "3-642-39362-4",
ISBN-13 = "978-3-642-39362-4",
ISSN = "0172-4568",
ISSN-L = "0172-4568",
LCCN = "QA273.A1-274.9; QA274-274.9",
bibdate = "Tue Apr 29 18:44:55 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/probstat2010.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "Stochastic Modelling and Applied Probability",
abstract = "In various scientific and industrial fields,
stochastic simulations are taking on a new importance.
This is due to the increasing power of computers and
practitioners and \#x2019; aim to simulate more and
more complex systems, and thus use random parameters as
well as random noises to model the parametric
uncertainties and the lack of knowledge on the physics
of these systems. The error analysis of these
computations is a highly complex mathematical
undertaking. Approaching these issues, the authors
present stochastic numerical methods and prove accurate
convergence rate estimates in terms of their numerical
parameters (number of simulations, time discretization
steps). As a result, the book is a self-contained and
rigorous study of the numerical methods within a
theoretical framework. After briefly reviewing the
basics, the authors first introduce fundamental notions
in stochastic calculus and continuous-time martingale
theory, then develop the analysis of pure-jump Markov
processes, Poisson processes, and stochastic
differential equations. In particular, they review the
essential properties of {It{\^o}} integrals and prove
fundamental results on the probabilistic analysis of
parabolic partial differential equations. These results
in turn provide the basis for developing stochastic
numerical methods, both from an algorithmic and
theoretical point of view. and The book combines
advanced mathematical tools, theoretical analysis of
stochastic numerical methods, and practical issues at a
high level, so as to provide optimal results on the
accuracy of Monte Carlo simulations of stochastic
processes. It is intended for master and Ph.D. students
in the field of stochastic processes and their
numerical applications, as well as for physicists,
biologists, economists and other professionals working
with stochastic simulations, who will benefit from the
ability to reliably estimate and control the accuracy
of their simulations. and .",
acknowledgement = ack-nhfb,
subject = "Mathematics; Finance; Numerical analysis; Distribution
(Probability theory)",
tableofcontents = "Part I:Principles of Monte Carlo Methods \\
1.Introduction \\
2.Strong Law of Large Numbers and Monte Carlo Methods
\\
3.Non Asymptotic Error Estimates for Monte Carlo
Methods \\
Part II:Exact and Approximate Simulation of Markov
Processes \\
4.Poisson Processes \\
5.Discrete-Space Markov Processes \\
6.Continuous-Space Markov Processes with Jumps \\
7.Discretization of Stochastic Differential Equations
\\
Part III:Variance Reduction, Girsanov and \#x2019;s
Theorem, and Stochastic Algorithms \\
8.Variance Reduction and Stochastic Differential
Equations \\
9.Stochastic Algorithms \\
References \\
Index",
}
@Book{Hansen:2013:LSD,
author = "Per Christian Hansen and V. (V{\'\i}ctor) Pereyra and
Godela Scherer",
title = "Least Squares Data Fitting with Applications",
publisher = pub-JOHNS-HOPKINS,
address = pub-JOHNS-HOPKINS:adr,
pages = "xv + 305",
year = "2013",
ISBN = "1-4214-0786-8 (hardcover), 1-4214-0858-9 (e-book)",
ISBN-13 = "978-1-4214-0786-9 (hardcover), 978-1-4214-0858-3
(e-book)",
LCCN = "QA275 .H26 2013",
MRclass = "65-01 (62J05 65Fxx)",
MRnumber = "3012616",
bibdate = "Sat Feb 2 09:11:29 MST 2019",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
prodorbis.library.yale.edu:7090/voyager;
z3950.loc.gov:7090/Voyager
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://muse.jhu.edu/books/9781421408583/",
abstract = "As one of the classical statistical regression
techniques, and often the first to be taught to new
students, least squares fitting can be a very effective
tool in data analysis. Given measured data, we
establish a relationship between independent and
dependent variables so that we can use the data
predictively. The main concern of Least Squares Data
Fitting with Applications is how to do this on a
computer with efficient and robust computational
methods for linear and nonlinear relationships. The
presentation also establishes a link between the
statistical setting and the computational issues. In a
number of applications, the accuracy and efficiency of
the least squares fit is central, and Per Christian
Hansen, V{\'i}ctor Pereyra, and Godela Scherer survey
modern computational methods and illustrate them in
fields ranging from engineering and environmental
sciences to geophysics. Anyone working with problems of
linear and nonlinear least squares fitting will find
this book invaluable as a hands-on guide, with
accessible text and carefully explained problems.",
acknowledgement = ack-nhfb,
remark = "In his interview \cite[page 44]{Haigh:2005:IGG}, Gene
Golub notes that he was working on a book with
V{\'\i}ctor Pereyra. This is the further development of
that book, as the preface reports on page xi: ``Prior
to his untimely death in November 2007, Professor Gene
Golub had been an integral part of the project team.
Although the book has changed significantly since then,
it has greatly benefitted from his insight and
knowledge. He was an aspiring mentor and great friend,
and we miss him dearly.''",
subject = "Least squares; Mathematical models; MATHEMATICS;
General.; Least squares.; Mathematical models.",
tableofcontents = "Preface / ix \\
Symbols and Acronyms / xiii \\
1 The Linear Data Fitting Problem / 1 \\
1.1 Parameter estimation, data approximation / 1 \\
1.2 Formulation of the data fitting problem / 4 \\
1.3 Maximum likelihood estimation / 9 \\
1.4 The residuals and their properties / 13 \\
1.5 Robust regression / 19 \\
2 The Linear Least Squares Problem / 25 \\
2.1 Linear least squares problem formulation / 25 \\
2.2 The QR factorization and its role / 33 \\
2.3 Permuted QR factorization / 39 \\
3 Analysis of Least Squares Problems / 47 \\
3.1 The pseudoinverse / 47 \\
3.2 The singular value decomposition / 50 \\
3.3 Generalized singular value decomposition / 54 \\
3.4 Condition number and column scaling / 55 \\
3.5 Perturbation analysis / 58 \\
4 Direct Methods for Full-Rank Problems / 65 \\
4.1 Normal equations / 65 \\
4.2 LU factorization / 68 \\
4.3 QR factorization / 70 \\
4.4 Modifying least squares problems / 80 \\
4.5 Iterative refinement / 85 \\
4.6 Stability and condition number estimation / 88 \\
4.7 Comparison of the methods / 89 \\
5 Direct Methods for Rank-Deficient Problems / 91 \\
5.1 Numerical rank / 92 \\
5.2 Peters-Wilkinson LU factorization / 93 \\
5.3 QR factorization with column permutations / 94 \\
5.4 UTV and VSV decompositions / 98 \\
5.5 Bidiagonalization / 99 \\
5.6 SVD computations / 101 \\
6 Methods for Large-Scale Problems / 105 \\
6.1 Iterative versus direct methods / 105 \\
6.2 Classical stationary methods / 107 \\
6.3 Non-stationary methods, Krylov methods / 108 \\
6.4 Practicalities: preconditioning and stopping
criteria / 114 \\
6.5 Block methods / 117 \\
7 Additional Topics in Least Squares / 121 \\
7.1 Constrained linear least squares problems / 121 \\
7.2 Missing data problems / 131 \\
7.3 Total least squares (TLS) / 136 \\
7.4 Convex optimization / 143 \\
7.5 Compressed sensing / 144 \\
8 Nonlinear Least Squares Problems / 147 \\
8.1 Introduction / 147 \\
8.2 Unconstrained problems / 150 \\
8.3 Optimality conditions for constrained problems /
156 \\
8.4 Separable nonlinear least squares problems / 158
\\
8.5 Multiobjective optimization / 160 \\
9 Algorithms for Solving Nonlinear LSQ Problems / 163
\\
9.1 Newton's method / 164 \\
9.2 The Gauss-Newton method / 166 \\
9.3 The Levenberg-Marquardt method / 170 \\
9.4 Additional considerations and software / 176 \\
9.5 Iteratively reweighted LSQ algorithms for robust
data fitting problems / 178 \\
9.6 Variable projection algorithm / 181 \\
9.7 Block methods for large-scale problems / 186 \\
10 Ill-Conditioned Problems / 191 \\
10.1 Characterization / 191 \\
10.2 Regularization methods / 192 \\
10.3 Parameter selection techniques / 195 \\
10.4 Extensions of Tikhonov regularization / 198 \\
10.5 Ill-conditioned NLLSQ problems / 201 \\
11 Linear Least Squares Applications / 203 \\
11.1 Splines in approximation / 203 \\
11.2 Global temperatures data fitting / 212 \\
11.3 Geological surface modeling / 221 \\
12 Nonlinear Least Squares Applications / 231 \\
12.1 Neural networks training / 231 \\
12.2 Response surfaces, surrogates or proxies / 238 \\
12.3 Optimal design of a supersonic aircraft / 241 \\
12.4 NMR spectroscopy / 248 \\
12.5 Piezoelectric crystal identification / 251 \\
12.6 Travel time inversion of seismic data / 258 \\
Appendix A Sensitivity Analysis / 263 \\
A.l Floating-point arithmetic / 263 \\
A.2 Stability, conditioning and accuracy / 264 \\
Appendix B Linear Algebra Background / 267 \\
B.l Norms / 267 \\
B.2 Condition number / 268 \\
B.3 Orthogonality / 269 \\
B.4 Some additional matrix properties / 270 \\
Appendix C Advanced Calculus Background / 271 \\
C.l Convergence rates / 271 \\
C.2 Multivariable calculus / 272 \\
Appendix D Statistics / 275 \\
D.l Definitions / 275 \\
D.2 Hypothesis testing / 280 \\
References / 281 \\
Index / 301",
}
@Book{Hilber:2013:CMQ,
author = "Norbert Hilber and Oleg Reichmann and Ch. (Christoph)
Schwab and Christoph Winter",
title = "Computational Methods for Quantitative Finance: Finite
Element Methods for Derivative Pricing",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiii + 299 + 57",
year = "2013",
DOI = "https://doi.org/10.1007/978-3-642-35401-4",
ISBN = "3-642-35400-9",
ISBN-13 = "978-3-642-35400-7",
ISSN = "1616-0533",
ISSN-L = "1616-0533",
LCCN = "QA273.A1-274.9; QA274-274.9",
bibdate = "Tue Apr 29 18:44:55 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/probstat2010.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "Springer Finance",
abstract = "Many mathematical assumptions on which classical
derivative pricing methods are based have come under
scrutiny in recent years. The present volume offers an
introduction to deterministic algorithms for the fast
and accurate pricing of derivative contracts in modern
finance. This unified, non-Monte-Carlo computational
pricing methodology is capable of handling rather
general classes of stochastic market models with jumps,
including, in particular, all currently used L{\'e}vy
and stochastic volatility models. It allows us e.g. to
quantify model risk in computed prices on plain
vanilla, as well as on various types of exotic
contracts. The algorithms are developed in classical
Black-Scholes markets, and then extended to market
models based on multiscale stochastic volatility, to
L{\'e}vy, additive and certain classes of Feller
processes. and The volume is intended for graduate
students and researchers, as well as for practitioners
in the fields of quantitative finance and applied and
computational mathematics with a solid background in
mathematics, statistics or economics.",
acknowledgement = ack-nhfb,
subject = "Mathematics; Finance; Numerical analysis; Distribution
(Probability theory)",
tableofcontents = "Part I. Basic techniques and models: \\
1. Introduction \\
2. Notions of mathematical finance \\
3. Elements of numerical methods for PDEs \\
4. Finite element methods for parabolic problems \\
5. European options in BS markets \\
6. American options \\
7. Exotic options \\
8. Interest rate models \\
9. Multi-asset options \\
10. Stochastic volatility models \\
11. L{\'e}vy models \\
12. Sensitivities and Greeks \\
Part II. Advanced techniques and models 13. Wavelet
methods \\
14. Multidimensional diffusion models \\
15. Multidimensional L{\'e}vy models \\
16. Stochastic volatility models with jumps \\
17. Multidimensional Feller processes \\
Appendices: \\
A. Elliptic variational inequalities \\
B. Parabolic variational inequalities \\
References \\
Index",
}
@Book{Hollig:2013:AMB,
author = "Klaus H{\"o}llig and J{\"o}rg H{\"o}rner",
title = "Approximation and modeling with {B}-splines",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xiii + 214",
year = "2013",
ISBN = "1-61197-294-9",
ISBN-13 = "978-1-61197-294-8",
LCCN = "QA224 .H645 2013",
bibdate = "Tue Aug 12 15:33:22 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Applied mathematics",
acknowledgement = ack-nhfb,
subject = "Spline theory; Approximation theory; Numerical
analysis; Mathematical models; Engineering; Computer
science; Mathematics; Algorithms; Industrial
applications",
tableofcontents = "Polynomials \\
B\'ezier Curves \\
Rational B\'ezier Curves \\
B-Splines \\
Approximation \\
Spline Curves \\
Multivariate Splines \\
Surfaces and Solids \\
Finite Elements \\
Appendix \\
Notation and Symbols",
}
@Book{Kiusalaas:2013:NME,
author = "Jaan Kiusalaas",
title = "Numerical methods in engineering with {Python 3}",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xi + 423",
year = "2013",
ISBN = "1-107-03385-3",
ISBN-13 = "978-1-107-03385-6",
LCCN = "TA345 .K584 2013",
MRclass = "65-01",
MRnumber = "3026375",
bibdate = "Tue May 27 12:31:32 MDT 2014",
bibsource = "clas.caltech.edu:210/INNOPAC;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/python.bib",
abstract = "This book is an introduction to numerical methods for
students in engineering. It covers solution of
equations, interpolation and data fitting, solution of
differential equations, eigenvalue problems and
optimisation. The algorithms are implemented in Python
3, a high-level programming language that rivals MATLAB
in readability and ease of use. All methods include
programs showing how the computer code is utilised in
the solution of problems. The book is based on
Numerical Methods in Engineering with Python, which
used Python 2. This new edition demonstrates the use of
Python 3 and includes an introduction to the Python
plotting package Matplotlib. This comprehensive book is
enhanced by the addition of numerous examples and
problems throughout.",
acknowledgement = ack-nhfb,
subject = "Engineering mathematics; Data processing; Python
(Computer program language)",
tableofcontents = "1. Introduction to Python \\
2. Systems of linear algebraic equations \\
3. Interpolation and curve fitting \\
4. Roots of equations \\
5. Numerical differentiation \\
6. Numerical integration \\
7. Initial value problems \\
8. Two-point boundary value problems \\
9. Symmetric matrix eigenvalue problems \\
10. Introduction to optimization",
}
@Book{Kutz:2013:DDM,
author = "Jose Nathan Kutz",
title = "Data-driven modeling and scientific computation:
methods for complex systems and big data",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xvii + 638",
year = "2013",
ISBN = "0-19-966033-6 (hardcover), 0-19-966034-4 (paperback)",
ISBN-13 = "978-0-19-966033-9 (hardcover), 978-0-19-966034-6
(paperback)",
LCCN = "Q183.9 .K88 2013",
bibdate = "Tue Jan 12 16:17:35 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/s-plus.bib;
z3950.loc.gov:7090/Voyager",
abstract = "The burgeoning field of data analysis is expanding at
an incredible pace due to the proliferation of data
collection in almost every area of science. The
enormous data sets now routinely encountered in the
sciences provide an incentive to develop mathematical
techniques and computational algorithms that help
synthesize, interpret and give meaning to the data in
the context of its scientific setting. A specific aim
of this book is to integrate standard scientific
computing methods with data analysis. By doing so, it
brings together, in a self-consistent fashion, the key
ideas from: statistics, \ldots{}",
abstract = "Prolegomenon \\
How to Use This Book \\
About MATLAB \\
PART I: Basic Computations and Visualization \\
1 MATLAB Introduction \\
1.1 Vectors and Matrices \\
1.2 Logic, Loops and Iterations \\
1.3 Iteration: The Newton-Raphson Method \\
1.4 Function Calls, Input/Output Interactions and
Debugging \\
1.5 Plotting and Importing/Exporting Data \\
2 Linear Systems \\
2.1 Direct Solution Methods for $ A x = b $ \\
2.2 Iterative Solution Methods for $ A x = b $ \\
2.3 Gradient (Steepest) Descent for $ A x = b $ \\
2.4 Eigenvalues, Eigenvectors and Solvability \\
2.5 Eigenvalues and Eigenvectors for Face Recognition.
2.6 Nonlinear Systems \\
3 Curve Fitting \\
3.1 Least-Square Fitting Methods \\
3.2 Polynomial Fits and Splines \\
3.3 Data Fitting with MATLAB \\
4 Numerical Differentiation and Integration \\
4.1 Numerical Differentiation \\
4.2 Numerical Integration \\
4.3 Implementation of Differentiation and Integration
\\
5 Basic Optimization \\
5.1 Unconstrained Optimization (Derivative-Free
Methods) \\
5.2 Unconstrained Optimization (Derivative Methods) \\
5.3 Linear Programming \\
5.4 Simplex Method \\
5.5 Genetic Algorithms \\
6 Visualization \\
6.1 Customizing Plots and Basic 2D Plotting \\
6.2 More 2D and 3D Plotting. 6.3 Movies and Animations
\\
PART II: Differential and Partial Differential
Equations \\
7 Initial and Boundary Value Problems of Differential
Equations \\
7.1 Initial Value Problems: Euler, Runge-Kutta and
Adams Methods \\
7.2 Error Analysis for Time-Stepping Routines \\
7.3 Advanced Time-Stepping Algorithms \\
7.4 Boundary Value Problems: The Shooting Method \\
7.5 Implementation of Shooting and Convergence Studies
\\
7.6 Boundary Value Problems: Direct Solve and
Relaxation \\
7.7 Implementing MATLAB for Boundary Value Problems \\
7.8 Linear Operators and Computing Spectra \\
8 Finite Difference Methods. 8.1 Finite Difference
Discretization \\
8.2 Advanced Iterative Solution Methods for $ A x = b $
\\
8.3 Fast Poisson Solvers: The Fourier Transform \\
8.4 Comparison of Solution Techniques for $ A x = b $:
Rules of Thumb \\
8.5 Overcoming Computational Difficulties \\
9 Time and Space Stepping Schemes: Method of Lines \\
9.1 Basic Time-Stepping Schemes \\
9.2 Time-Stepping Schemes: Explicit and Implicit
Methods \\
9.3 Stability Analysis \\
9.4 Comparison of Time-Stepping Schemes \\
9.5 Operator Splitting Techniques \\
9.6 Optimizing Computational Performance: Rules of
Thumb \\
10 Spectral Methods \\
10.1 Fast Fourier Transforms and Cosine/Sine Transform
\\
10.2 Chebychev Polynomials and Transform \\
10.3 Spectral Method Implementation \\
10.4 Pseudo-Spectral Techniques with Filtering \\
10.5 Boundary Conditions and the Chebychev Transform
\\
10.6 Implementing the Chebychev Transform \\
10.7 Computing Spectra: The Floquet-Fourier-Hill Method
\\
11 Finite Element Methods \\
11.1 Finite Element Basis \\
11.2 Discretizing with Finite Elements and Boundaries
\\
11.3 MATLAB for Partial Differential Equations \\
11.4 MATLAB Partial Differential Equations Toolbox \\
PART III: Computational Methods for Data Analysis. 12
Statistical Methods and Their Applications",
acknowledgement = ack-nhfb,
subject = "MATLAB; Science; Data processing; Numerical analysis;
Differential equations",
}
@Book{Larson:2013:FEM,
author = "Mats G. Larson and Fredrik Bengzon",
title = "The finite element method: theory, implementation, and
applications",
volume = "10",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xviii + 385",
year = "2013",
DOI = "https://doi.org/10.1007/978-3-642-33287-6",
ISBN = "3-642-33286-2, 3-642-33287-0 (e-book)",
ISBN-13 = "978-3-642-33286-9, 978-3-642-33287-6 (e-book)",
ISSN = "1611-0994",
LCCN = "TA347.F5 L37 2013",
MRclass = "65-01 (65M60 65N30)",
MRnumber = "3015004",
bibdate = "Tue May 27 12:31:33 MDT 2014",
bibsource = "clas.caltech.edu:210/INNOPAC;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Texts in Computational Science and Engineering",
acknowledgement = ack-nhfb,
subject = "Finite element method",
}
@Book{Ochsner:2013:ODF,
author = "Andreas {\"O}chsner and Markus Merkel",
title = "One-dimensional finite elements: an introduction to
the FE method",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxiii + 398",
year = "2013",
DOI = "https://doi.org/10.1007/978-3-642-31797-2",
ISBN = "3-642-31796-0 (hardcover); 3-642-31797-9 (e-book)",
ISBN-13 = "978-3-642-31796-5 (hardcover); 978-3-642-31797-2
(e-book)",
LCCN = "TA347.F5 O24 2013",
MRclass = "65-01 (65M60 65N30 74S05)",
MRnumber = "2985770",
MRreviewer = "Alexandre L. Madureira",
bibdate = "Tue May 27 12:31:35 MDT 2014",
bibsource = "clas.caltech.edu:210/INNOPAC;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
note = "An introduction to the FE method",
abstract = "``This textbook presents finite element methods using
exclusively one-dimensional elements. The aim is to
present the complex methodology in an easily
understandable but mathematically correct fashion. The
approach of one-dimensional elements enables the reader
to focus on the understanding of the principles of
basic and advanced mechanical problems. The reader
easily understands the assumptions and limitations of
mechanical modeling as well as the underlying physics
without struggling with complex mathematics. But
although the description is easy it remains
scientifically correct.The approach using only
one-dimensional elements covers not only standard
problems but allows also for advanced topics like
plasticity or the mechanics of composite materials.
Many examples illustrate the concepts and problems at
the end of every chapter help to familiarize with the
topics.'' -- Publisher's description.",
acknowledgement = ack-nhfb,
subject = "Finite element method",
tableofcontents = "Motivation for the finite element method \\
Bar element \\
Torsion bar \\
Bending element \\
General 1D element \\
Plane and spatial frame structures \\
Beam with shear contribution \\
Beams of composite materials \\
Nonlinear elasticity \\
Plasticity \\
Stability (buckling) \\
Dynamics",
}
@Book{Pozrikidis:2013:XSC,
author = "C. Pozrikidis",
title = "{XML} in scientific computing",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xv + 243 pages",
year = "2013",
ISBN = "1-4665-1227-X (hardback)",
ISBN-13 = "978-1-4665-1227-6 (hardback)",
LCCN = "Q183.9 .P69 2013",
bibdate = "Fri Nov 16 06:32:54 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/sgml2010.bib;
https://www.math.utah.edu/pub/tex/bib/super.bib;
z3950.loc.gov:7090/Voyager",
series = "Chapman and Hall/CRC numerical analysis and scientific
computing series",
acknowledgement = ack-nhfb,
subject = "XML (Document markup language); Science; Data
processing; Numerical analysis; COMPUTERS / Internet /
General.; MATHEMATICS / General.; MATHEMATICS / Number
Systems.",
}
@Book{Rossant:2013:LII,
author = "Cyrille Rossant",
title = "Learning {IPython} for interactive computing and data
visualization: Learn {IPython} for interactive
{Python} programming, high-performance numerical
computing, and data visualization",
publisher = "Packt Publishing",
address = "Birmingham, UK",
pages = "iv + 123",
year = "2013",
ISBN = "1-78216-993-8 (paperback), 1-78216-994-6 (e-book),
1-299-54508-4 (e-book)",
ISBN-13 = "978-1-78216-993-2 (paperback), 978-1-78216-994-9
(e-book), 978-1-299-54508-3 (e-book)",
LCCN = "QA76.73.P98 .R677 2013",
bibdate = "Sat Mar 21 07:03:35 MDT 2015",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/python.bib",
series = "Open source: community experience distilled",
acknowledgement = ack-nhfb,
author-dates = "1985--",
subject = "Python (langage de programmation).; Python (Computer
program language); Python (Computer program language)",
}
@Book{Singh:2013:LAS,
author = "Kuldeep Singh",
title = "Linear Algebra: Step by Step",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "viii + 608",
year = "2013",
ISBN = "0-19-965444-1 (paperback), 0-19-150776-8 (e-book)",
ISBN-13 = "978-0-19-965444-4 (paperback), 978-0-19-150776-2
(e-book)",
LCCN = "QA184.2 .S56 2014",
bibdate = "Mon Sep 15 18:07:52 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
abstract = "Linear algebra is a fundamental area of mathematics,
and is arguably the most powerful mathematical tool
ever developed. It is a core topic of study within
fields as diverse as: business, economics, engineering,
physics, computer science, ecology, sociology,
demography and genetics. For an example of linear
algebra at work, one needs to look no further than the
Google search engine, which relies upon linear algebra
to rank the results of a search with respect to
relevance. The strength of the text is in the large
number of examples and the step-by-step explanation of
each topic as it is introduced\ldots{}.",
abstract = "Cover \\
Contents \\
1 Linear Equations and Matrices \\
1.1 Systems of Linear Equations \\
1.2 Gaussian Elimination \\
1.3 Vector Arithmetic \\
1.4 Arithmetic of Matrices \\
1.5 Matrix Algebra \\
1.6 The Transpose and Inverse of a Matrix \\
1.7 Types of Solutions \\
1.8 The Inverse Matrix Method \\
Des Higham Interview \\
2 Euclidean Space \\
2.1 Properties of Vectors \\
2.2 Further Properties of Vectors \\
2.3 Linear Independence \\
2.4 Basis and Spanning Set \\
Chao Yang Interview \\
3 General Vector Spaces \\
3.1 Introduction to General Vector Spaces \\
3.2 Subspace of a Vector Space \\
3.3 Linear Independence and Basis \\
3.4 Dimension 3.5 Properties of a Matrix \\
3.6 Linear Systems Revisited \\
Janet Drew Interview \\
4 Inner Product Spaces \\
4.1 Introduction to Inner Product Spaces \\
4.2 Inequalities and Orthogonality \\
4.3 Orthonormal Bases \\
4.4 Orthogonal Matrices \\
Anshul Gupta Interview \\
5 Linear Transformations \\
5.1 Introduction to Linear Transformations \\
5.2 Kernel and Range of a Linear Transformation \\
5.3 Rank and Nullity \\
5.4 Inverse Linear Transformations \\
5.5 The Matrix of a Linear Transformation \\
5.6 Composition and Inverse Linear Transformations \\
Petros Drineas Interview. \\
6 Determinants and the Inverse Matrix \\
6.1 Determinant of a Matrix \\
6.2 Determinant of Other Matrices \\
6.3 Properties of Determinants \\
6.4 LU Factorization \\
Fran{\c{c}}oise Tisseur Interview \\
7 Eigenvalues and Eigenvectors \\
7.1 Introduction to Eigenvalues and Eigenvectors \\
7.2 Properties of Eigenvalues and Eigenvectors \\
7.3 Diagonalization \\
7.4 Diagonalization of Symmetric Matrices \\
7.5 Singular Value Decomposition \\
Brief Solutions \\
Index",
acknowledgement = ack-nhfb,
}
@Book{Anastassiou:2014:IRI,
author = "George A. Anastassiou and Iuliana F. Iatan",
title = "Intelligent Routines {II}: Solving Linear Algebra and
Differential Geometry with {Sage}",
volume = "58",
publisher = "Springer International Publishing",
address = "Cham, Switzerland",
pages = "xiv + 306",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-319-01967-3",
ISBN = "3-319-01966-X, 3-319-01967-8 (e-book)",
ISBN-13 = "978-3-319-01966-6, 978-3-319-01967-3 (e-book)",
ISSN = "1868-4394",
LCCN = "QA614 .A63 2014",
bibdate = "Mon Sep 15 18:20:07 MDT 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Intelligent systems reference library",
URL = "http://d-nb.info/1045077038/34;
http://nbn-resolving.de/urn:nbn:de:1111-201312062402;
http://www.springerlink.com/content/978-3-319-01967-3",
abstract = "This book contains numerous examples and problems as
well as many unsolved problems. It applies the
successful software Sage, used for mathematical
computation.",
acknowledgement = ack-nhfb,
author-dates = "1952--",
remark = "``ISSN: 1868-4394.''.",
subject = "Engineering; Algebras, Linear; Geometry, Differential;
Algebras, Linear.; Engineering.; Geometry,
Differential.",
tableofcontents = "1. Vector spaces \\
2. Plane and straight line in E3 \\
3. Linear transformations \\
4. Euclidean vector spaces \\
5. Bilinear and quadratic forms \\
6. Differential geometry of curves and surfaces \\
7. Conics and quadrics",
}
@Book{Anonymous:2014:NMO,
author = "Eric Walter",
title = "Numerical Methods and Optimization: a Consumer Guide",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xv + 476",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-319-07671-3",
ISBN = "3-319-07670-1, 3-319-07671-X (e-book)",
ISBN-13 = "978-3-319-07670-6, 978-3-319-07671-3 (e-book)",
LCCN = "QA402.5 .W358 2014eb",
bibdate = "Tue Sep 9 14:27:31 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy1411/2014940746-d.html;
http://www.loc.gov/catdir/enhancements/fy1411/2014940746-t.html",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic",
tableofcontents = "From Calculus to Computation \\
Notation and Norms \\
Solving Systems of Linear Equations \\
Solving Other Problems in Linear Algebra \\
Interpolation and Extrapolation \\
Integrating and Differentiating Functions \\
Solving Systems of Nonlinear Equations \\
Introduction to Optimization \\
Optimizing Without Constraint \\
Optimizing Under Constraints \\
Combinatorial Optimization \\
Solving Ordinary Differential Equations \\
Solving Partial Differential Equations \\
Assessing Numerical Errors \\
WEB Resources to go Further \\
Problems",
}
@Book{Bloomfield:2014:URN,
author = "Victor A. Bloomfield",
title = "Using {R} for Numerical Analysis in Science and
Engineering",
publisher = "CRC Press, Taylor and Francis Group",
address = "Boca Raton, FL, USA",
pages = "xxii + 335",
year = "2014",
ISBN = "1-4398-8448-X (hardcover)",
ISBN-13 = "978-1-4398-8448-5 (hardcover)",
LCCN = "Q183.9 .B56 2014",
bibdate = "Mon Sep 28 08:51:19 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/jrss-a-2010.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/s-plus.bib;
z3950.loc.gov:7090/Voyager",
series = "Chapman and Hall/CRC the R series",
URL = "http://www.crcnetbase.com/isbn/9781439884492",
abstract = "This book shows how the free and open-source R
environment can be used as a powerful and comprehensive
platform for the kinds of numerical analysis that are
traditionally employed by MATLAB. With R code fully
integrated, the book offers brief descriptions of basic
approaches and emphasizes detailed worked examples. It
covers functions in the base installation of R as well
as those in contributed packages, which greatly enhance
the numerical analysis capabilities of R''-- ``The
complex mathematical problems faced by scientists and
engineers rarely can be solved by analytical
approaches, so numerical methods are often necessary.
There are many books that deal with numerical methods
for scientists and engineers; their content is fairly
standardized: solution of systems of linear algebraic
equations and nonlinear equations, finding eigenvalues
and eigenfunctions, interpolation and curve fitting,
numerical differentiation and integration,
optimization, solution of ordinary differential
equations and partial differential equations, and
Fourier analysis. Sometimes statistical analysis of
data is included, as it should be. As powerful personal
computers have become virtually universal on the desks
of scientists and engineers, computationally intensive
Monte Carlo methods are joining the numerical analysis
armamentarium. If there are many books on these
well-established topics, why am I writing another one?
The answer is to propose and demonstrate the use of a
language relatively new to the field: R. My approach in
this book is not to present the standard theoretical
treatments that underlie the various numerical methods
used by scientists and engineers. There are many fine
books and online resources that do that, including one
that uses R: Owen Jones, Robert Maillardet, and Andrew
Robinson. Introduction to Scientific Programming and
Simulation Using R. Chapman and Hall/CRC, Boca Raton,
FL, 2009. Instead, I have tried to write a guide to the
capabilities of R and its add-on packages in the realm
of numerical methods, with simple but useful examples
of how the most pertinent functions can be employed in
practical situations.",
acknowledgement = ack-nhfb,
subject = "Science; Data processing; Engineering; Numerical
analysis; R (Computer program language); MATHEMATICS /
General.; MATHEMATICS / Number Systems.; MATHEMATICS /
Probability and Statistics / General.",
tableofcontents = "1. Introduction \\
2. Calculating \\
3. Graphing \\
4. Programming and functions \\
5. Solving systems of algebraic equations \\
6. Numerical differentiation and integration \\
7. Optimization \\
8. Ordinary differential equations \\
9. Partial differential equations \\
10. Analyzing data \\
11. Fitting models to data",
}
@Article{Borrelli:2014:BRB,
author = "Arianna Borrelli",
title = "Book Review: {{\booktitle{Le destin douloureux de
Walther Ritz (1878--1909), physicien th{\'e}oricien de
g{\'e}nie}}, Jean-Claude Pont (Ed.). Vallesia, Archive
de l'{\'E}tat du Valais, Sion (2012), ISBN
978-2-9700636-5-0}",
journal = j-HIST-MATH,
volume = "41",
number = "1",
pages = "107--110",
month = feb,
year = "2014",
CODEN = "HIMADS",
ISSN = "0315-0860 (print), 1090-249X (electronic)",
ISSN-L = "0315-0860",
bibdate = "Mon Apr 21 12:33:22 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/histmath.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0315086013000396",
acknowledgement = ack-nhfb,
fjournal = "Historia Mathematica",
journal-URL = "http://www.sciencedirect.com/science/journal/03150860/",
}
@Book{Boyd:2014:STE,
author = "John P. (John Philip) Boyd",
title = "Solving transcendental equations: the {Chebyshev}
polynomial proxy and other numerical rootfinders,
perturbation series, and oracles",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xviii + 460",
year = "2014",
ISBN = "1-61197-351-1 (paperback)",
ISBN-13 = "978-1-61197-351-8 (paperback)",
LCCN = "QA353.T7 B69 2014",
bibdate = "Wed Sep 23 17:10:53 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy1503/2014017078-b.html;
http://www.loc.gov/catdir/enhancements/fy1503/2014017078-d.html;
http://www.loc.gov/catdir/enhancements/fy1503/2014017078-t.html",
acknowledgement = ack-nhfb,
author-dates = "1951--",
subject = "Transcendental functions; Chebyshev polynomials;
Transcendental numbers",
tableofcontents = "I: Introduction and overview \\
Introduction: Key themes in rootfinding \\
II: the Chebyshev-Proxy rootfinder and its
generalizations \\
The Chebyshev-Proxy/Companion matrix rootfinder \\
Adaptive Chebyshev interpolation \\
Adaptive Fourier interpolation and rootfinding \\
Complex zeros: Interpolation on a disk, the
Delves--Lyness algorithm, and contour integrals \\
III: Fundamentals: Iterations, bifurcation, and
continuation \\
Newton iteration and its kin \\
Bifurcation theory \\
Continuation in a parameter \\
IV: Polynomials \\
Polynomial equations and the irony of Galois Theory \\
The Quadratic Equation \\
Roots of a cubic polynomial \\
Roots of a quartic polynomial \\
V: Analytical methods \\
Methods for explicit solutions \\
Regular perturbation methods for roots \\
Singular perturbation methods: fractional powers,
logarithms, and exponential asymptotics \\
VI: Classics, special functions, inverses, and oracles
\\
Classical methods for solving one equation in one
unknown \\
Special algorithms for special functions \\
Inverse functions of one unknown \\
Oracles: Theorems and algorithms for determining the
existence, nonexistence, and number of zeros \\
VII: Bivariate systems \\
Two equations in two unknowns \\
VIII: Challenges \\
Past and future \\
A: Companion matrices \\
B: Chebyshev interpolation and quadrature \\
Marching triangles \\
D: Imbricate-Fourier series and the Poisson Summation
Theorem",
}
@Book{Brandt:2014:DAS,
author = "Siegmund Brandt",
title = "Data analysis: statistical and computational methods
for scientists and engineers",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Fourth",
pages = "????",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-319-03762-2",
ISBN = "3-319-03762-5 (e-book)",
ISBN-13 = "978-3-319-03762-2 (e-book), 978-3-319-03761-5,
978-3-319-03761-5",
LCCN = "QA273; QA273",
bibdate = "Sun May 4 11:27:21 MDT 2014",
bibsource = "catalog.princeton.edu:7090/voyager;
https://www.math.utah.edu/pub/tex/bib/java2010.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/probstat2010.bib;
libraries.colorado.edu:210/INNOPAC",
abstract = "The fourth edition of this successful textbook
presents a comprehensive introduction to statistical
and numerical methods for the evaluation of empirical
and experimental data. Equal weight is given to
statistical theory and practical problems. The concise
mathematical treatment of the subject matter is
illustrated by many examples, and for the present
edition a library of Java programs has been developed.
It comprises methods of numerical data analysis and
graphical representation as well as many example
programs and solutions to programming problems. The
programs (source code, Java classes, and documentation)
and extensive appendices to the main text are available
for free download from the books page at
www.springer.com. Contents Probabilities. Random
variables. Random numbers and the Monte Carlo Method.
Statistical distributions (binomial, Gauss, Poisson).
Samples. Statistical tests. Maximum Likelihood. Least
Squares. Regression. Minimization. Analysis of
Variance. Time series analysis. Audience The book is
conceived both as an introduction and as a work of
reference. In particular it addresses itself to
students, scientists and practitioners in science and
engineering as a help in the analysis of their data in
laboratory courses, working for bachelor or master
degrees, in thesis work, and in research and
professional work. The book is concise, but gives a
sufficiently rigorous mathematical treatment of
practical statistical methods for data analysis; it can
be of great use to all who are involved with data
analysis. Physicalia. This lively and erudite treatise
covers the theory of the main statistical tools and
their practical applications. A first rate university
textbook, and good background material for the
practicing physicist. Physics Bulletin.",
acknowledgement = ack-nhfb,
subject = "Probabilities; Mathematical statistics",
tableofcontents = "Introduction \\
Probabilities \\
Random Variables: Distributions \\
Computer-Generated Random Numbers: The Monte Carlo
Method \\
Some Important Distributions and Theorems \\
Samples \\
The Method of Maximum Likelihood \\
Testing Statistical Hypotheses \\
The Method of Least Squares \\
Function Minimization \\
Analysis of Variance \\
Linear and Polynomial Regression \\
Time-Series Analysis \\
(A) Matrix Calculations \\
(B) Combinatorics \\
(C) Formulas and Methods for the Computation of
Statistical Functions \\
(D) The Gamma Function and Related Functions: Methods
and Programs for their Computation \\
(E) Utility Programs \\
(F) The Graphics Class DatanGraphics \\
(G) Problems, Hints and Solutions and Programming
Problems \\
(H) Collection of Formulas \\
(I) Statistical Formulas \\
List of Computer Programs",
}
@Book{Bronson:2014:LAA,
author = "Richard Bronson and Gabriel B. Costa and John T.
Saccoman",
title = "Linear Algebra: Algorithms, Applications, and
Techniques",
publisher = pub-ELSEVIER-ACADEMIC,
address = pub-ELSEVIER-ACADEMIC:adr,
edition = "Third",
pages = "xi + 519",
year = "2014",
ISBN = "0-12-391420-5 (paperback), 0-12-397811-4 (e-book)",
ISBN-13 = "978-0-12-391420-0 (paperback), 978-0-12-397811-0
(e-book)",
LCCN = "QA184.2 .B76 2014",
bibdate = "Mon Sep 15 18:03:00 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.sciencedirect.com/science/book/9780123914200",
acknowledgement = ack-nhfb,
subject = "Algebras, Linear; Lineare Algebra.",
tableofcontents = "1: Matrices / 1--91 \\
2: Vector Spaces / 93--173 \\
3: Linear Transformations / 175--235 \\
4: Eigenvalues, Eigenvectors, and Differential
Equations / 237--288 \\
5: Applications of Eigenvalues / 289--321 \\
6: Euclidean Inner Product / 323--378 \\
Appendix A: Jordan Canonical Forms / 379--411 \\
Appendix B: Markov Chains / 413--424 \\
Appendix C: More on Spanning Trees of Graphs / 425--431
\\
Appendix D: Technology / 433--434 \\
Appendix E: Mathematical Induction / 435 \\
Answers and Hints to Selected Problems / 437--514",
}
@Book{Colonius:2014:DSL,
author = "Fritz Colonius and Wolfgang Kliemann",
title = "Dynamical Systems and Linear Algebra",
volume = "ume 158",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "????",
year = "2014",
ISBN = "0-8218-8319-4",
ISBN-13 = "978-0-8218-8319-8",
LCCN = "QA184.2 .C65 2014",
MRclass = "15-01 34-01 37-01 39-01 60-01 93-01",
bibdate = "Mon Sep 15 18:24:05 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Graduate studies in mathematics",
acknowledgement = ack-nhfb,
subject = "Algebras, Linear; Topological dynamics; Linear and
multilinear algebra; matrix theory -- Instructional
exposition (textbooks, tutorial papers, etc.).;
Ordinary differential equations -- Instructional
exposition (textbooks, tutorial papers, etc.).;
Dynamical systems and ergodic theory -- Instructional
exposition (textbooks, tutorial papers, etc.).;
Difference and functional equations -- Instructional
exposition (textbooks, tutorial papers, etc.).;
Probability theory and stochastic processes --
Instructional exposition (textbooks, tutorial papers,
etc.).; Systems theory; control -- Instructional
exposition (textbooks, tutorial papers, etc.).",
}
@Book{Gruber:2014:MAL,
author = "Marvin H. J. Gruber",
title = "Matrix Algebra for Linear Models",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xv + 375",
year = "2014",
ISBN = "1-118-59255-7 (hardcover), 1-118-60881-X (e-book),
1-118-60874-7 (e-book), 1-118-80041-9 (e-book)",
ISBN-13 = "978-1-118-59255-7 (hardcover), 978-1-118-60881-4
(e-book), 978-1-118-60874-6 (e-book), 978-1-118-80041-6
(e-book)",
LCCN = "QA279 .G78 2014",
bibdate = "Mon Sep 15 18:17:46 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Linear models (Statistics); Matrices",
}
@Book{Hanson:2014:NCM,
author = "Richard J. Hanson and Tim Hopkins",
title = "Numerical computing with modern {Fortran}",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xv + 244",
year = "2014",
ISBN = "1-61197-311-2 (paperback), 1-61197-312-0 (e-book)",
ISBN-13 = "978-1-61197-311-2 (paperback), 978-1-61197-312-9
(e-book)",
LCCN = "QA76.73.F25 H367 2013",
bibdate = "Wed Mar 12 11:09:16 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/pvm.bib;
z3950.loc.gov:7090/Voyager",
series = "Applied mathematics",
abstract = "The Fortran language standard has undergone
significant upgrades in recent years (1990, 1995, 2003,
and 2008). \booktitle{Numerical Computing with Modern
Fortran} illustrates many of these improvements through
practical solutions to a number of scientific and
engineering problems. Readers will discover: techniques
for modernizing algorithms written in Fortran; examples
of Fortran interoperating with C or C++ programs, plus
using the IEEE floating-point standard for efficiency;
illustrations of parallel Fortran programming using
coarrays, MPI, and OpenMP; and a supplementary website
with downloadable source codes discussed in the book.",
acknowledgement = ack-nhfb,
subject = "FORTRAN (Computer program language); Numerical
analysis; Computer programs; Science; Mathematics",
tableofcontents = "Introduction \\
The modern Fortran source \\
Modules for subprogram libraries \\
Generic subprograms \\
Sparse matrices, defined operations, overloaded
assignment \\
Object-oriented programming for numerical applications
\\
Recursion in Fortran \\
Case study: toward a modern QUADPACK routine \\
Case study: quadrature routine qag2003 \\
IEEE arithmetic features and exception handling \\
Interoperability with C \\
Defined operations for sparse matrix solutions \\
Case study: two sparse least-squares system examples
\\
Message passing with MPI in standard Fortran \\
Coarrays in standard Fortran \\
OpenMP in Fortran \\
Modifying source to remove obsolescent or deleted
features \\
Software testing \\
Compilers \\
Software tools \\
Fortran book code on SIAM web site \\
Bibliography \\
Index",
}
@Book{Hogben:2014:HLA,
editor = "Leslie Hogben",
title = "Handbook of Linear Algebra",
publisher = "CRC Press/Taylor and Francis Group",
address = "Boca Raton, FL, USA",
edition = "Second",
pages = "????",
year = "2014",
ISBN = "1-4665-0728-4 (hardcover)",
ISBN-13 = "978-1-4665-0728-9 (hardcover)",
LCCN = "QA184.2 .H36 2014",
bibdate = "Mon Sep 15 18:11:33 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Discrete mathematics and its applications",
URL = "http://marc.crcnetbase.com/isbn/9781466507296",
abstract = "Preface to the Second Edition: Both the format and
guiding vision of \booktitle{Handbook of Linear Algebra
remain} unchanged, but a substantial amount of new
material has been included in the second edition. The
length has increased from 1400 pages to 1900 pages.
There are 20 new chapters. Subjects such as Schur
complements, special types of matrices, generalized
inverses, matrices over nite elds, and invariant
subspaces are now treated in separate chapters. There
are additional chapters on applications of linear
algebra, for example, to epidemiology. There is a new
chapter on using the free open source computer
mathematics system Sage for linear algebra, which also
provides a general introduction to Sage. Additional
surveys of currently active research topics such as
tournaments are also included. Many of the existing
articles have been revised and updated, in some cases
adding a substantial amount of new material. For
example, the chapters on sign pattern matrices and on
applications to geometry have additional sections. As
was true in the rst edition, the topics range from the
most basic linear algebra to advanced topics including
background for active research areas. In this edition,
many of the chapters on advanced topics now include
Conjectures and Open Problems, either as a part of some
sections or as a new section at the end of the chapter.
The conjectures and questions listed in such sections
have been in the literature for more than ve years at
the time of writing, and often a number of partial
results have been obtained. In most cases, the current
(at the time of writing) state of research related to
the question is summarized as facts. Of course, there
is no guarantee that (years after the writing date)
such problems have not been solved (in fact, we hope
they \ldots{})''",
acknowledgement = ack-nhfb,
subject = "Algebras, Linear; MATHEMATICS / General.; MATHEMATICS
/ Algebra / General.; MATHEMATICS / Applied.",
tableofcontents = "Front Cover \\
Dedication \\
Acknowledgments \\
The Editor \\
Contributors \\
Contents \\
Preface \\
Preliminaries \\
I. Linear Algebra \\
Linear Algebra \\
1. Vectors, Matrices, and Systems of Linear Equations
\\
2. Linear Independence, Span, and Bases \\
3. Linear Transformations \\
4. Determinants and Eigenvalues \\
5. Inner Product Spaces, Orthogonal Projection, Least
Squares, and Singular Value Decomposition \\
6. Canonical Forms for Similarity \\
7. Other Canonical Forms \\
8. Unitary Similarity, Normal Matrices, and Spectral
Theory \\
9. Hermitian and Positive Definite Matrices \\
10. Nonnegative Matrices and Stochastic Matrices \\
11. Partitioned Matrices \\
Topics in Linear Algebra \\
12. Schur Complements \\
13. Quadratic, Bilinear, and Sesquilinear Forms \\
14. Multilinear Algebra \\
15. Tensors and Hypermatrices \\
16. Matrix Equalities and Inequalities \\
17. Functions of Matrices \\
18. Matrix Polynomials \\
19. Matrix Equations \\
20. Invariant Subspaces \\
21. Matrix Perturbation Theory \\
22. Special Types of Matrices \\
23. Pseudospectra \\
24. Singular Values and Singular Value Inequalities \\
25. Numerical Range \\
26. Matrix Stability and Inertia \\
27. Generalized Inverses of Matrices \\
28. Inverse Eigenvalue Problems \\
29. Totally Positive and Totally Nonnegative Matrices
\\
30. Linear Preserver Problems \\
31. Matrices over Finite Fields \\
32. Matrices over Integral Domains \\
33. Similarity of Families of Matrices \\
34. Representations of Quivers and Mixed Graphs \\
35. Max-Plus Algebra \\
36. Matrices Leaving a Cone Invariant \\
37. Spectral Sets \\
II. Combinatorial Matrix Theory and Graphs \\
Combinatorial Matrix Theory \\
38. Combinatorial Matrix Theory \\
39. Matrices and Graphs \\
40. Digraphs and Matrices \\
41. Bipartite Graphs and Matrices \\
42. Sign Pattern Matrices: Topics in Combinatorial
Matrix Theory \\
43. Permanents \\
44. D-Optimal Matrices \\
45. Tournaments \\
46. Minimum Rank, Maximum Nullity, and Zero Forcing
Number of Graphs \\
47. Spectral Graph Theory \\
48. Algebraic Connectivity \\
49. Matrix Completion Problems \\
III. Numerical Methods \\
Numerical Methods for Linear Systems \\
50. Vector and Matrix Norms, Error Analysis,
Efficiency, and Stability \\
51. Matrix Factorizations and Direct Solution of Linear
Systems \\
52. Least Squares Solution of Linear Systems \\
53. Sparse Matrix Methods \\
54. Iterative Solution Methods for Linear Systems:
Numerical Methods for Eigenvalues \\
55. Symmetric Matrix Eigenvalue Techniques \\
56. Unsymmetric Matrix Eigenvalue Techniques \\
57. The Implicitly Restarted Arnoldi Method \\
58. Computation of the Singular Value Decomposition \\
59. Computing Eigenvalues and Singular Values to High
Relative Accuracy \\
60. Nonlinear Eigenvalue Problems \\
Topics in Numerical Linear Algebra \\
61. Fast Matrix Multiplication \\
62. Fast Algorithms for Structured Matrix Computations
\\
63. Structured Eigenvalue Problems:
Structure-Preserving Algorithms, Structured Error
Analysis \\
64. Large-Scale Matrix Computations",
}
@Book{Hunt:2014:GMB,
author = "Brian R. Hunt and Ronald L. Lipsman and Jonathan M.
(Jonathan Micah) Rosenberg",
title = "A guide to {MATLAB}: for beginners and experienced
users: updated for {MATLAB 8} and {Simulink 8}",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Third",
pages = "????",
year = "2014",
ISBN = "1-107-66222-2 (paperback)",
ISBN-13 = "978-1-107-66222-3 (paperback)",
LCCN = "QA297 .H86 2014",
bibdate = "Thu Aug 28 08:17:57 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
abstract = "MATLAB is a high-level language and interactive
environment for numerical computation, visualization,
and programming. Using MATLAB, you can analyze data,
develop algorithms, and create models and applications.
The language, tools, and built-in math functions enable
you to explore multiple approaches and reach a solution
faster than with spreadsheets or traditional
programming languages.",
acknowledgement = ack-nhfb,
subject = "MATLAB; Numerical analysis; Data processing;
MATHEMATICS / General.",
tableofcontents = "Preface \\
1. Getting started \\
2. MATLAB basics \\
3. Interacting with MATLAB \\
Practice Set A. Algebra and arithmetic \\
4. Beyond the basics \\
5. MATLAB graphics \\
6. MATLAB programming \\
7. Publishing and M-books \\
Practice Set B. Math, graphics, and programming \\
8. MuPAD \\
9. Simulink \\
10. GUIs \\
11. Applications \\
Practice Set C. Developing your MATLAB skills \\
12. Troubleshooting \\
Solutions to the practice sets \\
Glossary \\
Index",
}
@Book{Jones:2014:ISP,
author = "Owen (Owen Dafydd) Jones and Robert Maillardet and
Andrew (Andrew P.) Robinson",
title = "Introduction to scientific programming and simulation
using {R}",
publisher = pub-CRC,
address = pub-CRC:adr,
edition = "Second",
pages = "xxiv + 582",
year = "2014",
ISBN = "1-4665-6999-9, 1-4665-7001-6",
ISBN-13 = "978-1-4665-6999-7, 978-1-4665-7001-6",
LCCN = "Q183.9 .J65 2014",
bibdate = "Thu Jul 21 05:52:46 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/s-plus.bib;
z3950.loc.gov:7090/Voyager",
series = "The R series",
acknowledgement = ack-nhfb,
subject = "Science; Data processing; Computer simulation;
Stochastic processes; Mathematical models; Numerical
analysis; Computer programming; R (Computer program
language); Computer simulation; Data processing",
}
@Book{Kushner:2014:NMS,
author = "Harold J. Kushner and Paul Dupuis",
title = "Numerical Methods for Stochastic Control Problems in
Continuous Time",
volume = "24",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xii + 476",
year = "2014",
DOI = "https://doi.org/10.1007/978-1-4613-0007-6",
ISBN = "1-4612-6531-2",
ISBN-13 = "978-1-4612-6531-3",
ISSN = "0172-4568",
ISSN-L = "0172-4568",
LCCN = "QA273.A1-274.9; QA274-274.9",
bibdate = "Tue Apr 29 18:44:55 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/probstat2010.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "Stochastic Modelling and Applied Probability",
abstract = "This book presents a comprehensive development of
effective numerical methods for stochastic control
problems in continuous time. The process models are
diffusions, jump-diffusions, or reflected diffusions of
the type that occur in the majority of current
applications. All the usual problem formulations are
included, as well as those of more recent interest such
as ergodic control, singular control and the types of
reflected diffusions used as models of queuing
networks. Applications to complex deterministic
problems are illustrated via application to a large
class of problems from the calculus of variations. The
general approach is known as the Markov Chain
Approximation Method. The required background to
stochastic processes is surveyed, there is an extensive
development of methods of approximation, and a chapter
is devoted to computational techniques. The book is
written on two levels, that of practice (algorithms and
applications) and that of the mathematical development.
Thus the methods and use should be broadly accessible.
This update to the first edition will include added
material on the control of the 'jump term' and the
'diffusion term.' There will be additional material on
the deterministic problems, solving the Hamilton-Jacobi
equations, for which the authors' methods are still
among the most useful for many classes of problems. All
of these topics are of great and growing current
interest.",
acknowledgement = ack-nhfb,
subject = "Mathematics; System theory; Mathematical optimization;
Distribution (Probability theory)",
tableofcontents = "Review of Continuous Time Models \\
Controlled Markov Chains \\
Dynamic Programming Equations \\
Markov Chain Approximation Method \\
The Approximating Markov Chains \\
Computational Methods \\
The Ergodic Cost Problem \\
Heavy Traffic and Singular Control \\
Weak Convergence and the Characterization of Processes
\\
Convergence Proofs \\
Convergence Proofs Continued \\
Finite Time and Filtering Problems \\
Controlled Variance and Jumps \\
Problems from the Calculus of Variations: Finite Time
Horizon \\
Problems from the Calculus of Variations: Infinite Time
Horizon \\
The Viscosity Solution Approach",
}
@Book{Lay:2014:LAAb,
author = "David C. Lay",
title = "Linear Algebra and its Applications",
publisher = "Pearson Education Limited",
address = "Harlow, Essex",
edition = "Fourth",
pages = "ii + 784",
year = "2014",
ISBN = "1-292-02055-5",
ISBN-13 = "978-1-292-02055-6",
LCCN = "????",
bibdate = "Mon Sep 15 18:22:44 MDT 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
acknowledgement = ack-nhfb,
remark = "Oorspr. uitg.: 1994.",
subject = "Lineaire algebra.; Toepassingen.",
tableofcontents = "Linear Equations in Linear Algebra \\
Matrix Algebra \\
Determinants \\
Vector Spaces \\
Eigenvalues and Eigenvectors \\
Orthogonality and Least Squares \\
Symmetric Matrices and Quadratic Forms \\
The Geometry of Vector Spaces \\
Appendix: Uniqueness of the Reduced Echelon Form \\
Complex Numbers \\
Study guide for each chapter",
}
@Book{Miller:2014:NAE,
author = "G. Miller",
title = "Numerical Analysis for Engineers and Scientists",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "x + 572",
year = "2014",
DOI = "https://doi.org/10.1017/CBO9781139108188",
ISBN = "1-107-02108-1 (hardcover), 1-139-10818-2 (ebook)",
ISBN-13 = "978-1-107-02108-2 (hardcover), 978-1-139-10818-8
(ebook)",
LCCN = "QA297 .M55 2014",
bibdate = "Tue Aug 12 15:47:25 MDT 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
acknowledgement = ack-nhfb,
}
@Book{Nassif:2014:INA,
author = "Nabil Nassif and Dolly Khuwayri Fayyad",
title = "Introduction to Numerical Analysis and Scientific
Computing",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xix + 311",
year = "2014",
ISBN = "1-4665-8948-5 (hardcover)",
ISBN-13 = "978-1-4665-8948-3 (hardcover)",
LCCN = "QA297 .N37 2014",
MRclass = "65-01",
MRnumber = "3112293",
bibdate = "Tue May 27 11:27:40 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
abstract = "Designed for a one-semester course on the subject,
this classroom-tested text presents fundamental
concepts of numerical mathematics and explains how to
implement and program numerical methods. Drawing on
their years of teaching students in mathematics,
engineering, and the sciences, the authors cover
floating-point number representations, nonlinear
equations, linear algebra concepts, the Lagrange
interpolation theorem, numerical differentiation and
integration, and ODEs. They also focus on the
implementation of the algorithms using MATLAB.\par
This work is the result of several years of teaching a
one-semester course on Numerical Analysis and Scienti c
Computing, addressed primarily to stu- dents in
Mathematics, Engineering, and Sciences. Our purpose is
to provide those students with fundamental concepts of
Numerical Mathematics and at the same time stir their
interest in the art of implementing and programming
Numerical Methods.",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Textbooks; Computer science;
Mathematics; MATHEMATICS / Advanced.; MATHEMATICS /
Applied.; MATHEMATICS / Number Systems.",
}
@Book{Quarteroni:2014:SCM,
author = "Alfio Quarteroni and Fausto Saleri and Paola
Gervasio",
title = "Scientific computing with {Matlab} and {Octave}",
volume = "2",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xviii + 450 (est.)",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-642-45367-0",
ISBN = "3-642-45366-X (hard cover)",
ISBN-13 = "978-3-642-45366-3 (hard cover)",
LCCN = "????",
bibdate = "Sun Apr 13 16:57:12 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Texts in Computational Science and Engineering",
URL = "http://link.springer.com/book/10.1007/978-3-642-45367-0",
acknowledgement = ack-nhfb,
tableofcontents = "Front Matter / i--xviii \\
What can't be ignored / 1--40 \\
Nonlinear equations / 41--76 \\
Approximation of functions and data / 77--111 \\
Numerical differentiation and integration / 113--136
\\
Linear systems / 137--191 \\
Eigenvalues and eigenvectors / 193--211 \\
Numerical optimization / 213--269 \\
Ordinary differential equations / 271--328 \\
Numerical approximation of boundary-value problems /
329--376 \\
Solutions of the exercises / 377--428 \\
Back Matter / 429--450",
}
@Book{Rossant:2014:IIC,
author = "Cyrille Rossant",
title = "{IPython} interactive computing and visualization
cookbook: over 100 hands-on recipes to sharpen your
skills in high-performance numerical computing and data
science with {Python}",
publisher = "Packt Publishing Ltd.",
address = "Birmingham, UK",
pages = "v + 494",
year = "2014",
ISBN = "1-78328-481-1, 1-78328-482-X (e-book), 1-322-16622-6
(e-book)",
ISBN-13 = "978-1-78328-481-8, 978-1-78328-482-5 (e-book),
978-1-322-16622-3 (e-book)",
LCCN = "QA76.73.P98 R677 2014",
bibdate = "Sat Mar 21 07:16:36 MDT 2015",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/python.bib",
abstract = "IPython Interactive Computing and Visualization
Cookbook contains many ready-to-use focused recipes for
high-performance scientific computing and data
analysis. The first part covers programming techniques,
including code quality and reproducibility, code
optimization, high-performance computing through
dynamic compilation, parallel computing, and graphics
card programming. The second part tackles data science,
statistics, machine learning, signal and image
processing, dynamical systems, and pure and applied
mathematics.",
acknowledgement = ack-nhfb,
subject = "Python (Computer program language); Command languages
(Computer science); Information visualization;
Interactive computer systems; Command languages
(Computer science); Information visualization;
Interactive computer systems; Python (Computer program
language)",
}
@Book{Stewart:2014:PS,
author = "John Stewart",
title = "Python for scientists",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "????",
year = "2014",
ISBN = "1-107-06139-3 (hardcover), 1-107-68642-3",
ISBN-13 = "978-1-107-06139-2 (hardcover), 978-1-107-68642-7",
LCCN = "Q183.9 .S865 2014",
bibdate = "Thu Jun 26 09:42:41 MDT 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/python.bib",
URL = "http://assets.cambridge.org/97811070/61392/cover/9781107061392.jpg",
abstract = "Python is a free, open source, easy-to-use software
tool that offers a significant alternative to
proprietary packages such as MATLAB and Mathematica.
This book covers everything the working scientist needs
to know to start using Python effectively. The author
explains scientific Python from scratch, showing how
easy it is to implement and test non-trivial
mathematical algorithms and guiding the reader through
the many freely available add-on modules. A range of
examples, relevant to many different fields, illustrate
the program's capabilities. In particular, readers are
shown how to use pre-existing legacy code (usually in
Fortran77) within the Python environment, thus avoiding
the need to master the original code. Instead of
exercises the book contains useful snippets of tested
code which the reader can adapt to handle problems in
their own field, allowing students and researchers with
little computer expertise to get up and running as soon
as possible.",
acknowledgement = ack-nhfb,
author-dates = "1943 July 1",
subject = "Science; Data processing; Python (Computer program
language); COMPUTERS / General.",
tableofcontents = "Preface \\
1. Introduction \\
2. Getting started with IPython \\
3. A short Python tutorial \\
4. Numpy \\
5. Two-dimensional graphics \\
6. Three-dimensional graphics \\
7. Ordinary differential equations \\
8. Partial differential equations: a pseudospectral
approach \\
9. Case study: multigrid \\
Appendix A. Installing a Python environment \\
Appendix B. Fortran77 subroutines for pseudospectral
methods \\
References \\
Index",
}
@Book{Stys:2014:LNN,
author = "Tadeusz Sty{\'s} and Krystyna Sty{\'s}",
title = "Lecture Notes in Numerical Analysis with
{Mathematica}",
publisher = "Bentham Science Publishers, Inc.",
address = "Sharjah, United Arab Emirates",
pages = "243",
year = "2014",
DOI = "https://doi.org/10.2174/97816080594231140101",
ISBN = "1-60805-942-1 (e-book), 1-60805-943-X",
ISBN-13 = "978-1-60805-942-3 (e-book), 978-1-60805-943-0",
LCCN = "QA298 .S797 2014",
bibdate = "Tue Apr 28 16:22:45 MDT 2015",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
URL = "http://ebooks.benthamsciencepublisher.org/book/9781608059423/",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Simulation methods; Mathematical
physics; Data processing; MATHEMATICS / Numerical
Analysis",
tableofcontents = "Foreword / O. A. Daman / i \\
Preface / iii--iv (2) \\
The List of Mathematica Functions and Modulae / v \\
Floating Point Computer Arithmetic / 1--26 (26) \\
Natural and Generalized Interpolating Polynomials /
27--62 (36) \\
Polynomial Splines / 63--102 (40) \\
Uniform Approximation / 103--132 (30) \\
Introduction to the Least Squares Analysis / 133--156
(24) \\
Selected Methods for Numerical Integration / 157--198
(42) \\
Solving Nonlinear Equations by Iterative Methods /
199--229 (31) \\
References / 230--231 (2) \\
Index / 233--235 (3)",
}
@Book{Hill:2015:LSP,
author = "Christian Hill",
title = "Learning scientific programming with {Python}",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "vii + 452",
year = "2015",
ISBN = "1-107-07541-6 (hardcover), 1-107-42822-X (paperback)",
ISBN-13 = "978-1-107-07541-2 (hardcover), 978-1-107-42822-5
(paperback)",
LCCN = "Q183.9 .H58 2015",
bibdate = "Mon Aug 21 08:44:22 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/python.bib;
z3950.loc.gov:7090/Voyager",
abstract = "Learn to master basic programming tasks from scratch
with real-life scientifically relevant examples and
solutions drawn from both science and engineering.
Students and researchers at all levels are increasingly
turning to the powerful Python programming language as
an alternative to commercial packages and this
fast-paced introduction moves from the basics to
advanced concepts in one complete volume, enabling
readers to quickly gain proficiency. Beginning with
general programming concepts such as loops and
functions within the core Python 3 language, and moving
onto the NumPy, SciPy and Matplotlib libraries for
numerical programming and data visualisation, this
textbook also discusses the use of IPython notebooks to
build rich-media, shareable documents for scientific
analysis. Including a final chapter introducing
challenging topics such as floating-point precision and
algorithm stability, and with extensive online
resources to support advanced study, this textbook
represents a targeted package for students requiring a
solid foundation in Python programming.",
acknowledgement = ack-nhfb,
author-dates = "1974--",
subject = "Science; Data processing; Mathematics; Python
(Computer program language); SCIENCE / Mathematical
Physics.",
tableofcontents = "1. Introduction \\
2. The core Python language I \\
3. Interlude: simple plotting with Pylab \\
4. The core Python language II \\
5. IPython and IPython notebook \\
6. NumPy \\
7. Matplotlib \\
8. SciPy \\
9. General scientific programming \\
Appendix A \\
Solutions \\
Index",
}
@Book{Mehta:2015:MPS,
author = "Hemant Kumar Mehta",
title = "Mastering {Python} scientific computing: a complete
guide for {Python} programmers to master scientific
computing using {Python APIs} and tools",
publisher = pub-PACKT,
address = pub-PACKT:adr,
pages = "????",
year = "2015",
ISBN = "1-78328-883-3, 1-78328-882-5",
ISBN-13 = "978-1-78328-883-0, 978-1-78328-882-3",
LCCN = "QA76.73.P98",
bibdate = "Fri Oct 23 15:54:07 MDT 2015",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/python.bib",
series = "Community experience distilled",
URL = "http://proquest.safaribooksonline.com/?fpi=9781783288823",
acknowledgement = ack-nhfb,
subject = "Python (Computer program language); Computer science",
tableofcontents = "Mastering Python Scientific Computing \\
Table of Contents \\
Mastering Python Scientific Computing \\
Credits \\
About the Author \\
About the Reviewers \\
www.PacktPub.com \\
Support files, eBooks, discount offers, and more \\
Why subscribe? \\
Free access for Packt account holders \\
Preface \\
What this book covers \\
What you need for this book \\
Who this book is for \\
Conventions \\
Reader feedback \\
Customer support \\
Downloading the example code \\
Downloading the color images of this book \\
Errata \\
Piracy \\
Questions \\
1. The Landscape of Scientific Computing --- and Why
Python? \\
Definition of scientific computing \\
A simple flow of the scientific computation process \\
Examples from scientific/engineering domains \\
A strategy for solving complex problems \\
Approximation, errors, and associated concepts and
terms \\
Error analysis \\
Conditioning, stability, and accuracy \\
Backward and forward error analysis \\
Is it okay to ignore these errors? \\
Computer arithmetic and floating-point numbers \\
The background of the Python programming language \\
The guiding principles of the Python language \\
Why Python for scientific computing? \\
Compact and readable code \\
Holistic language design \\
Free and open source \\
Language interoperability \\
Portable and extensible \\
Hierarchical module system \\
Graphical user interface packages \\
Data structures \\
Python's testing framework \\
Available libraries \\
The downsides of Python \\
Summary \\
2. A Deeper Dive into Scientific Workflows and the
Ingredients of Scientific Computing Recipes \\
Mathematical components of scientific computations \\
A system of linear equations \\
A system of nonlinear equations \\
Optimization \\
Interpolation \\
Extrapolation \\
Numerical integration \\
Numerical differentiation \\
Differential equations \\
The initial value problem \\
The boundary value problem \\
Random number generator \\
Python scientific computing \\
Introduction to NumPy \\
The SciPy library \\
The SciPy Subpackage \\
Data analysis using pandas \\
A brief idea of interactive programming using IPython
\\
IPython parallel computing \\
IPython Notebook \\
Symbolic computing using SymPy \\
The features of SymPy \\
Why SymPy? \\
The plotting library \\
Summary \\
3. Efficiently Fabricating and Managing Scientific Data
\\
The basic concepts of data \\
Data storage software and toolkits \\
Files \\
Structured files \\
Unstructured files \\
Database \\
Possible operations on data \\
Scientific data format \\
Ready-to-use standard datasets \\
Data generation \\
Synthetic data generation (fabrication) \\
Using Python's built-in functions for random number
generation \\
Bookkeeping functions \\
Functions for integer random number generation \\
Functions for sequences \\
Statistical-distribution-based functions \\
Nondeterministic random number generator \\
Designing and implementing random number generators
based on statistical distributions \\
A program with simple logic to generate five-digit
random numbers \\
A brief note about large-scale datasets \\
Summary \\
4. Scientific Computing APIs for Python \\
Numerical scientific computing in Python \\
The NumPy package \\
The ndarrays data structure \\
File handling \\
Some sample NumPy programs \\
The SciPy package \\
The optimization package \\
The interpolation package \\
Integration and differential equations in SciPy \\
The stats module \\
Clustering package and spatial algorithms in SciPy \\
Image processing in SciPy \\
Sample SciPy programs \\
Statistics using SciPy \\
Optimization in SciPy \\
Image processing using SciPy \\
Symbolic computations using SymPy \\
Computer Algebra System \\
Features of a general-purpose CAS \\
A brief idea of SymPy \\
Core capability \\
Polynomials \\
Calculus \\
Solving equations \\
Discrete math \\
Matrices \\
Geometry \\
Plotting \\
Physics \\
Statistics \\
Printing \\
SymPy modules \\
Simple exemplary programs \\
Basic symbol manipulation \\
Expression expansion in SymPy \\
Simplification of an expression or formula \\
Simple integrations \\
APIs and toolkits for data analysis and visualization
\\
Data analysis and manipulation using pandas \\
Important data structures of pandas \\
Special features of pandas \\
Data visualization using matplotlib \\
Interactive computing in Python using IPython \\
Sample data analysis and visualization programs \\
Summary \\
5. Performing Numerical Computing \\
The NumPy fundamental objects \\
The ndarray object \\
The attributes of an array \\
Basic operations on arrays \\
Special operations on arrays (shape change and
conversion) \\
Classes associated with arrays \\
The matrix sub class \\
Masked array \\
The structured/recor array \\
The universal function object \\
Attributes \\
Methods \\
Various available ufunc \\
The NumPy mathematical modules \\
Introduction to SciPy \\
Mathematical functions in SciPy \\
Advanced modules/packages \\
Integration \\
Signal processing (scipy.signal) \\
Fourier transforms (scipy.fftpack) \\
Spatial data structures and algorithms (scipy.spatial)
\\
Optimization (scipy.optimize) \\
Interpolation (scipy.interpolate) \\
Linear algebra (scipy.linalg) \\
Sparse eigenvalue problems with ARPACK \\
Statistics (scipy.stats) \\
Multidimensional image processing (scipy.ndimage) \\
Clustering \\
Curve fitting \\
File I/O (scipy.io) \\
Summary \\
6. Applying Python for Symbolic Computing \\
Symbols, expressions, and basic arithmetic \\
Equation solving \\
Functions for rational numbers, exponentials, and
logarithms \\
Polynomials \\
Trigonometry and complex numbers \\
Linear algebra \\
Calculus \\
Vectors \\
The physics module \\
Hydrogen wave functions \\
Matrices and Pauli algebra \\
The quantum harmonic oscillator in 1-D and 3-D \\
Second quantization \\
High-energy Physics \\
Mechanics \\
Pretty printing \\
LaTeX Printing \\
The cryptography module \\
Parsing input \\
The logic module \\
The geometry module \\
Symbolic integrals \\
Polynomial manipulation \\
Sets \\
The simplify and collect operations \\
Summary \\
7. Data Analysis and Visualization \\
Matplotlib \\
The architecture of matplotlib \\
The scripting layer (pyplot) \\
The artist layer \\
The backend layer \\
Graphics with matplotlib \\
Output generation \\
The pandas library \\
Series \\
DataFrame \\
Panel \\
The common functionality among the data structures \\
Time series and date functions \\
Handling missing data \\
I/O operations \\
Working on CSV files \\
Ready-to-eat datasets \\
The pandas plotting \\
IPython \\
The IPython console and system shell \\
The operating system interface \\
Nonblocking plotting \\
Debugging \\
IPython Notebook \\
Summary \\
8. Parallel and Large-scale Scientific Computing \\
Parallel computing using IPython \\
The architecture of IPython parallel computing \\
The components of parallel computing \\
The IPython engine \\
The IPython controller \\
IPython view and interfaces \\
The IPython client \\
Example of performing parallel computing \\
A parallel decorator \\
IPython's magic functions \\
Activating specific views \\
Engines and QtConsole \\
Advanced features of IPython \\
Fault-tolerant execution \\
Dynamic load balancing \\
Pushing and pulling objects between clients and engines
\\
Database support for storing the requests and results
\\
Using MPI in IPython \\
Managing dependencies among tasks \\
Functional dependency \\
Decorators for functional dependency \\
Graph dependency \\
Impossible dependencies \\
The DAG dependency and the NetworkX library \\
Using IPython on an Amazon EC2 cluster with StarCluster
\\
A note on security of IPython \\
Well-known parallel programming styles \\
Issues in parallel programming \\
Parallel programming \\
Concurrent programming \\
Distributed programming \\
Multiprocessing in Python \\
Multithreading in Python \\
Hadoop-based MapReduce in Python \\
Spark in Python \\
Summary \\
9. Revisiting Real-life Case Studies \\
Scientific computing applications developed in Python
\\
The one Laptop per Child project used Python for their
user interface \\
ExpEYES --- eyes for science \\
A weather prediction application in Python \\
An aircraft conceptual designing tool and API in Python
\\
OpenQuake Engine \\
SMS Siemag AG application for energy efficiency \\
Automated code generator for analysis of High-energy
Physics data \\
Python for computational chemistry applications \\
Python for developing a Blind Audio Tactile Mapping
System \\
TAPTools for air traffic control \\
Energy-efficient lights with an embedded system \\
Scientific computing libraries developed in Python \\
A maritime designing API by Tribon \\
Molecular Modeling Toolkit \\
Standard Python packages \\
Summary \\
10. Best Practices for Scientific Computing \\
The best practices for designing \\
The implementation of best practices \\
The best practices for data management and application
deployment \\
The best practices to achieving high performance \\
The best practices for data privacy and security \\
Testing and maintenance best practices \\
General Python best practices \\
Summary \\
Index",
}
@Book{Scherzer:2015:HMM,
editor = "Otmar Scherzer",
booktitle = "Handbook of Mathematical Methods in Imaging",
title = "Handbook of Mathematical Methods in Imaging",
publisher = "SpringerReference",
address = "New York, NY, USA",
edition = "Second",
pages = "xviii + 2178 (3 volumes)",
year = "2015",
DOI = "https://doi.org/10.1007/978-1-4939-0790-8",
ISBN = "1-4939-0789-1 (set), 1-4939-0790-5 (e-book)",
ISBN-13 = "978-1-4939-0789-2 (set), 978-1-4939-0790-8 (e-book)",
LCCN = "RC78.7.D53 H358 2015",
bibdate = "Sat Aug 13 16:08:19 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
abstract = "The Handbook of Mathematical Methods in Imaging
provides a comprehensive treatment of the mathematical
techniques used in imaging science. The material is
grouped into two central themes, namely, Inverse
Problems (Algorithmic Reconstruction) and Signal and
Image Processing. Each section within the themes covers
applications (modeling), mathematics, numerical methods
(using a case example) and open questions. Written by
experts in the area, the presentation is mathematically
rigorous. This expanded and revised second edition
contains updates to existing chapters and 16 additional
entries on important mathematical methods such as graph
cuts, morphology, discrete geometry, PDEs, conformal
methods, to name a few. The entries are
cross-referenced for easy navigation through connected
topics. Available in both print and electronic forms,
the handbook is enhanced by more than 200 illustrations
and an extended bibliography. It will benefit students,
scientists and researchers in applied mathematics.
Engineers and computer scientists working in imaging
will also find this handbook useful.",
acknowledgement = ack-nhfb,
subject = "Diagnostic imaging; Mathematical models; Image
processing; Digital techniques; Imaging systems in
medicine",
subject = "Mathematics; Medical radiology; Computer vision;
Numerical analysis; Computer vision; Mathematics;
Medical radiology; Numerical analysis",
tableofcontents = "Front Matter / i-xviii \\
Inverse Problems --- Methods \\
Front Matter / 1--1 \\
Linear Inverse Problems / Charles Groetsch / 3--46 \\
Large-Scale Inverse Problems in Imaging / Julianne
Chung, Sarah Knepper, James G. Nagy / 47--90 \\
Regularization Methods for Ill-Posed Problems / Jin
Cheng, Bernd Hofmann / 91--123 \\
Distance Measures and Applications to Multimodal
Variational Imaging / Christiane P{\"o}schl, Otmar
Scherzer / 125--155 \\
Energy Minimization Methods / Mila Nikolova / 157--204
\\
Compressive Sensing / Massimo Fornasier, Holger Rauhut
/ 205--256 \\
Duality and Convex Programming / Jonathan M. Borwein,
D. Russell Luke / 257--304 \\
EM Algorithms / Charles Byrne, Paul P. B. Eggermont /
305--388 \\
EM Algorithms from a Non-stochastic Perspective /
Charles Byrne / 389--429 \\
Iterative Solution Methods / Martin Burger, Barbara
Kaltenbacher, Andreas Neubauer / 431--470 \\
Level Set Methods for Structural Inversion and Image
Reconstruction / Oliver Dorn, Dominique Lesselier /
471--532 \\
Inverse Problems --- Case Examples \\
Front Matter / 533--533 \\
Expansion Methods / Habib Ammari, Hyeonbae Kang /
535--590 \\
Sampling Methods / Martin Hanke-Bourgeois, Andreas
Kirsch / 591--647 \\
Inverse Scattering / David Colton, Rainer Kress /
649--700 \\
Electrical Impedance Tomography / Andy Adler, Romina
Gaburro, William Lionheart / 701--762 \\
Synthetic Aperture Radar Imaging / Margaret Cheney,
Brett Borden / 763--799 \\
Tomography / Gabor T. Herman / 801--845 \\
Microlocal Analysis in Tomography / Venkateswaran P.
Krishnan, Eric Todd Quinto / 847--902 \\
Mathematical Methods in PET and SPECT Imaging /
Athanasios S. Fokas, George A. Kastis / 903--936 \\
Mathematics of Electron Tomography / Ozan {\"O}ktem /
937--1031 \\
Inverse Problems --- Case Examples Front Matter /
533--533 \\
Optical Imaging / Simon R. Arridge, Jari P. Kaipio,
Ville Kolehmainen, Tanja Tarvainen / 1033--1079 \\
Photoacoustic and Thermoacoustic Tomography: Image
Formation Principles / Kun Wang, Mark A. Anastasio /
1081--1116 \\
Mathematics of Photoacoustic and Thermoacoustic
Tomography / Peter Kuchment, Leonid Kunyansky /
1117--1167 \\
Mathematical Methods of Optical Coherence Tomography /
Peter Elbau, Leonidas Mindrinos, Otmar Scherzer /
1169--1204 \\
Wave Phenomena / Matti Lassas, Mikko Salo, Gunther
Uhlmann / 1205--1252 \\
Sonic Imaging / Frank Natterer / 1253--1278 \\
Imaging in Random Media / Liliana Borcea / 1279--1340
\\
Image Restoration and Analysis \\
Front Matter / 1341--1341 \\
Statistical Methods in Imaging / Daniela Calvetti,
Erkki Somersalo / 1343--1392 \\
Supervised Learning by Support Vector Machines /
Gabriele Steidl / 1393--1453 \\
Total Variation in Imaging / V. Caselles, A. Chambolle,
M. Novaga / 1455--1499 \\
Numerical Methods and Applications in Total Variation
Image Restoration / Raymond Chan, Tony F. Chan, Andy
Yip / 1501--1537 \\
Mumford and Shah Model and Its Applications to Image
Segmentation and Image Restoration / Leah Bar, Tony F.
Chan, Ginmo Chung, Miyoun Jung, Luminita A. Vese, Nahum
Kiryati, Nir Sochen / 1539--1597 \\
Local Smoothing Neighborhood Filters / Jean-Michel
Morel, Antoni Buades, Tomeu Coll / 1599--1643 \\
Neighborhood Filters and the Recovery of 3D Information
/ Julie Digne, Mariella Dimiccoli, Neus Sabater,
Philippe Salembier / 1645--1673 \\
Splines and Multiresolution Analysis / Brigitte Forster
/ 1675--1716 \\
Gabor Analysis for Imaging / Ole Christensen, Hans G.
Feichtinger, Stephan Paukner / 1717--1757 \\
Shape Spaces / Alain Trouv{\'e}, Laurent Younes /
1759--1817 \\
Variational Methods in Shape Analysis / Martin Rumpf,
Benedikt Wirth / 1819--1858 \\
Manifold Intrinsic Similarity / Alexander M. Bronstein,
Michael M. Bronstein / 1859--1908 \\
Image Segmentation with Shape Priors: Explicit Versus
Implicit Representations / Daniel Cremers / 1909--1944
\\
Image Restoration and Analysis \\
Front Matter / 1341--1341 \\
Optical Flow / Florian Becker, Stefania Petra,
Christoph Schn{\"o}rr / 1945--2004 \\
Non-linear Image Registration / Lars Ruthotto, Jan
Modersitzki / 2005--2051 \\
Starlet Transform in Astronomical Data Processing /
Jean-Luc Starck, Fionn Murtagh, Mario Bertero /
2053--2098 \\
Differential Methods for Multi-dimensional Visual Data
Analysis / Werner Benger, Ren{\'e} Heinzl, Dietmar
Hildenbrand, Tino Weinkauf, Holger Theisel, David
Tschumperl{\'e} / 2099--2162 \\
Back Matter / 2163--2178",
}
@Book{Snieder:2015:GTM,
author = "Roel Snieder and Kasper {Van Wijk}",
title = "A Guided Tour of Mathematical Methods for the Physical
Sciences",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Third",
pages = "xxii + 560",
year = "2015",
DOI = "https://doi.org/10.1017/CBO9781139013543",
ISBN = "1-107-08496-2 (hardcover), 1-107-64160-8 (paperback),
1-139-01354-8 (e-book)",
ISBN-13 = "978-1-107-08496-4 (hardcover), 978-1-107-64160-0
(paperback), 978-1-139-01354-3 (e-book)",
LCCN = "QA300 .S794 2015",
bibdate = "Fri Jun 15 08:11:31 MDT 2018",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
abstract = "Mathematical methods are essential tools for all
physical scientists. This book provides a comprehensive
tour of the mathematical knowledge and techniques that
are needed by students across the physical sciences. In
contrast to more traditional textbooks, all the
material is presented in the form of exercises. Within
these exercises, basic mathematical theory and its
applications in the physical sciences are well
integrated. In this way, the mathematical insights that
readers acquire are driven by their physical-science
insight. This third edition has been completely
revised: new material has been added to most chapters,
and two completely new chapters on probability and
statistics and on inverse problems have been added.
This guided tour of mathematical techniques is
instructive, applied, and fun. This book is targeted
for all students of the physical sciences. It can serve
as a stand-alone text, or as a source of exercises and
examples to complement other textbooks.",
acknowledgement = ack-nhfb,
author-dates = "1958--",
subject = "Mathematical analysis; Physical sciences; Mathematics;
Mathematical physics; Analyse math{\'e}matique;
Sciences physiques; Math{\'e}matiques; Physique
math{\'e}matique; Mathematical analysis; Mathematical
physics; Mathematics",
tableofcontents = "Introduction \\
Dimensional analysis \\
Power series \\
Spherical and cylindrical coordinates \\
Gradient \\
Divergence of a vector field \\
Curl of a vector field \\
Theorem of Gauss \\
Theorem of Stokes \\
The Laplacian \\
Scale analysis \\
Linear algebra \\
Dirac delta function \\
Fourier analysis \\
Analytic functions \\
Complex integration \\
Green's functions: principles \\
Green's functions: examples \\
Normal modes \\
Potential field theory \\
Probability and statistics \\
Inverse problems \\
Perturbation theory \\
Asymptotic evaluation of integrals \\
Conservation laws \\
Cartesian tensors \\
Variational calculus \\
Epilogue, on power and knowledge",
}
@Book{SouzadeCursi:2015:UQS,
author = "Eduardo {Souza de Cursi} and Rubens Sampaio",
title = "Uncertainty Quantification and Stochastic Modeling
with {Matlab}",
publisher = "ISTE Press Ltd",
address = "London, UK",
year = "2015",
ISBN = "0-08-100471-0 (e-book), 1-78548-005-7",
ISBN-13 = "978-0-08-100471-5 (e-book), 978-1-78548-005-8",
LCCN = "QA274.2",
bibdate = "Tue Jan 12 16:21:50 MST 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/s-plus.bib",
URL = "http://alltitles.ebrary.com/Doc?id=11040161;
http://lib.myilibrary.com?id=762946;
http://public.eblib.com/choice/PublicFullRecord.aspx?p=2007484;
http://www.sciencedirect.com/science/book/9781785480058",
abstract = "Uncertainty Quantification (UQ) is a relatively new
research area which describes the methods and
approaches used to supply quantitative descriptions of
the effects of uncertainty, variability and errors in
simulation problems and models. It is rapidly becoming
a field of increasing importance, with many real-world
applications within statistics, mathematics,
probability and engineering, but also within the
natural sciences. Literature on the topic has up until
now been largely based on polynomial chaos, which
raises difficulties when considering different types of
approximation and does not lead to a unified
presentation of the methods. Moreover, this description
does not consider either deterministic problems or
infinite dimensional ones. This book gives a unified,
practical and comprehensive presentation of the main
techniques used for the characterization of the effect
of uncertainty on numerical models and on their
exploitation in numerical problems. In particular,
applications to linear and nonlinear systems of
equations, differential equations, optimization and
reliability are presented. Applications of stochastic
methods to deal with deterministic numerical problems
are also discussed. Matlab? illustrates the
implementation of these methods and makes the book
suitable as a textbook and for self-study.",
acknowledgement = ack-nhfb,
subject = "Stochastic models; Uncertainty (Information theory);
MATHEMATICS / Applied; MATHEMATICS / Probability and
Statistics / General; Stochastic models.; Uncertainty
(Information theory); Stochastic partial differential
equations",
tableofcontents = "Introduction \\
1: Elements of Probability Theory and Stochastic
Processes \\
1.1. Notation \\
1.2. Numerical Characteristics of Finite Populations
\\
1.3. Matlab Implementation \\
1.4. Couples of Numerical Characteristics \\
1.5. Matlab Implementation \\
1.6. Hilbertian Properties of the Numerical
Characteristics \\
1.7. Measure and Probability \\
1.8. Construction of Measures \\
1.9. Measures, Probability and Integrals in Infinite
Dimensional Spaces \\
1.10. Random Variables \\
1.11. Hilbertian Properties of Random Variables \\
1.12. Sequences of Random Variables \\
1.13. Some Usual Distributions \\
1.14. Samples of Random Variables \\
1.15. Gaussian Samples \\
1.16. Stochastic Processes \\
1.17. Hilbertian Structure \\
1.18. Wiener Process \\
1.19. Ito Integrals \\
1.20. Ito Calculus \\
2: Maximum Entropy and Information \\
2.1. Construction of a Stochastic Model \\
2.2. The Principle of Maximum Entropy \\
2.3. Generating Samples of Random Variables, Random
Vectors and Stochastic Processes \\
2.4. Karhunen-Lo{\`e}ve Expansions and Numerical
Generation of Variates from Stochastic Processes 3:
Representation of Random Variables \\
3.1. Approximations Based on Hilbertian Properties \\
3.2. Approximations Based on Statistical Properties
(Moment Matching Method) \\
3.3. Interpolation-Based Approximations (Collocation)
\\
4: Linear Algebraic Equations Under Uncertainty \\
4.1. Representation of the Solution of Uncertain Linear
Systems \\
4.2. Representation of Eigenvalues and Eigenvectors of
Uncertain Matrices \\
4.3. Stochastic Methods for Deterministic Linear
Systems \\
5: Nonlinear Algebraic Equations Involving Random
Parameters 5.1. Nonlinear Systems of Algebraic
Equations \\
5.2. Numerical Solution of Noisy Deterministic Systems
of Nonlinear Equations \\
6: Differential Equations Under Uncertainty \\
6.1. The Case of Linear Differential Equations \\
6.2. The Case of Nonlinear Differential Equations \\
6.3. The Case of Partial Differential Equations \\
6.4. Reduction of Hamiltonian Systems \\
6.5. Local Solution of Deterministic Differential
Equations by Stochastic Simulation \\
6.6. Statistics of Dynamical Systems \\
7: Optimization Under Uncertainty 7.1. Representation
of the Solutions in Unconstrained Optimization \\
7.2. Stochastic Methods in Deterministic Continuous
Optimization \\
7.3. Population-Based Methods \\
7.4. Determination of Starting Points \\
8: Reliability-Based Optimization \\
8.1. The Model Situation \\
8.2. Reliability Index \\
8.3. FORM \\
8.4. The Bi-Level or Double-Loop Method \\
8.5. One-Level or Single-Loop Approach \\
8.6. Safety Factors \\
Bibliography \\
Index",
}
@Book{Temme:2015:AMI,
author = "Nico M. Temme",
title = "Asymptotic Methods for Integrals",
volume = "6",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xxii + 605",
year = "2015",
ISBN = "981-4612-15-4 (hardcover), 981-4612-16-2 (e-book)",
ISBN-13 = "978-981-4612-15-9 (hardcover), 978-981-4612-16-6
(e-book)",
MRclass = "41-02 (33Cxx 33E20 65D30)",
MRnumber = "3328507",
MRreviewer = "Jos{\'e} Luis L{\'o}pez",
bibdate = "Tue Feb 06 11:44:21 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Series in Analysis",
abstract = "This book gives introductory chapters on the classical
basic and standard methods for asymptotic analysis,
such as Watson's lemma, Laplace's method, the saddle
point and steepest descent methods, stationary phase
and Darboux's method. The methods, explained in great
detail, will obtain asymptotic approximations of the
well-known special functions of mathematical physics
and probability theory. After these introductory
chapters, the methods of uniform asymptotic analysis
are described in which several parameters have
influence on typical phenomena: turning points and
transition points, coinciding saddle and singularities.
In all these examples, the special functions are
indicated that describe the peculiar behavior of the
integrals. The text extensively covers the classical
methods with an emphasis on how to obtain expansions,
and how to use the results for numerical methods, in
particular for approximating special functions. In this
way, we work with a computational mind: how can we use
certain expansions in numerical analysis and in
computer programs, how can we compute coefficients, and
so on.",
acknowledgement = ack-nhfb,
shorttableofcontents = "Basic methods for integrals \\
Basic methods: examples for special functions \\
Other methods for integrals \\
Uniform methods for integrals \\
Uniform methods for Laplace-type integrals \\
Uniform examples for special functions \\
A class of cumulative distribution factors",
tableofcontents = "Preface / vii \\
Acknowledgments / ix \\
Part 1: Basic Methods for Integrals / 1 \\
1. Introduction / 3 \\
1.1 Symbols used in asymptotic estimates / 3 \\
1.2 Asymptotic expansions / 4 \\
1.3 A first example: Exponential integral / 5 \\
1.4 Generalized asymptotic expansions / 7 \\
1.5 Properties of asymptotic power series / 8 \\
1.6 Optimal truncation of asymptotic expansions / 10
\\
2. Expansions of Laplace-type integrals: Watson's lemma
/ 13 \\
2.1 Watson's lemma / 13 \\
2.1.1 Watson's lemma for extended sectors / 14 \\
2.1.2 More general forms of Watson's lemma / 16 \\
2.2 Watson's lemma for loop integrals / 16 \\
2.3 More general forms of Laplace-type integrals / 19
\\
2.3.1 Transformation to the standard form / 19 \\
2.4 How to compute the coefficients / 20 \\
2.4.1 Inversion method for computing the coefficients /
20 \\
2.4.2 Integrating by parts / 22 \\
2.4.3 Manipulating power series / 23 \\
2.4.4 Explicit forms of the coefficients in the
expansion / 25 \\
2.5 Other kernels / 26 \\
2.6 Exponentially improved asymptotic expansions / 27
\\
2.7 Singularities of the integrand / 29 \\
2.7.1 A pole near the endpoint / 29 \\
2.7.2 More general cases / 32 \\
3. The method of Laplace / 33 \\
3.1 A theorem for the general case / 33 \\
3.2 Constructing the expansion / 35 \\
3.2.1 Inversion method for computing the coefficients /
36 \\
3.3 Explicit forms of the coefficients in the expansion
/ 37 \\
3.4 The complementary error function / 38 \\
4. The saddle point method and paths of steepest
descent / 41 \\
4.1 The axis of the valley at the saddle point / 43 \\
4.2 Examples with simple exponentials / 43 \\
4.2.1 A first example / 43 \\
4.2.2 A cosine transform / 44 \\
4.3 Steepest descent paths not through a saddle point /
44 \\
4.3.1 A gamma function example / 45 \\
4.3.2 An integral related to the error function / 46
\\
4.4 An example with strong oscillations: A 100-digit
challenge / 48 \\
4.5 A Laplace inversion formula for $ \erfc z $ / 49
\\
4.6 A non-oscillatory integral for $ \erfc z $ , $ z
\in \mathbb{C} $ / 50 \\
4.7 The complex Airy function / 50 \\
4.8 A parabolic cylinder function / 53 \\
5. The Stokes phenomenon / 57 \\
5.1 The Airy function / 57 \\
5.2 The recent interest in the Stokes phenomenon / 58
\\
5.3 Exponentially small terms in the Airy expansions /
59 \\
5.4 Expansions in connection with the Stokes phenomenon
/ 60 \\
5.4.1 Applications to a Kummer function / 61 \\
Part 2: Basic Methods: Examples for Special Functions /
63 \\
6. The gamma function / 65 \\
6.1 $ \Gamma(z) $ by Laplace's method / 66 \\
6.1.1 Calculating the coefficients / 67 \\
6.1.2 Details on the transformation / 68 \\
6.2 $ 1 / \Gamma(z) $ by the saddle point method / 71
\\
6.2.1 Another integral representation of $ 1 /
\Gamma(z) $ / 72 \\
6.3 The logarithm of the gamma function / 72 \\
6.3.1 Estimations of the remainder / 73 \\
6.4 Expansions of $ \Gamma(z + a) $ and $ 1 / \Gamma(z
+ a) $ / 75 \\
6.5 The ratio of two gamma functions / 76 \\
6.5.1 A simple expansion / 77 \\
6.5.2 A more efficient expansion / 78 \\
6.6 A binomial coefficient / 80 \\
6.6.1 A uniform expansion of the binomial coefficient /
83 \\
6.7 Asymptotic expansion of a product of gamma
functions / 85 \\
6.8 Expansions of ratios of three gamma functions / 88
\\
7. Incomplete gamma functions / 91 \\
7.1 Integral representations / 91 \\
7.2 $ \Gamma(a, x) $ : Asymptotic expansion for $ x \gg
a $ / 92 \\
7.3 $ \gamma(a, x) $ : Asymptotic expansion for $ a > x
$ / 93 \\
7.3.1 Singularity of the integrand / 94 \\
7.3.2 More details on the transformation $ u = \phi(t)
$ / 96 \\
7.4 $ \Gamma(a, x) $ : Asymptotic expansion for $ x > a
$ / 97 \\
8. The Airy functions / 101 \\
8.1 Expansions of $ \Ai(z) $, $ \Bi(z) $ / 102 \\
8.1.1 Transforming the saddle point contour / 102 \\
8.2 Expansions of $ \Ai(-z) $, $ \Bi(-z) $ / 105 \\
8.3 Two simple ways to obtain the coefficients / 106
\\
8.4 A generalized form of the Airy function / 107 \\
9. Bessel functions: Large argument / 109 \\
9.1 The modified Bessel function $ K_\nu(z) $ / 109 \\
9.2 The ordinary Bessel functions / 110 \\
9.3 The modified Bessel function $ I_\nu(z) $ / 111
9.3.1 A compound expansion of $ I_\nu(z) $ / 111 9.4
Saddle point method for $ K_\nu(z) $ , $ z \in
\mathbb{C} $ / 113 \\
9.4.1 Integral representations from saddle point
analysis / 115 \\
9.4.2 Saddle point method for $ J_\nu(x) $ , $ x < \nu
$ / 116 \\
9.5 Debye-type expansions of the modified Bessel
functions / 117 \\
9.6 Modified Bessel functions of purely imaginary order
/ 119 \\
9.6.1 The monotonic case: $ x > \nu > 0 $ / 120 \\
9.6.2 The oscillatory case: $ \nu > x > 0 $ / 123 \\
9.7 A $ J $ -Bessel integral / 126 \\
10. Kummer functions / 129 \\
10.1 General properties / 129 \\
10.2 Asymptotic expansions for large $ z $ / 131 \\
10.3 Expansions for large $ a $ / 132 \\
10.3.1 Tricomi's function $ E_\nu(z) $ / 132 \\
10.3.2 Expansion of $ U(a, c, z) $ , $ a \to +\infty $
/ 133 \\
10.3.3 Expansion of $ _1F_1(a; c; z) $ , $ a \to
+\infty $ / 135 \\
10.3.4 Expansion of $ _1F_1(a; c; z) $ , $ a \to
-\infty $ / 137 \\
10.3.5 Expansion of $ U(a, c, z) $ , $ a \to -\infty $
/ 138 \\
10.3.6 Slater's results for large $ a $ / 140 \\
10.4 Expansions for large $ c $ / 142 \\
10.4.1 Expansion of $ _1F_1(a; c; z) $ , $ c \to
+\infty $ / 142 \\
10.4.2 Expansion of $ U(a, c, z) $ , $ c \to +\infty $
, $ z < c $ / 143 \\
10.4.3 Expansion of $ U(a, c, z) $ , $ c \to +\infty $
, $ z > e $ / 144 \\
10.4.4 Expansion of $ U(a, c, z) $ , $ c \to -\infty $
/ 145 \\
10.4.5 Expansion of $ _1F_1(a; c; z) $ , $ c \to
-\infty $ / 147 \\
10.5 Uniform expansions of the Kummer functions / 147
\\
11. Parabolic cylinder functions: Large argument / 149
\\
11.1 A few properties of the parabolic cylinder
functions / 149 \\
11.2 The function $ U(a, z) $ / 150 \\
11.3 The function $ U(a, -z) $ / 152 \\
11.4 The function $ V(a, z) $ / 153 \\
11.5 Expansions of the derivatives / 154 \\
12. The Gauss hypergeometric function / 155 \\
12.1 Large values of $ c $ / 156 \\
12.1.1 Large positive $ c $ ; $ |z| < z_0 $ / 156 \\
12.1.2 Large negative $ c $ ; $ |z| < z_0 $ / 157 \\
12.1.3 Large positive $ c $ ; $ |z| > z_0 $ / 158 \\
12.1.4 Large negative $ c $ ; $ |z| > z_0 $ / 158 \\
12.2 Large values of $ b $ / 158 \\
12.2.1 Large negative $ b $ ; $ |z| > z_0 $ / 159 \\
12.2.2 Large $ b $ , $ |z| < z_0 $ / 159 \\
12.3 Other large parameter cases / 160 \\
12.3.1 Jacobi polynomials of large degree / 161 \\
12.3.2 An example of the case $ _2F_1(a, b - \lambda; c
+ \lambda; z) $ / 163 \\
13. Examples of $ _3F_2 $ -polynomials / 167 \\
13.1 A $ _3F_2 $ associated with the
Catalan--Larcombe--French sequence / 167 \\
13.1.1 Transformations / 169 \\
13.1.2 Asymptotic analysis / 170 \\
13.1.3 Asymptotic expansion / 172 \\
13.1.4 An alternative method / 173 \\
13.2 An integral of Laguerre polynomials / 175 \\
13.2.1 A first approach / 176 \\
13.2.2 A generating function approach / 178 \\
Part 3: Other Methods for Integrals / 181 \\
14. The method of stationary phase / 183 \\
14.1 Critical points / 183 \\
14.2 Integrating by parts: No stationary points / 184
\\
14.3 Three critical points: A formal approach / 185 \\
14.4 On the use of neutralizes / 186 \\
14.5 How to avoid neutralizes? / 188 \\
14.5.1 A few details about the Fresnel integral / 190
\\
14.6 Algebraic singularities at both endpoints:
Erdelyi's example / 191 \\
14.6.1 Application: A conical function / 192 \\
14.6.2 Avoiding neutralizes in Erdelyi's example / 193
\\
14.7 Transformation to standard form / 194 \\
14.8 General order stationary points / 196 \\
14.8.1 Integrating by parts / 196 \\
14.9 The method fails: Examples / 197 \\
14.9.1 The Airy function / 198 \\
14.9.2 A more complicated example / 198 \\
15. Coefficients of a power series. Darboux's method /
203 \\
15.1 A first example: A binomial coefficient / 204 \\
15.2 Legendre polynomials of large degree / 205 \\
15.2.1 A paradox in asymptotics / 207 \\
15.3 Gegenbauer polynomials of large degree / 208 \\
15.4 Jacobi polynomials of large degree / 209 \\
15.5 Laguerre polynomials of large degree / 209 \\
15.6 Generalized Bernoulli polynomials $ B_n^{(\mu)}(z)
$ / 210 \\
15.6.1 Asymptotic expansions for large degree / 211 \\
15.6.2 An alternative expansion / 213 \\
15.7 Generalized Euler polynomials $ E_n^{(\mu)}(z) $ /
215 \\
15.7.1 Asymptotic expansions for large degree / 215 \\
15.7.2 An alternative expansion / 216 \\
15.8 Coefficients of expansions of the $ _1F_1 $
-function / 218 \\
15.8.1 Coefficients of Tricomi's expansion / 218 \\
15.8.2 Coefficients of Buchholz's expansion / 221 \\
16. Mellin--Barnes integrals and Mellin convolution
integrals / 225 \\
16.1 Mellin--Barnes integrals / 226 \\
16.2 Mellin convolution integrals / 228 \\
16.3 Error bounds / 230 \\
17. Alternative expansions of Laplace-type integrals /
231 \\
17.1 Hadamard-type expansions / 231 \\
17.2 An expansion in terms of Kummer functions / 233
\\
17.3 An expansion in terms of factorial series / 234
\\
17.4 The Franklin--Friedman expansion / 237 \\
18. Two-point Taylor expansions / 241 \\
18.1 The expansions / 242 \\
18.2 An alternative form of the expansion / 243 \\
18.3 Explicit forms of the coefficients / 244 \\
18.4 Manipulations with two-point Taylor expansions /
245 \\
19. Hermite polynomials as limits of other classical
orthogonal polynomials / 249 \\
19.1 Limits between orthogonal polynomials / 249 \\
19.2 The Askey scheme of orthogonal polynomials / 251
\\
19.3 Asymptotic representations / 251 \\
19.4 Gegenbauer polynomials / 253 \\
19.5 Laguerre polynomials / 254 \\
19.6 Generalized Bessel polynomials / 255 \\
19.7 Meixner--Pollaczek polynomials into Laguerre
polynomials / 257 \\
Part 4: Uniform Methods for Integrals / 259 \\
20. An overview of standard forms / 261 \\
20.1 Comments on the table / 263 \\
21. A saddle point near a pole / 267 \\
21.1 A saddle point near a pole: Van der Waerden's
method / 267 \\
21.2 An alternative expansion / 269 \\
21.3 An example from De Bruijn / 270 \\
21.4 A pole near a double saddle point / 271 \\
21.5 A singular perturbation problem and $ K $ -Bessel
integrals / 272 \\
21.5.1 A Bessel $ K_0 $ integral / 272 \\
21.5.2 A similar Bessel $ K_1 $ integral / 274 \\
21.5.3 A singular perturbation problem / 275 \\
21.6 A double integral with poles near saddle points /
277 \\
21.6.1 Application to a singular perturbation problem /
278 \\
21.7 The Fermi--Dirac integral / 281 \\
22. Saddle point near algebraic singularity / 285 \\
22.1 A saddle point near an endpoint of the interval /
285 \\
22.2 The Bleistein expansion / 286 \\
22.3 Extending the role of the parameter /3 / 289 \\
22.4 Contour integrals / 291 \\
22.5 Kummer functions in terms of parabolic cylinder
functions / 292 \\
22.5.1 Uniform expansion of $ U(a, c, z) $ , $ c \to
+\infty $ / 293 \\
22.5.2 Uniform expansion of $ _1F_1(a; c; z) $ , $ c
\to +\infty $ / 296 \\
23. Two coalescing saddle points: Airy-type expansions
/ 299 \\
23.1 The standard form / 299 \\
23.2 An integration by parts method / 300 \\
23.3 How to compute the coefficients / 302 \\
23.4 An Airy-type expansion of the Hermite polynomial /
305 \\
23.4.1 The cubic transformation / 306 \\
23.4.2 Details on the coefficients / 308 \\
23.5 An Airy-type expansion of the Bessel function $
J_\nu(z) $ / 309 \\
23.6 A semi-infinite interval: Incomplete Scorer
function / 313 \\
23.6.1 A singular perturbation problem inside a circle
/ 315 \\
24. Hermite-type expansions of integrals / 319 \\
24.1 An expansion in terms of Hermite polynomials / 320
\\
24.1.1 Cauchy-type integrals for the coefficients / 321
\\
24.2 Gegenbauer polynomials / 323 \\
24.2.1 Preliminary steps / 324 \\
24.2.2 A first approximation / 325 \\
24.2.3 Transformation to the standard form / 326 \\
24.2.4 Special cases of the expansion / 331 \\
24.2.5 Approximating the zeros / 332 \\
24.2.6 The relativistic Hermite polynomials / 333 \\
24.3 Tricomi--Carlitz polynomials / 333 \\
24.3.1 Contour integral and saddle points / 335 \\
24.3.2 A first approximation / 337 \\
24.3.3 Transformation to the standard form / 337 \\
24.3.4 Approximating the zeros / 339 \\
24.4 More examples / 340 \\
Part 5: Uniform Methods for Laplace-Type Integrals /
341 \\
25. The vanishing saddle point / 343 \\
25.1 Expanding at the saddle point / 344 \\
25.2 An integration by parts method / 346 \\
25.2.1 Representing coefficients as a Cauchy-type
integral / 347 \\
25.3 Expansions for loop integrals / 348 \\
25.4 Rummer functions / 350 \\
25.5 Generalized zeta function / 350 \\
25.6 Transforming to the standard form / 351 \\
25.6.1 The ratio of two gamma functions / 352 \\
25.6.2 Parabolic cylinder functions / 354 \\
26. A moving endpoint: Incomplete Laplace integrals /
355 \\
26.1 The standard form / 355 \\
26.2 Constructing the expansion / 356 \\
26.2.1 The complementary function / 357 \\
26.3 Application to the incomplete beta function / 358
\\
26.3.1 Expansions of the coefficients / 361 \\
26.4 A corresponding loop integral / 362 \\
26.4.1 Application to the incomplete beta function /
363 \\
27. An essential singularity: Bessel-type expansions /
365 \\
27.1 Expansions in terms of modified Bessel functions /
365 \\
27.2 A corresponding loop integral / 368 \\
27.3 Expansion at the internal saddle point / 368 \\
27.4 Application to Kummer functions / 369 \\
27.4.1 Expansion of $ U(a, c, z) $ , $ a \to +\infty $
, $ z > 0 $ / 369 \\
27.4.2 Auxiliary expansions and further details / 372
\\
27.4.3 Expansion of $ _1F_1(a: c; z) $ , $ a \to
+\infty $ , $ z > 0 $ / 374 \\
27.4.4 Expansion of $ _1F_1(a; c: z) $ , $ a \to
-\infty $ , $ 0 < z < -4a $ / 375 \\
27.4.5 Expansion of $ U(a, c, z) $ , $ a \to -\infty $
, $ 0 < z < -4a $ / 377 \\
27.5 A second uniformity parameter / 378 \\
27.5.1 Expansion of $ U(a, c, z) $ , $ a \to \infty $ ,
$ z > 0 $ , $ c < 1 $ / 380 \\
27.5.2 Expansion of $ _1F_1(a; c; z), $ a \to \infty $
, $ z > 0 $ , $ c > 1 $ / 381 \\
28. Expansions in terms of Kummer functions / 383 \\
28.1 Approximation in terms of the Kummer J7-function /
383 \\
28.1.1 Constructing the expansions / 384 \\
28.1.2 Expansion for the loop integral / 387 \\
28.2 The $ _2F_1 $ function, large $ c $ , in terms of
$ U $ / 387 \\
28.2.1 Legendre polynomials: Uniform expansions / 388
\\
28.3 The $ _2F_1 $ -function, large $ b $ : in terms of
$ _1F_1 $ / 389 \\
28.3.1 Using a real integral / 390 \\
28.3.2 Using a loop integral / 394 \\
28.4 Jacobi polynomials of large degree: Laguerre-type
expansion / 394 \\
28.4.1 Laguerre-type expansion for large values of /3 /
398 \\
28.5 Expansion of a Dirichlet-type integral / 401 \\
Part 6: Uniform Examples for Special Functions / 403
\\
29. Legendre functions / 405 \\
29.1 Expansions of $ P_\nu^\mu(z) $ , $ Q_\nu^\mu(z) $
; $ \nu \to \infty $ , $ z \geq 1 $ / 406 \\
29.1.1 Expansions for $ z > z_0 > 1 $ / 400 \\
29.1.2 Expansion in terms of modified Bessel functions
/ 407 \\
29.1.3 Expansions of $ P_\nu^\mu(z) $ and $
Q_\nu^\mu(z) $ in terms of Bessel functions / 411 \\
29.2 Expansions of $ P_\nu^\mu(z) $ , $ Q_\nu^\mu(z) $
; $ p \to \infty $ , $ z > 1 $ / 412 \\
29.2.1 Expansions for bounded $ z $ / 412 \\
29.2.2 Expansions in terms of modified Bessel functions
/ 412 \\
29.2.3 Expansions of $ P_\nu^\mu(z) $ and $
Q_\nu^\mu(z) $ / 413 \\
29.3 Integrals with nearly coincident branch points /
414 \\
29.3.1 Ursell's expansions of Legendre functions / 415
\\
29.3.2 Coefficients of the expansion / 416 \\
29.3.3 An alternative expansion of $ P_n^m(\cosh z) $ /
417 \\
29.3.4 A related integral with nearly coincident branch
points / 418 \\
29.4 Toroidal harmonics and conical functions / 418 \\
30. Parabolic cylinder functions: Large parameter / 419
\\
30.1 Notation for uniform asymptotic expansions / 419
\\
30.2 The case $ a < 0 $ / 421 \\
30.2.1 The case $ z > 2\sqrt{-a} $ : $ -a + z \to
\infty $ / 421 \\
30.2.2 The case $ z < -2\sqrt{-a} $ : $ -a - z \to
\infty $ / 422 \\
30.2.3 The case -2\sqrt{-a} < z < 2\sqrt{-a} / 423 \\
30.3 The case $ a > 0 $ / 424 \\
30.3.1 The case $ z > 0 $ , $ a + z \to \infty $ / 425
\\
30.3.2 The case $ z < 0 $ , $ a - z \to \infty $ / 425
\\
30.4 Expansions from integral representations / 426 \\
30.4.1 The case $ a > 0 $ , $ z > 0 $ ; $ a + z \to
\infty $ / 426 \\
30.4.2 The case $ a > 0 $ , $ z < 0 $ ; $ a - z \to
\infty $ / 428 \\
30.4.3 The case $ a < 0 $ , $ |z| > 2\sqrt{-a} $ ; $ -a
+ |z| \to \infty $ / 429 \\
30.5 Airy-type expansions / 430 \\
31. Coulomb wave functions / 433 \\
31.1 Contour integrals for Coulomb functions / 434 \\
31.2 Expansions for $ \rho \to \infty $ and bounded $
\eta $ / / 435 \\
31.3 Expansions for $ \eta \to \infty $ and bounded $
\rho $ / 437 \\
31.4 Expansions for $ \eta \to -\infty $ and bounded $
\rho $ / 439 \\
31.5 Expansions for $ \eta \to -\infty and $ \rho \geq
\rho_0 > 0 $ / 440 \\
31.6 Expansions for $ \eta \to -\infty $ and $ \rho
\geq 0 $ / 442 \\
31.7 Expansions for $ \eta $ , $ \rho \to \infty $ ;
Airy-type expansions / 444 \\
32. Laguerre polynomials: Uniform expansions / 449 \\
32.1 An expansion for bounded $ z $ and $ a $ / 449 \\
32.2 An expansion for bounded $ z $ ; $ a $ depends on
$ n $ / 451 \\
32.3 Expansions for bounded $ a $ ; $ z $ depends on $
n $ / 454 \\
32.3.1 An expansion in terms of Airy functions / 455
\\
32.3.2 An expansion in terms of Bessel functions / 456
\\
32.4 An expansion in terms of Hermite polynomials;
large $ a $ / 458 \\
32.4.1 A first approximation / 459 \\
32.4.2 Transformation to the standard form / 460 \\
32.4.3 Approximating the zeros / 462 \\
33. Generalized Bessel polynomials / 465 \\
33.1 Relations to Bessel and Kummer functions / 466 \\
33.2 An expansion in terms of Laguerre polynomials /
467 \\
33.3 Expansions in terms of elementary functions / 470
\\
33.3.1 The case $ |\ph z| < \pi/2 $ / 470 \\
33.3.2 The case $ |\ph(-z)| < \pi/2 $ / 471 \\
33.3.3 Integral representations / 472 \\
33.3.4 Construction of the expansions / 472 \\
33.4 Expansions in terms of modified Bessel functions /
476 \\
33.4.1 Construction of the expansion / 476 \\
34. Stirling numbers / 479 \\
34.1 Definitions and integral representations / 479 \\
34.2 Stirling number of the second kind / 481 \\
34.2.1 Higher-order approximations / 483 \\
34.2.2 About the positive saddle point / 486 \\
34.2.3 About the quantity $ A $ / 487 \\
34.3 Stirling numbers of the first kind / 488 \\
35. Asymptotics of the integral $ \int_0^1 \cos(b x + a
/ x) \, dx $ / 491 \\
35.1 The case $ b < a $ / 491 \\
35.2 The case $ a = b $ / 493 \\
35.3 The case $ b > a $ / 494 \\
35.3.1 The contribution from $ \mathcal{P}_1 $ / 495
\\
35.3.2 The contribution from $ \mathcal{P}_2 $ / 496
\\
35.4 A Fresnel-type expansion / 497 \\
Part 7: A Class of Cumulative Distribution Functions /
499 \\
36. Expansions of a class of cumulative distribution
functions / 501 \\
36.1 Cumulative distribution functions: A standard form
/ 501 \\
36.2 An incomplete normal distribution function / 505
\\
36.3 The Sievert integral / 506 \\
36.4 The Pearson type IV distribution / 507 \\
36.5 The Von Mises distribution / 509 \\
36.5.1 An expansion near the lower endpoint of
integration / 511 \\
37. Incomplete gamma functions: Uniform expansions /
513 \\
37.1 Using the standard integral representations / 513
\\
37.2 Representations by contour integrals / 514 \\
37.2.1 Constructing the expansions / 516 \\
37.2.2 Details on the coefficients / 518 \\
37.2.3 Relations to the coefficients of earlier
expansions / 520 \\
37.3 Incomplete gamma functions, negative parameters /
520 \\
37.3.1 Expansions near the transition point / 522 \\
37.3.2 A real expansion of 7*(-a, -z) / 524 \\
38. Incomplete beta function / 525 \\
38.1 A power series expansion for large p / 526 \\
38.2 A uniform expansion for large p / 526 \\
38.3 The nearly symmetric case / 527 \\
38.4 The general error function case / 529 \\
39. Non-central chi-square, Marcum functions / 531 \\
39.1 Properties of the Marcum functions / 532 \\
39.2 More integral representations / 533 \\
39.3 Asymptotic expansion; $ \mu $ fixed, $ \xi $ large
/ 535 \\
39.4 Asymptotic expansion; $ \xi + \mu $ large / 537
\\
39.5 An expansion in terms of the incomplete gamma
function / 540 \\
39.6 Comparison of the expansions numerically / 543 \\
40. A weighted sum of exponentials / 545 \\
40.1 An integral representation / 546 \\
40.2 Saddle point analysis / 547 \\
40.3 Details on the coefficients / 548 \\
40.4 Auxiliary expansions / 550 \\
40.5 Numerical verification / 551 \\
41. A generalized incomplete gamma function / 553 \\
41.1 An expansion in terms of incomplete gamma
functions / 554 \\
41.2 An expansion in terms of Laguerre polynomials /
554 \\
41.3 An expansion in terms of Kummer functions / 555
\\
41.4 An expansion in terms of the error function / 555
\\
42. Asymptotic inversion of cumulative distribution
functions / 559 \\
42.1 The asymptotic inversion method / 559 \\
42.2 Asymptotic inversion of the gamma distribution /
561 \\
42.2.1 Numerical verification / 563 \\
42.2.2 Other asymptotic inversion methods / 564 \\
42.2.3 Asymptotics of the zeros of $ \Gamma(a, z) $ /
565 \\
42.3 Asymptotic inversion of the incomplete beta
function / 567 \\
42.3.1 Inverting by using the error function / 568 \\
42.3.2 Inverting by using the incomplete gamma function
/ 569 \\
42.3.3 Numerical verification / 572 \\
42.4 The hyperbolic cumulative distribution / 573 \\
42.4.1 Numerical verification / 574 \\
42.5 The Marcum functions / 575 \\
42.5.1 Asymptotic inversion / 576 \\
42.5.2 Asymptotic inversion with respect to $ x $ / 576
\\
42.5.3 Asymptotic inversion with respect to $ y $ / 579
\\
Bibliography / 583 \\
Index / 597",
}
@Book{Gautschi:2016:OPM,
author = "Walter Gautschi",
title = "Orthogonal polynomials in {MATLAB}: exercises and
solutions",
volume = "26",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "ix + 335",
year = "2016",
ISBN = "1-61197-429-1 (paperback), 1-61197-430-5",
ISBN-13 = "978-1-61197-429-4 (paperback), 978-1-61197-430-0",
LCCN = "QA404.5 .G3564 2016",
bibdate = "Thu Jan 9 19:03:59 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Software, environments, and tools",
abstract = "Techniques for generating orthogonal polynomials
numerically have appeared only recently, within the
last 30 or so years. \booktitle{Orthogonal Polynomials
in MATLAB: Exercises and Solutions} describes these
techniques and related applications, all supported by
MATLAB programs, and presents them in a unique format
of exercises and solutions designed by the author to
stimulate participation. Important computational
problems in the physical sciences are included as
models for readers to solve their own problems.",
acknowledgement = ack-nhfb,
subject = "MATLAB; MATLAB; Orthogonal polynomials; Problems,
exercises, etc; Data processing; Orthogonal
polynomials; Algorithmus; Orthogonale Polynome;
Approximation; MATLAB",
tableofcontents = "Preface \\
1. A guide to the software packages OPQ and SOPQ \\
2. Answers to exercises on orthogonal polynomials \\
3. Answers to exercises on Sobolev orthogonal
polynomials \\
4. Answers to exercises on quadrature \\
5. Answers to exercises on approximation \\
A. The software package OPQ (Orthogonal Polynomials and
Quadrature) \\
B The software package SOPQ (Symbolic Orthogonal
Polynomials and Quadrature)",
}
@Book{Green:2016:CMC,
author = "Dan Green",
title = "Cosmology with {MATLAB}: with companion media pack",
publisher = "World Scientific Publishing Co. Pte. Ltd.",
address = "Singapore",
pages = "xi + 250",
year = "2016",
ISBN = "981-310-839-8 (hardcover), 981-310-840-1 (paperback)",
ISBN-13 = "978-981-310-839-4 (hardcover), 978-981-310-840-0
(paperback)",
LCCN = "QB981 .G74 2016",
bibdate = "Thu Nov 30 10:51:08 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/contempphys.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
abstract = "This volume makes explicit use of the synergy between
cosmology and high energy physics, for example,
supersymmetry and dark matter, or nucleosynthesis and
the baryon-to-photon ratio. In particular the exciting
possible connection between the recently discovered
Higgs scalar and the scalar field responsible for
inflation is explored. The recent great advances in the
accuracy of the basic cosmological parameters is
exploited in that no free scale parameters such as h
appear, rather the basic calculations are done
numerically using all sources of energy density
simultaneously. Scripts are provided that allow the
reader to calculate exact results for the basic
parameters. Throughout MATLAB tools such as symbolic
math, numerical solutions, plots and ``movies'' of the
dynamical evolution of systems are used. The GUI
package is also shown as an example of the real time
manipulation of parameters which is available to the
reader. All the MATLAB scripts are made available to
the reader to explore examples of the uses of the suite
of tools which are available. Indeed, readers should be
able to engage in a command line ``dialogue'' or go on
to edit the scripts and write their own versions.",
acknowledgement = ack-nhfb,
author-dates = "1943--",
subject = "Cosmology; Data processing; Data processing",
tableofcontents = "1. Introduction \\
2. From the Big Bang \\
3. Inflation and Big Bang issues \\
4. Fluctuations to Perturbations \\
5. The Cosmic Microwave background \\
6. Large Scale Structure \\
7. The Higgs Boson and Inflation \\
Appendix A: Matlab tools \\
Appendix B: Power law, RD or MD Formulae \\
Appendix C: Symbol and Acronym Tables \\
Appendix D: MATLAB Script (with Companion Media Pack)",
}
@Book{Kneusel:2016:NC,
author = "Ronald T. Kneusel",
title = "Numbers and Computers",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xi + 231",
year = "2016",
ISBN = "3-319-35940-1 (softcover), 3-319-17260-3 (e-book)",
ISBN-13 = "978-3-319-35940-3 (softcover), 978-3-319-17260-6
(e-book)",
LCCN = "QA241 .K54 2016",
bibdate = "Tue Aug 22 05:53:26 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
abstract = "This is a book about numbers and how those numbers are
represented in and operated on by computers. It is
crucial that developers understand this area because
the numerical operations allowed by computers, and the
limitations of those operations, especially in the area
of floating point math, affect virtually everything
people try to do with computers. This book aims to fill
this gap by exploring, in sufficient but not
overwhelming detail, just what it is that computers do
with numbers. Divided into two parts, the first deals
with standard representations of integers and floating
point numbers, while the second details several other
number representations. Each chapter ends with
exercises to review the key points. Topics covered
include interval arithmetic, fixed-point numbers,
floating point numbers, big integers and rational
arithmetic. This book is for anyone who develops
software including software engineering, scientists,
computer science students, engineering students and
anyone who programs for fun.",
acknowledgement = ack-nhfb,
subject = "Number theory; Numerals; Numeration; Computer science;
Mathematics",
tableofcontents = "Number Systems \\
Integers \\
Floating Point \\
Big Integers and Rational Arithmetic \\
Fixed-Point Numbers \\
Decimal Floating Point \\
Interval Arithmetic",
}
@Book{Muller:2016:EFA,
author = "Jean-Michel Muller",
title = "Elementary Functions: Algorithms and Implementation",
publisher = pub-BIRKHAUSER-BOSTON,
address = pub-BIRKHAUSER-BOSTON:adr,
edition = "Third",
pages = "xxv + 283",
year = "2016",
DOI = "https://doi.org/10.1007/978-1-4899-7983-4",
ISBN = "1-4899-7981-6 (print), 1-4899-7983-2 (e-book)",
ISBN-13 = "978-1-4899-7981-0 (print), 978-1-4899-7983-4
(e-book)",
LCCN = "QA331 .M866 2016",
bibdate = "Sun Dec 04 15:12:36 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
abstract = "This textbook presents the concepts and tools
necessary to understand, build, and implement
algorithms for computing elementary functions (e.g.,
logarithms, exponentials, and the trigonometric
functions). Both hardware- and software-oriented
algorithms are included, along with issues related to
accurate floating-point implementation. This third
edition has been updated and expanded to incorporate
the most recent advances in the field, new elementary
function algorithms, and function software. After a
preliminary chapter that briefly introduces some
fundamental concepts of computer arithmetic, such as
floating-point arithmetic and redundant number systems,
the text is divided into three main parts. Part I
considers the computation of elementary functions using
algorithms based on polynomial or rational
approximations and using table-based methods; the final
chapter in this section deals with basic principles of
multiple-precision arithmetic. Part II is devoted to a
presentation of shift-and-add algorithms
(hardware-oriented algorithms that use additions and
shifts only). Issues related to accuracy, including
range reduction, preservation of monotonicity, and
correct rounding, as well as some examples of
implementation are explored in Part III. Numerous
examples of command lines and full programs are
provided throughout for various software packages,
including Maple, Sollya, and Gappa. New to this edition
are an in-depth overview of the IEEE-754-2008 standard
for floating-point arithmetic; a section on using
double- and triple-word numbers; a presentation of new
tools for designing accurate function software; and a
section on the Toom--Cook family of multiplication
algorithms. The techniques presented in this book will
be of interest to implementors of elementary function
libraries or circuits and programmers of numerical
applications. Additionally, graduate and advanced
undergraduate students, professionals, and researchers
in scientific computing, numerical analysis, software
engineering, and computer engineering will find this a
useful reference and resource.",
acknowledgement = ack-nhfb,
subject = "Functions; Data processing; Algorithms",
tableofcontents = "Introduction \\
Introduction to Computer Arithmetic \\
Part I: Algorithms Based on Polynomial Approximation
and/or Table Lookup, Multiple-Precision Evaluation of
Functions \\
The Classical Theory of Polynomial or Rational
Approximations \\
Polynomial Approximations with Special Constraints \\
Polynomial Evaluation \\
Table-Based Methods \\
Multiple-Precision Evaluation of Functions \\
Part II: Shift-and-Add Algorithms \\
Introduction to Shift-and-Add Algorithms \\
The CORDIC Algorithm \\
Some Other Shift-and-Add Algorithms \\
Part III: Range Reduction, Final Rounding, and
Exceptions \\
Range Reduction \\
Final Rounding \\
Miscellaneous \\
Examples of Implementation \\
References \\
Index",
}
@Book{Romisch:2016:MAM,
author = "Werner R{\"o}misch and Thomas Zeugmann",
title = "Mathematical Analysis and the Mathematics of
Computation",
publisher = "Springer",
address = "Cham, Switzerland",
pages = "xxiii + 704",
year = "2016",
DOI = "https://doi.org/10.1007/978-3-319-42755-3",
ISBN = "3-319-42753-9 (hardcover), 3-319-42755-5 (e-book)",
ISBN-13 = "978-3-319-42753-9 (hardcover), 978-3-319-42755-3
(e-book)",
MRclass = "26-01 (34-01 41-01 65Jxx)",
MRnumber = "3524911",
MRreviewer = "Sorin Gheorghe Gal",
bibdate = "Sat Feb 2 16:19:35 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/z/zeugmann-thomas-u.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
URL = "http://link.springer.com/10.1007/978-3-319-42755-3",
abstract = "This book is a comprehensive, unifying introduction to
the field of mathematical analysis and the mathematics
of computing. It develops the relevant theory at a
modern level and it directly relates modern
mathematical ideas to their diverse applications. The
authors develop the whole theory. Starting with a
simple axiom system for the real numbers, they then lay
the foundations, developing the theory, exemplifying
where it's applicable, in turn motivating further
development of the theory. They progress from sets,
structures, and numbers to metric spaces, continuous
functions in metric spaces, linear normed spaces and
linear mappings; and then differential calculus and its
applications, the integral calculus, the gamma
function, and linear integral operators. They then
present important aspects of approximation theory,
including numerical integration. The remaining parts of
the book are devoted to ordinary differential
equations, the discretization of operator equations,
and numerical solutions of ordinary differential
equations. This textbook contains many exercises of
varying degrees of difficulty, suitable for self-study,
and at the end of each chapter the authors present more
advanced problems that shed light on interesting
features, suitable for classroom seminars or study
groups. It will be valuable for undergraduate and
graduate students in mathematics, computer science, and
related fields such as engineering. This is a rich
field that has experienced enormous development in
recent decades, and the book will also act as a
reference for graduate students and practitioners who
require a deeper understanding of the methodologies,
techniques, and foundations.",
acknowledgement = ack-nhfb,
subject = "Mathematical analysis; Computer science; Mathematics;
Mathematics.; Mathematical analysis.",
tableofcontents = "Sets, Structures, Numbers \\
Metric Spaces \\
Continuous Functions in Metric Spaces \\
Linear Normed Spaces, Linear Operators \\
The Differential Calculus \\
Applications of the Differential Calculus \\
The Integral Calculus \\
Linear Integral Operators \\
Inner Product Spaces \\
Approximative Representation of Functions \\
Ordinary Differential Equations \\
Discretization of Operator Equations \\
Numerical Solution of Ordinary Differential Equations",
}
@Book{Beebe:2017:MFC,
author = "Nelson H. F. Beebe",
title = "The Mathematical-Function Computation Handbook:
Programming Using the {MathCW} Portable Software
Library",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxxvi + 1114",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-64110-2",
ISBN = "3-319-64109-3 (hardcover), 3-319-64110-7 (e-book)",
ISBN-13 = "978-3-319-64109-6 (hardcover), 978-3-319-64110-2
(e-book)",
LCCN = "QA75.5-76.95",
bibdate = "Sat Jul 15 19:34:43 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/mupad.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
https://www.math.utah.edu/pub/tex/bib/redbooks.bib;
https://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib",
URL = "http://www.springer.com/us/book/9783319641096",
acknowledgement = ack-nhfb,
ORCID-numbers = "Beebe, Nelson H. F./0000-0001-7281-4263",
tableofcontents = "List of figures / xxv \\
List of tables / xxxi \\
Quick start / xxxv \\
1: Introduction / 1 \\
1.1: Programming conventions / 2 \\
1.2: Naming conventions / 4 \\
1.3: Library contributions and coverage / 5 \\
1.4: Summary / 6 \\
2: Iterative solutions and other tools / 7 \\
2.1: Polynomials and Taylor series / 7 \\
2.2: First-order Taylor series approximation / 8 \\
2.3: Second-order Taylor series approximation / 9 \\
2.4: Another second-order Taylor series approximation /
9 \\
2.5: Convergence of second-order methods / 10 \\
2.6: Taylor series for elementary functions / 10 \\
2.7: Continued fractions / 12 \\
2.8: Summation of continued fractions / 17 \\
2.9: Asymptotic expansions / 19 \\
2.10: Series inversion / 20 \\
2.11: Summary / 22 \\
3: Polynomial approximations / 23 \\
3.1: Computation of odd series / 23 \\
3.2: Computation of even series / 25 \\
3.3: Computation of general series / 25 \\
3.4: Limitations of Cody\slash Waite polynomials / 28
\\
3.5: Polynomial fits with Maple / 32 \\
3.6: Polynomial fits with Mathematica / 33 \\
3.7: Exact polynomial coefficients / 42 \\
3.8: Cody\slash Waite rational polynomials / 43 \\
3.9: Chebyshev polynomial economization / 43 \\
3.10: Evaluating Chebyshev polynomials / 48 \\
3.11: Error compensation in Chebyshev fits / 50 \\
3.12: Improving Chebyshev fits / 51 \\
3.13: Chebyshev fits in rational form / 52 \\
3.14: Chebyshev fits with Mathematica / 56 \\
3.15: Chebyshev fits for function representation / 57
\\
3.16: Extending the library / 57 \\
3.17: Summary and further reading / 58 \\
4: Implementation issues / 61 \\
4.1: Error magnification / 61 \\
4.2: Machine representation and machine epsilon / 62
\\
4.3: IEEE 754 arithmetic / 63 \\
4.4: Evaluation order in C / 64 \\
4.5: The {\tt volatile} type qualifier / 65 \\
4.6: Rounding in floating-point arithmetic / 66 \\
4.7: Signed zero / 69 \\
4.8: Floating-point zero divide / 70 \\
4.9: Floating-point overflow / 71 \\
4.10: Integer overflow / 72 \\
4.11: Floating-point underflow / 77 \\
4.12: Subnormal numbers / 78 \\
4.13: Floating-point inexact operation / 79 \\
4.14: Floating-point invalid operation / 79 \\
4.15: Remarks on NaN tests / 80 \\
4.16: Ulps --- units in the last place / 81 \\
4.17: Fused multiply-add / 85 \\
4.18: Fused multiply-add and polynomials / 88 \\
4.19: Significance loss / 89 \\
4.20: Error handling and reporting / 89 \\
4.21: Interpreting error codes / 93 \\
4.22: C99 changes to error reporting / 94 \\
4.23: Error reporting with threads / 95 \\
4.24: Comments on error reporting / 95 \\
4.25: Testing function implementations / 96 \\
4.26: Extended data types on Hewlett--Packard HP-UX
IA-64 / 100 \\
4.27: Extensions for decimal arithmetic / 101 \\
4.28: Further reading / 103 \\
4.29: Summary / 104 \\
5: The floating-point environment / 105 \\
5.1: IEEE 754 and programming languages / 105 \\
5.2: IEEE 754 and the mathcw library / 106 \\
5.3: Exceptions and traps / 106 \\
5.4: Access to exception flags and rounding control /
107 \\
5.5: The environment access pragma / 110 \\
5.6: Implementation of exception-flag and
rounding-control access / 110 \\
5.7: Using exception flags: simple cases / 112 \\
5.8: Using rounding control / 115 \\
5.9: Additional exception flag access / 116 \\
5.10: Using exception flags: complex case / 120 \\
5.11: Access to precision control / 123 \\
5.12: Using precision control / 126 \\
5.13: Summary / 127 \\
6: Converting floating-point values to integers / 129
\\
6.1: Integer conversion in programming languages / 129
\\
6.2: Programming issues for conversions to integers /
130 \\
6.3: Hardware out-of-range conversions / 131 \\
6.4: Rounding modes and integer conversions / 132 \\
6.5: Extracting integral and fractional parts / 132 \\
6.6: Truncation functions / 135 \\
6.7: Ceiling and floor functions / 136 \\
6.8: Floating-point rounding functions with fixed
rounding / 137 \\
6.9: Floating-point rounding functions: current
rounding / 138 \\
6.10: Floating-point rounding functions without {\em
inexact\/} exception / 139 \\
6.11: Integer rounding functions with fixed rounding /
140 \\
6.12: Integer rounding functions with current rounding
/ 142 \\
6.13: Remainder / 143 \\
6.14: Why the remainder functions are hard / 144 \\
6.15: Computing {\tt fmod} / 146 \\
6.16: Computing {\tt remainder} / 148 \\
6.17: Computing {\tt remquo} / 150 \\
6.18: Computing one remainder from the other / 152 \\
6.19: Computing the remainder in nonbinary bases / 155
\\
6.20: Summary / 156 \\
7: Random numbers / 157 \\
7.1: Guidelines for random-number software / 157 \\
7.2: Creating generator seeds / 158 \\
7.3: Random floating-point values / 160 \\
7.4: Random integers from floating-point generator /
165 \\
7.5: Random integers from an integer generator / 166
\\
7.6: Random integers in ascending order / 168 \\
7.7: How random numbers are generated / 169 \\
7.8: Removing generator bias / 178 \\
7.9: Improving a poor random number generator / 178 \\
7.10: Why long periods matter / 179 \\
7.11: Inversive congruential generators / 180 \\
7.12: Inversive congruential generators, revisited /
189 \\
7.13: Distributions of random numbers / 189 \\
7.14: Other distributions / 195 \\
7.15: Testing random-number generators / 196 \\
7.16: Applications of random numbers / 202 \\
7.17: The \textsf {mathcw} random number routines / 208
\\
7.18: Summary, advice, and further reading / 214 \\
8: Roots / 215 \\
8.1: Square root / 215 \\
8.2: Hypotenuse and vector norms / 222 \\
8.3: Hypotenuse by iteration / 227 \\
8.4: Reciprocal square root / 233 \\
8.5: Cube root / 237 \\
8.6: Roots in hardware / 240 \\
8.7: Summary / 242 \\
9: Argument reduction / 243 \\
9.1: Simple argument reduction / 243 \\
9.2: Exact argument reduction / 250 \\
9.3: Implementing exact argument reduction / 253 \\
9.4: Testing argument reduction / 265 \\
9.5: Retrospective on argument reduction / 265 \\
10: Exponential and logarithm / 267 \\
10.1: Exponential functions / 267 \\
10.2: Exponential near zero / 273 \\
10.3: Logarithm functions / 282 \\
10.4: Logarithm near one / 290 \\
10.5: Exponential and logarithm in hardware / 292 \\
10.6: Compound interest and annuities / 294 \\
10.7: Summary / 298 \\
11: Trigonometric functions / 299 \\
11.1: Sine and cosine properties / 299 \\
11.2: Tangent properties / 302 \\
11.3: Argument conventions and units / 304 \\
11.4: Computing the cosine and sine / 306 \\
11.5: Computing the tangent / 310 \\
11.6: Trigonometric functions in degrees / 313 \\
11.7: Trigonometric functions in units of $ \pi $ / 315
\\
11.8: Computing the cosine and sine together / 320 \\
11.9: Inverse sine and cosine / 323 \\
11.10: Inverse tangent / 331 \\
11.11: Inverse tangent, take two / 336 \\
11.12: Trigonometric functions in hardware / 338 \\
11.13: Testing trigonometric functions / 339 \\
11.14: Retrospective on trigonometric functions / 340
\\
12: Hyperbolic functions / 341 \\
12.1: Hyperbolic functions / 341 \\
12.2: Improving the hyperbolic functions / 345 \\
12.3: Computing the hyperbolic functions together / 348
\\
12.4: Inverse hyperbolic functions / 348 \\
12.5: Hyperbolic functions in hardware / 350 \\
12.6: Summary / 352 \\
13: Pair-precision arithmetic / 353 \\
13.1: Limitations of pair-precision arithmetic / 354
\\
13.2: Design of the pair-precision software interface /
355 \\
13.3: Pair-precision initialization / 356 \\
13.4: Pair-precision evaluation / 357 \\
13.5: Pair-precision high part / 357 \\
13.6: Pair-precision low part / 357 \\
13.7: Pair-precision copy / 357 \\
13.8: Pair-precision negation / 358 \\
13.9: Pair-precision absolute value / 358 \\
13.10: Pair-precision sum / 358 \\
13.11: Splitting numbers into pair sums / 359 \\
13.12: Premature overflow in splitting / 362 \\
13.13: Pair-precision addition / 365 \\
13.14: Pair-precision subtraction / 367 \\
13.15: Pair-precision comparison / 368 \\
13.16: Pair-precision multiplication / 368 \\
13.17: Pair-precision division / 371 \\
13.18: Pair-precision square root / 373 \\
13.19: Pair-precision cube root / 377 \\
13.20: Accuracy of pair-precision arithmetic / 379 \\
13.21: Pair-precision vector sum / 384 \\
13.22: Exact vector sums / 385 \\
13.23: Pair-precision dot product / 385 \\
13.24: Pair-precision product sum / 386 \\
13.25: Pair-precision decimal arithmetic / 387 \\
13.26: Fused multiply-add with pair precision / 388 \\
13.27: Higher intermediate precision and the FMA / 393
\\
13.28: Fused multiply-add without pair precision / 395
\\
13.29: Fused multiply-add with multiple precision / 401
\\
13.30: Fused multiply-add, Boldo/\penalty
\exhyphenpenalty Melquiond style / 403 \\
13.31: Error correction in fused multiply-add / 406 \\
13.32: Retrospective on pair-precision arithmetic / 407
\\
14: Power function / 411 \\
14.1: Why the power function is hard to compute / 411
\\
14.2: Special cases for the power function / 412 \\
14.3: Integer powers / 414 \\
14.4: Integer powers, revisited / 420 \\
14.5: Outline of the power-function algorithm / 421 \\
14.6: Finding $a$ and $p$ / 423 \\
14.7: Table searching / 424 \\
14.8: Computing $\log_n(g/a)$ / 426 \\
14.9: Accuracy required for $\log_n(g/a)$ / 429 \\
14.10: Exact products / 430 \\
14.11: Computing $w$, $w_1$ and $w_2$ / 433 \\
14.12: Computing $n^{w_2}$ / 437 \\
14.13: The choice of $q$ / 438 \\
14.14: Testing the power function / 438 \\
14.15: Retrospective on the power function / 440 \\
15: Complex arithmetic primitives / 441 \\
15.1: Support macros and type definitions / 442 \\
15.2: Complex absolute value / 443 \\
15.3: Complex addition / 445 \\
15.4: Complex argument / 445 \\
15.5: Complex conjugate / 446 \\
15.6: Complex conjugation symmetry / 446 \\
15.7: Complex conversion / 448 \\
15.8: Complex copy / 448 \\
15.9: Complex division: C99 style / 449 \\
15.10: Complex division: Smith style / 451 \\
15.11: Complex division: Stewart style / 452 \\
15.12: Complex division: Priest style / 453 \\
15.13: Complex division: avoiding subtraction loss /
455 \\
15.14: Complex imaginary part / 456 \\
15.15: Complex multiplication / 456 \\
15.16: Complex multiplication: error analysis / 458 \\
15.17: Complex negation / 459 \\
15.18: Complex projection / 460 \\
15.19: Complex real part / 460 \\
15.20: Complex subtraction / 461 \\
15.21: Complex infinity test / 462 \\
15.22: Complex NaN test / 462 \\
15.23: Summary / 463 \\
16: Quadratic equations / 465 \\
16.1: Solving quadratic equations / 465 \\
16.2: Root sensitivity / 471 \\
16.3: Testing a quadratic-equation solver / 472 \\
16.4: Summary / 474 \\
17: Elementary functions in complex arithmetic / 475
\\
17.1: Research on complex elementary functions / 475
\\
17.2: Principal values / 476 \\
17.3: Branch cuts / 476 \\
17.4: Software problems with negative zeros / 478 \\
17.5: Complex elementary function tree / 479 \\
17.6: Series for complex functions / 479 \\
17.7: Complex square root / 480 \\
17.8: Complex cube root / 485 \\
17.9: Complex exponential / 487 \\
17.10: Complex exponential near zero / 492 \\
17.11: Complex logarithm / 495 \\
17.12: Complex logarithm near one / 497 \\
17.13: Complex power / 500 \\
17.14: Complex trigonometric functions / 502 \\
17.15: Complex inverse trigonometric functions / 504
\\
17.16: Complex hyperbolic functions / 509 \\
17.17: Complex inverse hyperbolic functions / 514 \\
17.18: Summary / 520 \\
18: The Greek functions: gamma, psi, and zeta / 521 \\
18.1: Gamma and log-gamma functions / 521 \\
18.2: The {\tt psi} and {\tt psiln} functions / 536 \\
18.3: Polygamma functions / 547 \\
18.4: Incomplete gamma functions / 560 \\
18.5: A Swiss diversion: Bernoulli and Euler / 568 \\
18.6: An Italian excursion: Fibonacci numbers / 575 \\
18.7: A German gem: the Riemann zeta function / 579 \\
18.8: Further reading / 590 \\
18.9: Summary / 591 \\
19: Error and probability functions / 593 \\
19.1: Error functions / 593 \\
19.2: Scaled complementary error function / 598 \\
19.3: Inverse error functions / 600 \\
19.4: Normal distribution functions and inverses / 610
\\
19.5: Summary / 617 \\
20: Elliptic integral functions / 619 \\
20.1: The arithmetic-geometric mean / 619 \\
20.2: Elliptic integral functions of the first kind /
624 \\
20.3: Elliptic integral functions of the second kind /
627 \\
20.4: Elliptic integral functions of the third kind /
630 \\
20.5: Computing $K(m)$ and $K'(m)$ / 631 \\
20.6: Computing $E(m)$ and $E'(m)$ / 637 \\
20.7: Historical algorithms for elliptic integrals /
643 \\
20.8: Auxiliary functions for elliptic integrals / 645
\\
20.9: Computing the elliptic auxiliary functions / 648
\\
20.10: Historical elliptic functions / 650 \\
20.11: Elliptic functions in software / 652 \\
20.12: Applications of elliptic auxiliary functions /
653 \\
20.13: Elementary functions from elliptic auxiliary
functions / 654 \\
20.14: Computing elementary functions via $R_C(x,y)$ /
655 \\
20.15: Jacobian elliptic functions / 657 \\
20.16: Inverses of Jacobian elliptic functions / 664
\\
20.17: The modulus and the nome / 668 \\
20.18: Jacobian theta functions / 673 \\
20.19: Logarithmic derivatives of the Jacobian theta
functions / 675 \\
20.20: Neville theta functions / 678 \\
20.21: Jacobian Eta, Theta, and Zeta functions / 679
\\
20.22: Weierstrass elliptic functions / 682 \\
20.23: Weierstrass functions by duplication / 689 \\
20.24: Complete elliptic functions, revisited / 690 \\
20.25: Summary / 691 \\
21: Bessel functions / 693 \\
21.1: Cylindrical Bessel functions / 694 \\
21.2: Behavior of $J_n(x)$ and $Y_n(x)$ / 695 \\
21.3: Properties of $J_n(z)$ and $Y_n(z)$ / 697 \\
21.4: Experiments with recurrences for $J_0(x)$ / 705
\\
21.5: Computing $J_0(x)$ and $J_1(x)$ / 707 \\
21.6: Computing $J_n(x)$ / 710 \\
21.7: Computing $Y_0(x)$ and $Y_1(x)$ / 713 \\
21.8: Computing $Y_n(x)$ / 715 \\
21.9: Improving Bessel code near zeros / 716 \\
21.10: Properties of $I_n(z)$ and $K_n(z)$ / 718 \\
21.11: Computing $I_0(x)$ and $I_1(x)$ / 724 \\
21.12: Computing $K_0(x)$ and $K_1(x)$ / 726 \\
21.13: Computing $I_n(x)$ and $K_n(x)$ / 728 \\
21.14: Properties of spherical Bessel functions / 731
\\
21.15: Computing $j_n(x)$ and $y_n(x)$ / 735 \\
21.16: Improving $j_1(x)$ and $y_1(x)$ / 740 \\
21.17: Modified spherical Bessel functions / 743 \\
21.18: Software for Bessel-function sequences / 755 \\
21.19: Retrospective on Bessel functions / 761 \\
22: Testing the library / 763 \\
22.1: Testing {\tt tgamma} and {\tt lgamma} / 765 \\
22.2: Testing {\tt psi} and {\tt psiln} / 768 \\
22.3: Testing {\tt erf} and {\tt erfc} / 768 \\
22.4: Testing cylindrical Bessel functions / 769 \\
22.5: Testing exponent/\penalty \exhyphenpenalty
significand manipulation / 769 \\
22.6: Testing inline assembly code / 769 \\
22.7: Testing with Maple / 770 \\
22.8: Testing floating-point arithmetic / 773 \\
22.9: The Berkeley Elementary Functions Test Suite /
774 \\
22.10: The AT\&T floating-point test package / 775 \\
22.11: The Antwerp test suite / 776 \\
22.12: Summary / 776 \\
23: Pair-precision elementary functions / 777 \\
23.1: Pair-precision integer power / 777 \\
23.2: Pair-precision machine epsilon / 779 \\
23.3: Pair-precision exponential / 780 \\
23.4: Pair-precision logarithm / 787 \\
23.5: Pair-precision logarithm near one / 793 \\
23.6: Pair-precision exponential near zero / 793 \\
23.7: Pair-precision base-$n$ exponentials / 795 \\
23.8: Pair-precision trigonometric functions / 796 \\
23.9: Pair-precision inverse trigonometric functions /
801 \\
23.10: Pair-precision hyperbolic functions / 804 \\
23.11: Pair-precision inverse hyperbolic functions /
808 \\
23.12: Summary / 808 \\
24: Accuracy of the Cody\slash Waite algorithms / 811
\\
25: Improving upon the Cody\slash Waite algorithms /
823 \\
25.1: The Bell Labs libraries / 823 \\
25.2: The {Cephes} library / 823 \\
25.3: The {Sun} libraries / 824 \\
25.4: Mathematical functions on EPIC / 824 \\
25.5: The GNU libraries / 825 \\
25.6: The French libraries / 825 \\
25.7: The NIST effort / 826 \\
25.8: Commercial mathematical libraries / 826 \\
25.9: Mathematical libraries for decimal arithmetic /
826 \\
25.10: Mathematical library research publications / 826
\\
25.11: Books on computing mathematical functions / 827
\\
25.12: Summary / 828 \\
26: Floating-point output / 829 \\
26.1: Output character string design issues / 830 \\
26.2: Exact output conversion / 831 \\
26.3: Hexadecimal floating-point output / 832 \\
26.4: Octal floating-point output / 850 \\
26.5: Binary floating-point output / 851 \\
26.6: Decimal floating-point output / 851 \\
26.7: Accuracy of output conversion / 865 \\
26.8: Output conversion to a general base / 865 \\
26.9: Output conversion of Infinity / 866 \\
26.10: Output conversion of NaN / 866 \\
26.11: Number-to-string conversion / 867 \\
26.12: The {\tt printf} family / 867 \\
26.13: Summary / 878 \\
27: Floating-point input / 879 \\
27.1: Binary floating-point input / 879 \\
27.2: Octal floating-point input / 894 \\
27.3: Hexadecimal floating-point input / 895 \\
27.4: Decimal floating-point input / 895 \\
27.5: Based-number input / 899 \\
27.6: General floating-point input / 900 \\
27.7: The {\tt scanf} family / 901 \\
27.8: Summary / 910 \\
A: Ada interface / 911 \\
A.1: Building the Ada interface / 911 \\
A.2: Programming the Ada interface / 912 \\
A.3: Using the Ada interface / 915 \\
B: C\# interface / 917 \\
B.1: C\# on the CLI virtual machine / 917 \\
B.2: Building the C\# interface / 918 \\
B.3: Programming the C\# interface / 920 \\
B.4: Using the C\# interface / 922 \\
C: C++ interface / 923 \\
C.1: Building the C++ interface / 923 \\
C.2: Programming the C++ interface / 924 \\
C.3: Using the C++ interface / 925 \\
D: Decimal arithmetic / 927 \\
D.1: Why we need decimal floating-point arithmetic /
927 \\
D.2: Decimal floating-point arithmetic design issues /
928 \\
D.3: How decimal and binary arithmetic differ / 931 \\
D.4: Initialization of decimal floating-point storage /
935 \\
D.5: The {\tt } header file / 936 \\
D.6: Rounding in decimal arithmetic / 936 \\
D.7: Exact scaling in decimal arithmetic / 937 \\
E: Errata in the Cody\slash Waite book / 939 \\
F: Fortran interface / 941 \\
F.1: Building the Fortran interface / 943 \\
F.2: Programming the Fortran interface / 944 \\
F.3: Using the Fortran interface / 945 \\
H: Historical floating-point architectures / 947 \\
H.1: CDC family / 949 \\
H.2: Cray family / 952 \\
H.3: DEC PDP-10 / 953 \\
H.4: DEC PDP-11 and VAX / 956 \\
H.5: General Electric 600 series / 958 \\
H.6: IBM family / 959 \\
H.7: Lawrence Livermore S-1 Mark IIA / 965 \\
H.8: Unusual floating-point systems / 966 \\
H.9: Historical retrospective / 967 \\
I: Integer arithmetic / 969 \\
I.1: Memory addressing and integers / 971 \\
I.2: Representations of signed integers / 971 \\
I.3: Parity testing / 975 \\
I.4: Sign testing / 975 \\
I.5: Arithmetic exceptions / 975 \\
I.6: Notations for binary numbers / 977 \\
I.7: Summary / 978 \\
J: Java interface / 979 \\
J.1: Building the Java interface / 979 \\
J.2: Programming the Java MathCW class / 980 \\
J.3: Programming the Java C interface / 982 \\
J.4: Using the Java interface / 985 \\
L: Letter notation / 987 \\
P: Pascal interface / 989 \\
P.1: Building the Pascal interface / 989 \\
P.2: Programming the Pascal MathCW module / 990 \\
P.3: Using the Pascal module interface / 993 \\
P.4: Pascal and numeric programming / 994 \\
Bibliography / 995 \\
Author/editor index / 1039 \\
Function and macro index / 1049 \\
Subject index / 1065 \\
Colophon / 1115",
}
@Book{Boldo:2017:CAF,
author = "Sylvie Boldo and Guillaume Melquiond",
title = "Computer arithmetic and formal proofs: verifying
floating-point algorithms with the {Coq} system",
publisher = "ISTE Press",
address = "London, UK",
year = "2017",
ISBN = "1-78548-112-6, 0-08-101170-9 (e-book)",
ISBN-13 = "978-1-78548-112-3, 978-0-08-101170-6 (e-book)",
LCCN = "QA76.9.C62",
bibdate = "Tue Nov 28 08:55:56 MST 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
URL = "http://iste.co.uk/book.php?id=1238",
abstract = "Floating-point arithmetic is ubiquitous in modern
computing, as it is the tool of choice to approximate
real numbers. Due to its limited range and precision,
its use can become quite involved and potentially lead
to numerous failures. One way to greatly increase
confidence in floating-point software is by
computer-assisted verification of its correctness
proofs. This book provides a comprehensive view of how
to formally specify and verify tricky floating-point
algorithms with the Coq proof assistant. It describes
the Flocq formalization of floating-point arithmetic
and some methods to automate theorem proofs. It then
presents the specification and verification of various
algorithms, from error-free transformations to a
numerical scheme for a partial differential equation.
The examples cover not only mathematical algorithms but
also C programs as well as issues related to
compilation. Describes the notions of specification and
weakest precondition computation and their practical
use. Shows how to tackle algorithms that extend beyond
the realm of simple floating-point arithmetic. Includes
real analysis and a case study about numerical
analysis.",
acknowledgement = ack-nhfb,
subject = "Coq (Electronic resource); Computer arithmetic;
Floating-point arithmetic; Computer algorithms;
COMPUTERS / Computer Literacy; COMPUTERS / Computer
Science; COMPUTERS / Data Processing; COMPUTERS /
Hardware / General; COMPUTERS / Information Technology;
COMPUTERS / Machine Theory; COMPUTERS / Reference;
MATHEMATICS / Discrete Mathematics",
tableofcontents = "1. Floating-Point Arithmetic \\
2. The Coq System \\
3. Formalization of Formats and Basic Operators \\
4. Automated Methods \\
5. Error-Free Computations and Applications \\
6. Example Proofs of Advanced Operators \\
7. Compilation of FP Programs \\
8. Deductive Program Verification \\
9. Real and Numerical Analysis",
}
@Book{Garcia:2017:SCL,
author = "Stephan Ramon Garcia and Roger A. Horn",
title = "A Second Course in Linear Algebra",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "442 (est.)",
year = "2017",
ISBN = "1-107-10381-9 (hardcover)",
ISBN-13 = "978-1-107-10381-8 (hardcover)",
LCCN = "QA184.2 .G37 2017",
bibdate = "Tue Jul 11 16:36:22 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Algebras, Linear; Textbooks",
URL = "http://www.cambridge.org/us/academic/subjects/mathematics/algebra/second-course-linear-algebra?format=HB",
}
@Book{Higham:2017:MG,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "{MATLAB} guide",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxvi + 476",
year = "2017",
ISBN = "1-61197-465-8",
ISBN-13 = "978-1-61197-465-2",
MRclass = "65-00 (00A20)",
MRnumber = "3601107",
bibdate = "Sat Aug 26 17:40:10 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
abstract = "MATLAB is an interactive system for numerical
computation that is widely used for teaching and
research in industry and academia. It provides a modern
programming language and problem solving environment,
with powerful data structures, customizable graphics,
and easy-to-use editing and debugging tools. This third
edition of MATLAB Guide completely revises and updates
the best-selling second edition and is more than 25
percent longer. The book remains a lively, concise
introduction to the most popular and important features
of MATLAB and the Symbolic Math Toolbox. Key features
are a tutorial in Chapter 1 that gives a hands-on
overview of MATLAB, a thorough treatment of MATLAB
mathematics, including the linear algebra and numerical
analysis functions and the differential equation
solvers, and a web page that provides a link to example
program files, updates, and links to MATLAB resources.
The new edition contains color figures throughout,
includes pithy discussions of related topics in new
`Asides' boxes that augment the text, has new chapters
on the Parallel Computing Toolbox, object-oriented
programming, graphs, and large data sets, covers
important new MATLAB data types such as categorical
arrays, string arrays, tall arrays, tables, and
timetables, contains more on MATLAB workflow, including
the Live Editor and unit tests, and fully reflects
major updates to the MATLAB graphics system.",
acknowledgement = ack-nhfb,
remark = "Third edition of
\cite{Higham:2000:MG,Higham:2005:MG}.",
subject = "MATLAB (logiciel).; Analyse num{\'e}rique; Logiciels.;
Numerical analysis; Data processing; Data processing.",
tableofcontents = "1: A Brief Tutorial \\
2: Basics \\
3: Distinctive Features of MATLAB \\
4: Arithmetic \\
5: Matrices \\
6: Operators and Flow Control \\
7: Program Files \\
8: Graphics \\
9: Linear Algebra \\
10: More on Functions \\
11: Numerical Methods: Part I \\
12: Numerical Methods: Part II \\
13: Input and Output \\
14: Troubleshooting \\
15: Sparse Matrices \\
16: More on Coding \\
17: Advanced Graphics \\
18: Other Data Types and Multidimensional Arrays \\
19: Object-Oriented Programming \\
20: The Symbolic Math Toolbox \\
21: Graphs \\
22: Large Data Sets \\
23: Optimizing Codes \\
24: Tricks and Tips \\
25: The Parallel Computing Toolbox \\
26: Case Studies",
}
@Book{Howard:2017:CMN,
author = "James Patrick {Howard, II}",
title = "Computational methods, for numerical analysis with
{R}",
publisher = "CRC Press/Taylor and Francis Group",
address = "Boca Raton, FL, USA",
pages = "xx + 257",
year = "2017",
ISBN = "1-4987-2363-2 (hardcover), 1-4987-2364-0 (e-book),
1-315-12019-4 (e-book)",
ISBN-13 = "978-1-4987-2363-3 (hardcover), 978-1-4987-2364-0
(e-book), 978-1-315-12019-5 (e-book)",
LCCN = "QA297 .H67 2017",
bibdate = "Sat Mar 16 12:09:51 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/s-plus.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.crcnetbase.com/isbn/9781498723640",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Data processing; R (Computer
program language)",
tableofcontents = "1: Introduction to Numerical Analysis / 28 pages
\\
2: Error Analysis / 30 pages \\
3: Linear Algebra / 36 pages \\
4: Interpolation and Extrapolation / 38 pages \\
5: Differentiation and Integration / 42 pages \\
6: Root Finding and Optimization / 37 pages \\
7: Differential Equations / 35 pages",
}
@Book{Martinez:2017:EDA,
author = "Wendy L. Martinez and Angel R. Martinez and Jeffrey L.
Solka",
title = "Exploratory data analysis with {MATLAB}",
volume = "4",
publisher = pub-CHAPMAN-HALL-CRC,
address = pub-CHAPMAN-HALL-CRC:adr,
edition = "Third",
pages = "xv + 590",
year = "2017",
DOI = "https://doi.org/10.1201/9781315366968",
ISBN = "1-4987-7606-X (hardcover), 1-315-33081-4 (Mobi
e-book), 1-4987-7607-8 (PDF e-book), 1-315-34984-1
(ePub)",
ISBN-13 = "978-1-4987-7606-6 (hardcover), 978-1-315-33081-5 (Mobi
e-book), 978-1-4987-7607-3 (PDF e-book),
978-1-315-34984-8 (ePub)",
LCCN = "QA278 .M3735 2017",
bibdate = "Sat Dec 14 10:09:26 MST 2019",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Computer science and data analysis series",
acknowledgement = ack-nhfb,
remark = "Previous edition \cite{Martinez:2011:EDA}.",
subject = "MATLAB; Multivariate analysis; Numerical analysis;
Computer programs",
tableofcontents = "Preface to the Third Edition \\
Preface to the Second Edition \\
Preface to the First Edition \\
Part I Introduction to Exploratory Data Analysis \\
Chapter 1 Introduction to Exploratory Data Analysis \\
1.1 What is Exploratory Data Analysis \\
1.2 Overview of the Text \\
1.3 A Few Words about Notation \\
1.4 Data Sets Used in the Book \\
1.4.1 Unstructured Text Documents \\
1.4.2 Gene Expression Data \\
1.4.3 Oronsay Data Set \\
1.4.4 Software Inspection \\
1.5 Transforming Data \\
1.5.1 Power Transformations \\
1.5.2 Standardization \\
1.5.3 Sphering the Data \\
1.6 Further Reading \\
Exercises \\
Part II EDA as Pattern Discovery \\
Chapter 2 Dimensionality Reduction \\
Linear Methods \\
2.1 Introduction \\
2.2 Principal Component Analysis \\
PCA \\
2.2.1 PCA Using the Sample Covariance Matrix \\
2.2.2 PCA Using the Sample Correlation Matrix \\
2.2.3 How Many Dimensions Should We Keep \\
2.3 Singular Value Decomposition \\
SVD \\
2.4 Nonnegative Matrix Factorization \\
2.5 Factor Analysis \\
2.6 Fisher's Linear Discriminant \\
2.7 Random Projections \\
2.8 Intrinsic Dimensionality \\
2.8.1 Nearest Neighbor Approach \\
2.8.2 Correlation Dimension \\
2.8.3 Maximum Likelihood Approach \\
2.8.4 Estimation Using Packing Numbers \\
2.8.5 Estimation of Local Dimension \\
2.9 Summary and Further Reading \\
Exercises \\
Chapter 3 Dimensionality Reduction-Nonlinear Methods
\\
3.1 Multidimensional Scaling \\
MDS \\
3.1.1 Metric MDS \\
3.1.2 Nonmetric MDS \\
3.2 Manifold Learning \\
3.2.1 Locally Linear Embedding \\
3.2.2 Isometric Feature Mapping \\
ISOMAP \\
3.2.3 Hessian Eigenmaps \\
3.3 Artificial Neural Network Approaches \\
3.3.1 Self-Organizing Maps \\
3.3.2 Generative Topographic Maps \\
3.3.3 Curvilinear Component Analysis \\
3.3.4 Autoencoders3.4 Stochastic Neighbor Embedding \\
3.5 Summary and Further Reading \\
Exercises \\
Chapter 4 Data Tours \\
4.1 Grand Tour \\
4.1.1 Torus Winding Method \\
4.1.2 Pseudo Grand Tour \\
4.2 Interpolation Tours \\
4.3 Projection Pursuit \\
4.4 Projection Pursuit Indexes \\
4.4.1 Posse Chi-Square Index \\
4.4.2 Moment Index \\
4.5 Independent Component Analysis \\
4.6 Summary and Further Reading \\
Exercises \\
Chapter 5 Finding Clusters \\
5.1 Introduction \\
5.2 Hierarchical Methods \\
5.3 Optimization Methods- k-Means \\
5.4 Spectral Clustering \\
5.5 Document Clustering \\
5.5.1 Nonnegative Matrix Factorization \\
Revisited \\
5.5.2 Probabilistic Latent Semantic Analysis \\
5.6 Minimum Spanning Trees and Clustering \\
5.6.1 Definitions \\
5.6.2 Minimum Spanning Tree Clustering \\
5.7 Evaluating the Clusters \\
5.7.1 Rand Index \\
5.7.2 Cophenetic Correlation \\
5.7.3 Upper Tail Rule \\
5.7.4 Silhouette Plot \\
5.7.5 Gap Statistic \\
5.7.6 Cluster Validity Indices \\
5.8 Summary and Further Reading \\
Exercises \\
Chapter 6 Model-Based Clustering \\
6.1 Overview of Model-Based Clustering \\
6.2 Finite Mixtures \\
6.2.1 Multivariate Finite Mixtures \\
6.2.2 Component Models \\
Constraining the Covariances \\
6.3 Expectation-Maximization Algorithm \\
6.4 Hierarchical Agglomerative Model-Based Clustering
\\
6.5 Model-Based Clustering \\
6.6 MBC for Density Estimation and Discriminant
Analysis \\
6.6.1 Introduction to Pattern Recognition \\
6.6.2 Bayes Decision Theory \\
6.6.3 Estimating Probability Densities with MBC \\
6.7 Generating Random Variables from a Mixture Model
\\
6.8 Summary and Further Reading \\
Exercises \\
Chapter 7 Smoothing Scatterplots \\
7.1 Introduction \\
7.2 Loess \\
7.3 Robust Loess \\
7.4 Residuals and Diagnostics with Loess \\
7.4.1 Residual Plots \\
7.4.2 Spread Smooth \\
7.4.3 Loess Envelopes \\
Upper and Lower Smooths7.5 Smoothing Splines \\
7.5.1 Regression with Splines \\
7.5.2 Smoothing Splines \\
7.5.3 Smoothing Splines for Uniformly Spaced Data \\
7.6 Choosing the Smoothing Parameter \\
7.7 Bivariate Distribution Smooths \\
7.7.1 Pairs of Middle Smoothings \\
7.7.2 Polar Smoothing \\
7.8 Curve Fitting Toolbox \\
7.9 Summary and Further Reading \\
Exercises \\
Part III Graphical Methods for EDA \\
Chapter 8 Visualizing Clusters \\
8.1 Dendrogram \\
8.2 Treemaps \\
8.3 Rectangle Plots \\
8.4 ReClus Plots \\
8.5 Data Image \\
8.6 Summary and Further Reading \\
Exercises \\
Chapter 9 Distribution Shapes \\
9.1 Histograms \\
9.1.1 Univariate Histograms \\
9.1.2 Bivariate Histograms \\
9.2 Kernel Density \\
9.2.1 Univariate Kernel Density Estimation \\
9.2.2 Multivariate Kernel Density Estimation \\
9.3 Boxplots \\
9.3.1 The Basic Boxplot \\
9.3.2 Variations of the Basic Boxplot \\
9.3.3 Violin Plots \\
9.3.4 Beeswarm Plot \\
9.3.5 Beanplot \\
9.4 Quantile Plots \\
9.4.1 Probability Plots \\
9.4.2 Quantile-Quantile Plot \\
9.4.3 Quantile Plot \\
9.5 Bagplots \\
9.6 Rangefinder Boxplot \\
9.7 Summary and Further Reading \\
Exercises \\
Chapter 10 Multivariate Visualization \\
10.1 Glyph Plots \\
10.2 Scatterplots \\
10.2.1 2-D and 3-D Scatterplots \\
10.2.2 Scatterplot Matrices \\
10.2.3 Scatterplots with Hexagonal Binning \\
10.3 Dynamic Graphics \\
10.3.1 Identification of Data \\
10.3.2 Linking \\
10.3.3 Brushing \\
10.4 Coplots \\
10.5 Dot Charts \\
10.5.1 Basic Dot Chart \\
10.5.2 Multiway Dot Chart \\
10.6 Plotting Points as Curves \\
10.6.1 Parallel Coordinate Plots \\
10.6.2 Andrews' Curves \\
10.6.3 Andrews' Images \\
10.6.4 More Plot Matrices \\
10.7 Data Tours Revisited \\
10.7.1 Grand Tour \\
10.7.2 Permutation Tour \\
10.8 Biplots \\
10.9 Summary and Further Reading \\
Exercises \\
Chapter 11 Visualizing Categorical Data \\
11.1 Discrete Distributions11.1.1 Binomial Distribution
\\
11.1.2 Poisson Distribution \\
11.2 Exploring Distribution Shapes \\
11.2.1 Poissonness Plot \\
11.2.2 Binomialness Plot \\
11.2.3 Extensions of the Poissonness Plot \\
11.2.4 Hanging Rootogram \\
11.3 Contingency Tables \\
11.3.1 Background \\
11.3.2 Bar Plots \\
11.3.3 Spine Plots \\
11.3.4 Mosaic Plots \\
11.3.5 Sieve Plots \\
11.3.6 Log Odds Plot \\
11.4 Summary and Further Reading \\
Exercises \\
Appendix A Proximity Measures \\
A.1 Definitions \\
A.1.1 Dissimilarities \\
A.1.2 Similarity Measures \\
A.1.3 Similarity Measures for Binary Data \\
A.1.4 Dissimilarities for Probability Density Functions
\\
A.2 Transformations \\
A.3 Further Reading \\
Appendix B Software Resources for EDA \\
B.1 MATLAB Programs \\
B.2 Other Programs for EDA \\
B.3 EDA Toolbox \\
Appendix C Description of Data Sets \\
Appendix D MATLAB Basics \\
D.1 Desktop Environment \\
D.2 Getting Help and Other Documentation \\
D.3 Data Import and Export \\
D.3.1 Data Import and Export in Base MATLAB \\
D.3.2 Data Import and Export with the Statistics
Toolbox \\
D.4 Data in MATLAB \\
D.4.1 Data Objects in Base MATLAB \\
D.4.2 Accessing Data Elements \\
D.4.3 Object-Oriented Programming \\
D.5 Workspace and Syntax \\
D.5.1 File and Workspace Management \\
D.5.2 Syntax in MATLAB \\
D.5.3 Functions in MATLAB \\
D.6 Basic Plot Functions \\
D.6.1 Plotting 2D Data \\
D.6.2 Plotting 3D Data \\
D.6.3 Scatterplots \\
D.6.4 Scatterplot Matrix \\
D.6.5 GUIs for Graphics \\
D.7 Summary and Further Reading \\
References \\
Author Index \\
Subject Index",
}
@Book{Schiesser:2017:SCM,
author = "William E. Schiesser",
title = "Spline Collocation Methods for Partial Differential
Equations: with Applications in {R}",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xv + 549",
year = "2017",
DOI = "https://doi.org/10.1002/9781119301066",
ISBN = "1-119-30103-3 (hardcover), 1-119-30105-X (PDF),
1-119-30104-1 (ePub), 1-119-30106-8 (online)",
ISBN-13 = "978-1-119-30103-5 (hardcover), 978-1-119-30105-9
(PDF), 978-1-119-30104-2 (ePub), 978-1-119-30106-6
(online)",
LCCN = "QA377 .S355 2017",
bibdate = "Tue Mar 13 10:16:43 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clerk-maxwell-james.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/planck-max.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/s-plus.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
shorttableofcontents = "One-dimensional PDEs \\
Multidimensional PDEs \\
Navier--Stokes, Burgers equations \\
Korteweg--deVries equation \\
Maxwell equations \\
Poisson--Nernst--Planck equations \\
Fokker--Planck equation \\
Fisher--Kolmogorov equation \\
Klein--Gordon equation \\
Boussinesq equation \\
Cahn--Hilliard equation \\
Camassa--Holm equation \\
Burgers--Huxley equation \\
Gierer--Meinhardt equations \\
Keller--Segel equations \\
Fitzhugh--Nagumo equations \\
Euler--Poisson--Darboux equation \\
Kuramoto--Sivashinsky equation \\
Einstein--Maxwell equations",
subject = "Differential equations, Partial; Mathematical models;
Spline theory",
tableofcontents = "Preface / xiii \\
About the Companion Website / xv \\
1 Introduction / 1 \\
1.1 Uniform Grids / 2 \\
1.2 Variable Grids / 18 \\
1.3 Stagewise Differentiation / 24 \\
Appendix A1 --- Online Documentation for splinefun / 27
\\
Reference / 30 \\
2 One-Dimensional PDEs / 31 \\
2.1 Constant Coefficient / 31 \\
2.1.1 Dirichlet BCs / 32 \\
2.1.1.1 Main Program / 33 \\
2.1.1.2 ODE Routine / 40 \\
2.1.2 Neumann BCs / 43 \\
2.1.2.1 Main Program / 44 \\
2.1.2.2 ODE Routine / 46 \\
2.1.3 Robin BCs / 49 \\
2.1.3.1 Main Program / 50 \\
2.1.3.2 ODE Routine / 55 \\
2.1.4 Nonlinear BCs / 60 \\
2.1.4.1 Main Program / 61 \\
2.1.4.2 ODE Routine / 63 \\
2.2 Variable Coefficient / 64 \\
2.2.1 Main Program / 67 \\
2.2.2 ODE Routine / 71 \\
2.3 Inhomogeneous, Simultaneous, Nonlinear / 76 \\
2.3.1 Main Program / 78 \\
2.3.2 ODE routine / 85 \\
2.3.3 Subordinate Routines / 88 \\
2.4 First Order in Space and Time / 94 \\
2.4.1 Main Program / 96 \\
2.4.2 ODE Routine / 101 \\
2.4.3 Subordinate Routines / 105 \\
2.5 Second Order in Time / 107 \\
2.5.1 Main Program / 109 \\
2.5.2 ODE Routine / 114 \\
2.5.3 Subordinate Routine / 117 \\
2.6 Fourth Order in Space / 120 \\
2.6.1 First Order in Time / 120 \\
2.6.1.1 Main Program / 121 \\
2.6.1.2 ODE Routine / 125 \\
2.6.2 Second Order in Time / 138 \\
2.6.2.1 Main Program / 140 \\
2.6.2.2 ODE Routine / 143 \\
References / 155 \\
3 Multidimensional PDEs / 157 \\
3.1 2D in Space / 157 \\
3.1.1 Main Program / 158 \\
3.1.2 ODE Routine / 163 \\
3.2 3D in Space / 170 \\
3.2.1 Main Program, Case 1 / 170 \\
3.2.2 ODE Routine / 174 \\
3.2.3 Main Program, Case 2 / 183 \\
3.2.4 ODE Routine / 187 \\
3.3 Summary and Conclusions / 193 \\
4 Navier--Stokes, Burgers' Equations / 197 \\
4.1 PDE Model / 197 \\
4.2 Main Program / 198 \\
4.3 ODE Routine / 203 \\
4.4 Subordinate Routine / 205 \\
4.5 Model Output / 206 \\
4.6 Summary and Conclusions / 208 \\
Reference / 209 \\
5 Korteweg--de Vries Equation / 211 \\
5.1 PDE Model / 211 \\
5.2 Main Program / 212 \\
5.3 ODE Routine / 225 \\
5.4 Subordinate Routines / 228 \\
5.5 Model Output / 234 \\
5.6 Summary and Conclusions / 238 \\
References / 239 \\
6 Maxwell Equations / 241 \\
6.1 PDE Model / 241 \\
6.2 Main Program / 243 \\
6.3 ODE Routine / 248 \\
6.4 Model Output / 252 \\
6.5 Summary and Conclusions / 252 \\
Appendix A6.1. Derivation of the Analytical Solution /
257 \\
Reference / 259 \\
7 Poisson--Nernst--Planck Equations / 261 \\
7.1 PDE Model / 261 \\
7.2 Main Program / 265 \\
7.3 ODE Routine / 271 \\
7.4 Model Output / 276 \\
7.5 Summary and Conclusions / 284 \\
References / 286 \\
8 Fokker--Planck Equation / 287 \\
8.1 PDE Model / 287 \\
8.2 Main Program / 288 \\
8.3 ODE Routine / 293 \\
8.4 Model Output / 295 \\
8.5 Summary and Conclusions / 301 \\
References / 303 \\
9 Fisher--Kolmogorov Equation / 305 \\
9.1 PDE Model / 305 \\
9.2 Main Program / 306 \\
9.3 ODE Routine / 311 \\
9.4 Subordinate Routine / 313 \\
9.5 Model Output / 314 \\
9.6 Summary and Conclusions / 316 \\
Reference / 316 \\
10 Klein--Gordon Equation / 317 \\
10.1 PDE Model, Linear Case / 317 \\
10.2 Main Program / 318 \\
10.3 ODE Routine / 323 \\
10.4 Model Output / 326 \\
10.5 PDE Model, Nonlinear Case / 328 \\
10.6 Main Program / 330 \\
10.7 ODE Routine / 335 \\
10.8 Subordinate Routines / 338 \\
10.9 Model Output / 339 \\
10.10 Summary and Conclusions / 342 \\
Reference / 342 \\
11 Boussinesq Equation / 343 \\
11.1 PDE Model / 343 \\
11.2 Main Program / 344 \\
11.3 ODE Routine / 350 \\
11.4 Subordinate Routines / 354 \\
11.5 Model Output / 355 \\
11.6 Summary and Conclusions / 358 \\
References / 358 \\
12 Cahn--Hilliard Equation / 359 \\
12.1 PDE Model / 359 \\
12.2 Main Program / 360 \\
12.3 ODE Routine / 366 \\
12.4 Model Output / 369 \\
12.5 Summary and Conclusions / 379 \\
References / 379 \\
13 Camassa--Holm Equation / 381 \\
13.1 PDE Model / 381 \\
13.2 Main Program / 382 \\
13.3 ODE Routine / 388 \\
13.4 Model Output / 391 \\
13.5 Summary and Conclusions / 394 \\
13.6 Appendix A13.1: Second Example of a PDE with a
Mixed Partial Derivative / 395 \\
13.7 Main Program / 395 \\
13.8 ODE Routine / 398 \\
13.9 Model Output / 400 \\
Reference / 403 \\
14 Burgers--Huxley Equation / 405 \\
14.1 PDE Model / 405 \\
14.2 Main Program / 406 \\
14.3 ODE Routine / 411 \\
14.4 Subordinate Routine / 416 \\
14.5 Model Output / 417 \\
14.6 Summary and Conclusions / 422 \\
References / 422 \\
15 Gierer--Meinhardt Equations / 423 \\
15.1 PDE Model / 423 \\
15.2 Main Program / 424 \\
15.3 ODE Routine / 429 \\
15.4 Model Output / 432 \\
15.5 Summary and Conclusions / 437 \\
Reference / 440 \\
16 Keller--Segel Equations / 441 \\
16.1 PDE Model / 441 \\
16.2 Main Program / 443 \\
16.3 ODE Routine / 449 \\
16.4 Subordinate Routines / 453 \\
16.5 Model Output / 453 \\
16.6 Summary and Conclusions / 458 \\
Appendix A16.1. Diffusion Models / 458 \\
References / 459 \\
17 Fitzhugh--Nagumo Equations / 461 \\
17.1 PDE Model / 461 \\
17.2 Main Program / 462 \\
17.3 ODE Routine / 467 \\
17.4 Model Output / 470 \\
17.5 Summary and Conclusions / 475 \\
Reference / 475 \\
18 Euler--Poisson--Darboux Equation / 477 \\
18.1 PDE Model / 477 \\
18.2 Main Program / 478 \\
18.3 ODE Routine / 483 \\
18.4 Model Output / 488 \\
18.5 Summary and Conclusions / 493 \\
References / 493 \\
19 Kuramoto--Sivashinsky Equation / 495 \\
19.1 PDE Model / 495 \\
19.2 Main Program / 496 \\
19.3 ODE Routine / 503 \\
19.4 Subordinate Routines / 506 \\
19.5 Model Output / 508 \\
19.6 Summary and Conclusions / 513 \\
References / 514 \\
20 Einstein--Maxwell Equations / 515 \\
20.1 PDE Model / 515 \\
20.2 Main Program / 516 \\
20.3 ODE Routine / 521 \\
20.4 Model Output / 526 \\
20.5 Summary and Conclusions / 533 \\
Reference / 536 \\
A Differential Operators in Three Orthogonal Coordinate
Systems / 537 \\
References / 539 \\
Index / 541",
}
@Book{Boyd:2018:IAL,
author = "Stephen P. In. Boyd and Lieven Vandenberghe",
title = "Introduction to Applied Linear Algebra: Vectors,
Matrices, and Least Squares",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xii + 463",
year = "2018",
ISBN = "1-108-69394-6, 1-316-51896-5 (hardcover)",
ISBN-13 = "978-1-108-69394-3, 978-1-316-51896-0 (hardcover)",
LCCN = "QA184.2 .B69 2018",
bibdate = "Thu Mar 14 10:47:12 MDT 2019",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
abstract = "This groundbreaking textbook combines straightforward
explanations with a wealth of practical examples to
offer an innovative approach to teaching linear
algebra. Requiring no prior knowledge of the subject,
it covers the aspects of linear algebra --- vectors,
matrices, and least squares --- that are needed for
engineering applications, discussing examples across
data science, machine learning and artificial
intelligence, signal and image processing, tomography,
navigation, control, and finance. The numerous
practical exercises throughout allow students to test
their understanding and translate their knowledge into
solving real-world problems, with lecture slides,
additional computational exercises in Julia and MATLAB,
and data sets accompanying the book online. It is
suitable for both one-semester and one-quarter courses,
as well as self-study, this self-contained text
provides beginning students with the foundation they
need to progress to more advanced study.",
acknowledgement = ack-nhfb,
author-dates = "1958--",
subject = "Algebras, Linear; Textbooks; Matrices; Vector algebra;
Least squares",
tableofcontents = "Part I. Vectors: \\
1. Vectors \\
2. Linear functions \\
3. Norm and distance \\
4. Clustering \\
5. Linear independence \\
Part II. Matrices: \\
6. Matrices \\
7. Matrix examples \\
8. Linear equations \\
9. Linear dynamical systems \\
10. Matrix multiplication \\
11. Matrix inverses \\
Part III. Least Squares: \\
12. Least squares \\
13. Least squares data fitting \\
14. Least squares classification \\
15. Multi-objective least squares \\
16. Constrained least squares \\
17. Constrained least squares applications \\
18. Nonlinear least squares \\
19. Constrained nonlinear least squares \\
Appendix A \\
Appendix B \\
Appendix C \\
Appendix D \\
Index",
}
@Book{Hassanieh:2018:SFT,
author = "Haitham Hassanieh",
title = "The {Sparse Fourier Transform}: Theory and Practice",
volume = "19",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xvii + 260",
year = "2018",
DOI = "https://doi.org/10.1145/3166186",
ISBN = "1-947487-07-8 (hardcover), 1-947487-04-3 (paperback),
1-947487-05-1 (e-book)",
ISBN-13 = "978-1-947487-07-9 (hardcover), 978-1-947487-04-8
(paperback), 978-1-947487-05-5 (e-book)",
LCCN = "QC20.7.F67 H37 2018",
bibdate = "Tue Aug 6 15:47:06 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "ACM book series",
abstract = "The Fourier transform is one of the most fundamental
tools for computing the frequency representation of
signals. It plays a central role in signal processing,
communications, audio and video compression, medical
imaging, genomics, astronomy, as well as many other
areas. Because of its widespread use, fast algorithms
for computing the Fourier transform can benefit a large
number of applications. The fastest algorithm for
computing the Fourier transform is the Fast Fourier
Transform (FFT), which runs in near-linear time making
it an indispensable tool for many applications.
However, today, the runtime of the FFT algorithm is no
longer fast enough especially for big data problems
where each dataset can be few terabytes. Hence, faster
algorithms that run in sublinear time, i.e., do not
even sample all the data points, have become necessary.
This book addresses the above problem by developing the
Sparse Fourier Transform algorithms and building
practical systems that use these algorithms to solve
key problems in six different applications: wireless
networks; mobile systems; computer graphics; medical
imaging; biochemistry; and digital circuits. This is a
revised version of the thesis that won the 2016 ACM
Doctoral Dissertation Award.",
acknowledgement = ack-nhfb,
subject = "Fourier transformations; Sparse matrices",
tableofcontents = "1. Introduction \\
1.1 Sparse Fourier transform algorithms \\
1.2 Applications of the sparse Fourier transform \\
1.3 Book overview \\
Part I. Theory of the sparse Fourier transform \\
2. preliminaries \\
2.1 Notation \\
2.2 Basics \\
3. Simple and practical algorithm \\
3.1 Introduction \\
3.2 Algorithm \\
4. Optimizing runtime complexity \\
4.1 Introduction \\
4.2 Algorithm for the exactly sparse case \\
4.3 Algorithm for the general case \\
4.4 Extension to two dimensions \\
5. Optimizing sample complexity \\
5.1 Introduction \\
5.2 Algorithm for the exactly sparse case \\
5.3 Algorithm for the general case \\
6. Numerical evaluation \\
6.1 Implementation \\
6.2 Experimental setup \\
6.3 Numerical results \\
Part II. Applications of the sparse Fourier transform
\\
7. GHz-wide spectrum sensing and decoding \\
7.1 Introduction \\
7.2 Related work \\
7.3 BigBand \\
7.4 Channel estimation and calibration \\
7.5 Differential sensing of non-sparse spectrum \\
7.6 A USRP-based implementation \\
7.7 BigBand's spectrum sensing results \\
7.8 BigBand's decoding results \\
7.9 D-BigBand's sensing results \\
7.10 Conclusion \\
8. Faster GPS synchronization \\
8.1 Introduction \\
8.2 GPS primer \\
8.3 QuickSync \\
8.4 Theoretical guarantees \\
8.5 Doppler shift and frequency offset \\
8.6 Testing environment \\
8.7 Results \\
8.8 Related work \\
8.9 Conclusion \\
9. Light field reconstruction using continuous Fourier
sparsity \\
9.1 Introduction \\
9.2 Related work \\
9.3 Sparsity in the discrete vs. continuous Fourier
domain \\
9.4 Light field notation \\
9.5 Light field reconstruction algorithm \\
9.6 Experiments \\
9.7 Results \\
9.8 Discussion \\
9.9 Conclusion \\
10. Fast in-vivo MRS acquisition with artifact
suppression \\
10.1 Introduction \\
10.2 MRS-SFT \\
10.3 Methods \\
10.4 MRS results \\
10.5 Conclusion \\
11. Fast multi-dimensional NMR acquisition and
processing \\
11.1 Introduction \\
11.2 Multi-dimensional sparse Fourier transform \\
11.3 Materials and methods \\
11.4 Results \\
11.5 Discussion \\
11.6 Conclusion \\
12. Conclusion \\
12.1 Future directions \\
Appendix A. Proofs \\
Appendix B. The optimality of the exactly k-Sparse
algorithm 4.1 \\
Appendix C. Lower bound of the sparse Fourier transform
in the general case \\
Appendix D. Efficient constructions of window functions
\\
Appendix E. Sample lower bound for the Bernoulli
distribution \\
Appendix F. Analysis of the QuickSync system \\
Analysis of the baseline algorithm \\
Tightness of the variance bound \\
Analysis of the QuickSync algorithm \\
Appendix G. A 0.75 million point sparse Fourier
transform chip \\
The algorithm \\
The architecture \\
The chip \\
References \\
Author biography",
}
@Book{Li:2018:NSD,
author = "Zhilin Li and Zhonghua Qiao and Tao Tang",
title = "Numerical solution of differential equations:
introduction to finite difference and finite element
methods",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "ix + 293",
year = "2018",
DOI = "https://doi.org/10.1017/9781316678725",
ISBN = "1-107-16322-6 (hardcover), 1-316-61510-3 (paperback),
1-316-67872-5",
ISBN-13 = "978-1-107-16322-5 (hardcover), 978-1-316-61510-2
(paperback)",
LCCN = "QA371 .L59 2018",
bibdate = "Tue Jan 9 07:30:12 MST 2018",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
abstract = "This introduction to finite difference and finite
element methods is aimed at graduate students who need
to solve differential equations. The prerequisites are
few (basic calculus, linear algebra, and ODEs) and so
the book will be accessible and useful to readers from
a range of disciplines across science and engineering.
Part I begins with finite difference methods. Finite
element methods are then introduced in Part II. In each
part, the authors begin with a comprehensive discussion
of one-dimensional problems, before proceeding to
consider two or higher dimensions. An emphasis is
placed on numerical algorithms, related mathematical
theory, and essential details in the implementation,
while some useful packages are also introduced. The
authors also provide well-tested MATLAB codes, all
available online.",
acknowledgement = ack-nhfb,
author-dates = "1956--",
subject = "Differential equations; Numerical solutions",
}
@Book{Meckes:2018:LA,
author = "Elizabeth S. Meckes and Mark W. Meckes",
title = "Linear Algebra",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xvi + 427",
year = "2018",
ISBN = "1-107-17790-1 (hardcover)",
ISBN-13 = "978-1-107-17790-1 (hardcover)",
LCCN = "QA184.2 .M43 2018",
bibdate = "Tue Feb 26 17:13:01 MST 2019",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Cambridge mathematical textbooks",
abstract = "\booktitle{Linear Algebra} offers a unified treatment
of both matrix-oriented and theoretical approaches to
the course, which will be useful for classes with a mix
of mathematics, physics, engineering, and computer
science students. Major topics include singular value
decomposition, the spectral theorem, linear systems of
equations, vector spaces, linear maps, matrices,
eigenvalues and eigenvectors, linear independence,
bases, coordinates, dimension, matrix factorizations,
inner products, norms, and determinants.",
acknowledgement = ack-nhfb,
subject = "Algebras, Linear; Textbooks; Lineare Algebra",
}
@Book{Salehi:2018:NISa,
author = "Younes Salehi and William E. Schiesser",
title = "Numerical integration of space fractional partial
differential equations. {Volume 1}, {Introduction} to
algorithms and computer coding in {R}",
volume = "19",
publisher = "Morgan and Claypool Publishers",
address = "San Rafael, CA, USA",
pages = "xii + 189",
year = "2018",
DOI = "https://doi.org/10.2200/S00806ED1V01Y201709MAS019",
ISBN = "1-68173-207-6 (paperback), 1-68173-208-4 (e-book)",
ISBN-13 = "978-1-68173-207-7 (paperback), 978-1-68173-208-4
(e-book)",
ISSN = "1938-1743 (print), 1938-1751 (electronic)",
ISSN-L = "1938-1743",
LCCN = "QA372 .S266 2018",
bibdate = "Tue Mar 13 17:09:10 MDT 2018",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/s-plus.bib",
series = "Synthesis lectures on mathematics and statistics",
abstract = "Partial differential equations (PDEs) are one of the
most used widely forms of mathematics in science and
engineering. PDEs can have partial derivatives with
respect to (1) an initial value variable, typically
time, and (2) boundary value variables, typically
spatial variables. Therefore, two fractional PDEs can
be considered, (1) fractional in time (TFPDEs), and (2)
fractional in space (SFPDEs). The two volumes are
directed to the development and use of SFPDEs, with the
discussion divided as: Vol 1: Introduction to
Algorithms and Computer Coding in R Vol 2: Applications
from Classical Integer PDEs. Various definitions of
space fractional derivatives have been proposed. We
focus on the Caputo derivative, with occasional
reference to the Riemann--Liouville derivative. The
Caputo derivative is defined as a convolution integral.
Thus, rather than being local (with a value at a
particular point in space), the Caputo derivative is
non-local (it is based on an integration in space),
which is one of the reasons that it has properties not
shared by integer derivatives. A principal objective of
the two volumes is to provide the reader with a set of
documented R routines that are discussed in detail, and
can be downloaded and executed without having to first
study the details of the relevant numerical analysis
and then code a set of routines. In the first volume,
the emphasis is on basic concepts of SFPDEs and the
associated numerical algorithms. The presentation is
not as formal mathematics, e.g., theorems and proofs.
Rather, the presentation is by examples of SFPDEs,
including a detailed discussion of the algorithms for
computing numerical solutions to SFPDEs and a detailed
explanation of the associated source code.",
acknowledgement = ack-nhfb,
subject = "Fractional differential equations; Differential
equations, Partial; Spatial analysis (Statistics); R
(Computer program language); Differential equations,
Partial; Fractional differential equations; R (Computer
program language); Spatial analysis (Statistics)",
tableofcontents = "1. Introduction to fractional partial differential
equations \\
1.1 Introduction \\
1.2 Computer routines, example 1 \\
1.2.1 Main program \\
1.2.2 Subordinate ODE/MOL routine \\
1.2.3 Model output \\
1.3 Computer routines, example 2 \\
1.3.1 Main program \\
1.3.2 Subordinate ODE/MOL routine \\
1.3.3 Model output \\
1.3.4 Summary and conclusions \\
References \\
2. Variation in the order of the fractional derivatives
\\
2.1 Introduction \\
2.2 Computer routines, example 1 \\
2.2.1 Main program \\
2.2.2 Subordinate ODE/MOL routine \\
2.2.3 Model output \\
2.3 Computer routines, example 2 \\
2.3.1 Main program \\
2.3.2 Subordinate ODE/MOL routine \\
2.3.3 Model output \\
2.4 Summary and discussion \\
3. Dirichlet, Neumann, Robin BCs \\
3.1 Introduction \\
3.2 Example 1, Dirichlet BCs \\
3.2.1 Main program \\
3.2.2 Subordinate ODE/MOL routine \\
3.2.3 Model output \\
3.3 Example 2, Dirichlet BCs \\
3.3.1 Main program \\
3.3.2 Subordinate ODE/MOL routine \\
3.3.3 Model output \\
3.4 Example 2, Neumann BCs \\
3.4.1 Main program \\
3.4.2 Subordinate ODE/MOL routine \\
3.4.3 Model output \\
3.5 Example 2, Robin BCs \\
3.5.1 Main program \\
3.5.2 Subordinate ODE/MOL routine \\
3.5.3 Model output \\
3.6 Summary and conclusions \\
4. Convection SFPDEs \\
4.1 Introduction \\
4.2 Integer/fractional convection model \\
4.2.1 Main program \\
4.2.2 Subordinate ODE/MOL routine \\
4.2.3 SFPDE output \\
4.3 Summary and conclusions 5. Nonlinear SFPDEs \\
5.1 Introduction \\
5.1.1 Example 1 \\
5.1.2 Main program \\
5.1.3 Subordinate ODE/MOL routine \\
5.1.4 Model output \\
5.2 Example 2 \\
5.2.1 Main program \\
5.2.2 Subordinate ODE/MOL routine \\
5.2.3 Model output \\
5.3 Summary and conclusions \\
A. Analytical Caputo differentiation of selected
functions \\
B. Derivation of a SFPDE analytical solution \\
Introduction \\
SFPDE equations \\
Main program \\
ODE/MOL routine \\
Numerical output \\
Summary and conclusions \\
Authors' Biographies \\
Index",
}
@Book{Salehi:2018:NISb,
author = "Younes Salehi and William E. Schiesser",
title = "Numerical integration of space fractional partial
differential equations. {Volume 2}, {Applications} from
classical integer {PDEs}",
volume = "20",
publisher = "Morgan and Claypool Publishers",
address = "San Rafael, CA, USA",
pages = "xii + 183--375",
year = "2018",
DOI = "https://doi.org/10.2200/S00808ED1V02Y201710MAS020",
ISBN = "1-68173-209-2 (hardcover), 1-68173-210-6 (e-book)",
ISBN-13 = "978-1-68173-209-1 (hardcover), 978-1-68173-210-7
(e-book)",
ISSN = "1938-1743 (print), 1938-1751 (electronic)",
ISSN-L = "1938-1743",
LCCN = "QA372 .S2662 2018",
bibdate = "Tue Mar 13 17:13:47 MDT 2018",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/s-plus.bib",
series = "Synthesis lectures on mathematics and statistics",
abstract = "Partial differential equations (PDEs) are one of the
most used widely forms of mathematics in science and
engineering. PDEs can have partial derivatives with
respect to (1) an initial value variable, typically
time, and (2) boundary value variables, typically
spatial variables. Therefore, two fractional PDEs can
be considered, (1) fractional in time (TFPDEs), and (2)
fractional in space (SFPDEs). The two volumes are
directed to the development and use of SFPDEs, with the
discussion divided as: Vol 1: Introduction to
Algorithms and Computer Coding in R Vol 2: Applications
from Classical Integer PDEs. Various definitions of
space fractional derivatives have been proposed. We
focus on the Caputo derivative, with occasional
reference to the Riemann--Liouville derivative. In the
second volume, the emphasis is on applications of
SFPDEs developed mainly through the extension of
classical integer PDEs to SFPDEs. The example
applications are: Fractional diffusion equation with
Dirichlet, Neumann and Robin boundary conditions
Fisher--Kolmogorov SFPDE Burgers SFPDE Fokker--Planck
SFPDE Burgers--Huxley SFPDE Fitzhugh--Nagumo SFPDE.
These SFPDEs were selected because they are integer
first order in time and integer second order in space.
The variation in the spatial derivative from order two
(parabolic) to order one (first order hyperbolic)
demonstrates the effect of the spatial fractional order
$ \alpha $ with $ 1 \leq \alpha \leq 2 $. All of the
example SFPDEs are one dimensional in Cartesian
coordinates. Extensions to higher dimensions and other
coordinate systems, in principle, follow from the
examples in this second volume. The examples start with
a statement of the integer PDEs that are then extended
to SFPDEs. The format of each chapter is the same as in
the first volume. The R routines can be downloaded and
executed on a modest computer (R is readily available
from the Internet).",
acknowledgement = ack-nhfb,
subject = "Fractional differential equations; Differential
equations, Partial; Spatial analysis (Statistics);
Differential equations, Partial; Fractional
differential equations; Spatial analysis (Statistics)",
tableofcontents = "6. Simultaneous SFPDEs \\
6.1 Introduction \\
6.2 Simultaneous SFPDEs \\
6.2.1 Main program \\
6.2.2 ODE/MOL routine \\
6.2.3 SFPDEs output \\
6.2.4 Variation of the parameters \\
6.3 Summary and conclusions \\
7. Two sided SFPDEs \\
7.1 Introduction \\
7.2 Two-sided convective SFPDE, Caputo derivatives \\
7.2.1 Main program \\
7.2.2 ODE/MOL routine \\
7.2.3 SFPDE output \\
7.3 Two-sided convective SFPDE, Riemann--Liouville
derivatives \\
7.3.1 Main program \\
7.3.2 ODE/MOL routine \\
7.3.3 SFPDE output \\
7.4 Summary and conclusions \\
8. Integer to fractional extensions \\
8.1 Introduction \\
8.2 Fractional diffusion equation \\
8.2.1 Main program, Dirchlet BCs \\
8.2.2 ODE/MOL routine \\
8.2.3 Model output \\
8.2.4 Main program, Neumann BCs \\
8.2.5 ODE/MOL routine \\
8.2.6 Model output \\
8.2.7 Main program, Robin BCs \\
8.2.8 ODE/MOL routine \\
8.2.9 Model output \\
8.3 Fractional Burgers equation \\
8.3.1 Main program, Dirchlet BCs \\
8.3.2 ODE/MOL routine \\
8.3.3 Model output \\
8.4 Fractional Fokker--Planck equation \\
8.4.1 Main program \\
8.4.2 ODE/MOL routine \\
8.4.3 Model output \\
8.5 Fractional Burgers--Huxley equation \\
8.5.1 Main program \\
8.5.2 ODE/MOL routine \\
8.5.3 Model output \\
8.6 Fractional Fitzhugh--Nagumo equation \\
8.6.1 Main program \\
8.6.2 ODE/MOL routine \\
8.6.3 Model output \\
8.7 Summary and conclusions \\
Authors' biographies \\
Index",
}
@Book{Nakao:2019:NVM,
author = "Mitsuhiro T. Nakao and Michael Plum and Yoshitaka
Watanabe",
title = "Numerical Verification Methods and Computer-assisted
Proofs for Partial Differential Equations",
volume = "53",
publisher = "Springer",
address = "Singapore",
pages = "xiii + 467",
year = "2019",
DOI = "https://doi.org/10.1007/978-981-13-7669-6",
ISBN = "981-13-7668-9, 981-13-7669-7 (e-book)",
ISBN-13 = "978-981-13-7668-9 (print), 978-981-13-7669-6
(e-book)",
ISSN = "0179-3632",
LCCN = "QA377",
bibdate = "Fri Dec 6 08:15:05 MST 2019",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Springer series in computational mathematics",
URL = "https://www.springer.com/gp/book/9789811376689",
acknowledgement = ack-nhfb,
subject = "Differential equations, Partial; Automatic theorem
proving; Numerical calculations; Verification",
}
%%% ====================================================================
%%% Cross-referenced entries must come last; entries are sorted by year,
%%% and then by citation label.
@Proceedings{Bultheel:2010:BNA,
editor = "Adhemar Bultheel and Ronald Cools",
booktitle = "{The birth of numerical analysis}",
title = "{The birth of numerical analysis}",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xvii + 221",
year = "2010",
ISBN = "981-283-625-X",
ISBN-13 = "978-981-283-625-0",
LCCN = "QA297 .B54 2010",
bibdate = "Mon Aug 23 11:06:23 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
abstract = "The 1947 paper by John von Neumann and Herman
Goldstine, ``Numerical Inverting of Matrices of High
Order'' (Bulletin of the AMS, Nov. 1947), is considered
as the birth certificate of numerical analysis. Since
its publication, the evolution of this domain has been
enormous. This book is a unique collection of
contributions by researchers who have lived through
this evolution, testifying about their personal
experiences and sketching the evolution of their
respective subdomains since the early years.",
acknowledgement = ack-nhfb,
remark = "Proceedings of a symposium held at the Department of
Computer Science of the K.U. Leuven, October 29--30,
2007.",
subject = "numerical analysis; congresses; history",
}
@Book{Dick:2010:DNS,
author = "J. (Josef) Dick and Friedrich Pillichshammer",
booktitle = "Digital nets and sequences: discrepancy and
quasi-Monte Carlo integration",
title = "Digital nets and sequences: discrepancy and
quasi-Monte Carlo integration",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xvii + 600",
year = "2010",
ISBN = "0-521-19159-9 (hardback)",
ISBN-13 = "978-0-521-19159-3 (hardback)",
LCCN = "QA298 .D53 2010",
bibdate = "Fri Mar 9 13:05:10 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://assets.cambridge.org/97805211/91593/cover/9780521191593.jpg",
abstract = "This book is a comprehensive treatment of contemporary
quasi-Monte Carlo methods, digital nets and sequences,
and discrepancy theory which starts from scratch with
detailed explanations of the basic concepts and then
advances to current methods used in research. As
deterministic versions of the Monte Carlo method,
quasi-Monte Carlo rules have increased in popularity,
with many fruitful applications in mathematical
practice. These rules require nodes with good uniform
distribution properties, and digital nets and sequences
in the sense of Niederreiter are known to be excellent
candidates. Besides the classical theory, the book
contains chapters on reproducing kernel Hilbert spaces
and weighted integration, duality theory for digital
nets, polynomial lattice rules, the newest
constructions by Niederreiter and Xing and many more.
The authors present an accessible introduction to the
subject based mainly on material taught in
undergraduate courses with numerous examples, exercises
and illustrations.",
acknowledgement = ack-nhfb,
subject = "Monte Carlo method; nets (mathematics); sequences
(mathematics); numerical integration; digital filters
(mathematics)",
tableofcontents = "Preface \\
Notation \\
1. Introduction \\
2. Quasi-Monte Carlo integration, discrepancy and
reproducing kernel Hilbert spaces \\
3. Geometric discrepancy \\
4. Nets and sequences \\
5. Discrepancy estimates and average type results \\
6. Connections to other discrete objects \\
7. Duality Theory \\
8. Special constructions of digital nets and sequences
\\
9. Propagation rules for digital nets \\
10. Polynomial lattice point sets \\
11. Cyclic digital nets and hyperplane nets \\
12. Multivariate integration in weighted Sobolev spaces
\\
13. Randomisation of digital nets \\
14. The decay of the Walsh coefficients of smooth
functions \\
15. Arbitrarily high order of convergence of the
worst-case error \\
16. Explicit constructions of point sets with best
possible order of $L^2$-discrepancy \\
Appendix A. Walsh functions \\
Appendix B. Algebraic function fields \\
References \\
Index",
}
@Book{Forster:2010:FSC,
editor = "Brigitte Forster and Peter Robert Massopust",
booktitle = "Four short courses on harmonic analysis: wavelets,
frames, time-frequency methods, and applications to
signal and image analysis",
title = "Four short courses on harmonic analysis: wavelets,
frames, time-frequency methods, and applications to
signal and image analysis",
publisher = pub-BIRKHAUSER-BOSTON,
address = pub-BIRKHAUSER-BOSTON:adr,
pages = "xvii + 247",
year = "2010",
DOI = "https://doi.org/10.1007/978-0-8176-4891-6",
ISBN = "0-8176-4891-7, 0-8176-4890-9",
ISBN-13 = "978-0-8176-4891-6, 978-0-8176-4890-9",
LCCN = "QA403 .F68 2010",
bibdate = "Mon Aug 23 11:30:53 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
library.tufts.edu:210/INNOPAC",
note = "With contributions by Ole Christensen, Karlheinz
Gr{\"o}chenig, Demetrio Labate, Pierre Vandergheynst,
Guido Weiss, and Yves Wiaux.",
series = "Applied and numerical harmonic analysis",
acknowledgement = ack-nhfb,
subject = "mathematics; Fourier analysis; harmonic analysis;
abstract harmonic analysis; signal, image and speech
processing; theoretical, mathematical and computational
physics",
}
@Proceedings{Fukuda:2010:MSI,
editor = "Komei Fukuda and Joris {Van der Hoeven} and Michael
Joswig and Nobuki Takayama",
booktitle = "{Mathematical Software --- ICMS 2010: Third
International Congress on Mathematical Software, Kobe,
Japan, September 13--17, 2010, Proceedings}",
title = "{Mathematical Software --- ICMS 2010: Third
International Congress on Mathematical Software, Kobe,
Japan, September 13--17, 2010, Proceedings}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 368",
year = "2010",
ISBN = "3-642-15581-2 (paperback)",
ISBN-13 = "978-3-642-15581-9 (paperback)",
LCCN = "QA76.95 .I5654 2010",
bibdate = "Thu May 22 16:13:39 MDT 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/kepler.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Lecture Notes in Computer Science / Theoretical
Computer Science and General Issues Ser.",
URL = "http://link.springer.com/openurl?genre=book&isbn=978-3-642-15581-9",
abstract = "This book constitutes the refereed proceedings of the
Third International Congress on Mathematical Software,
ICMS 2010, held in Kobe, Japan in September 2010. The
49 revised full papers presented were carefully
reviewed and selected for presentation. The papers are
organized in topical sections on computational group
theory, computation of special functions, computer
algebra and reliable computing, computer tools for
mathematical editing and scientific visualization,
exact numeric computation for algebraic and geometric
computation, formal proof, geometry and visualization,
Groebner bases and applications, number theoretical
software as well as software for optimization and
polyhedral computation.",
acknowledgement = ack-nhfb,
keywords = "Project Flyspeck",
meetingname = "International Congress of Mathematical Software (3rd :
2010 : K{\=o}be-shi, Japan)",
subject = "Mathematics; Data processing; Congresses; Computer
software; Computer software.; Data processing.",
}
@Book{Kilmer:2010:GWS,
editor = "Misha Elena Kilmer and Dianne P. O'Leary",
booktitle = "{G. W. Stewart}: selected works with commentaries",
title = "{G. W. Stewart}: selected works with commentaries",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xii + 729",
year = "2010",
DOI = "https://doi.org/10.1007/978-0-8176-4968-5",
ISBN = "0-8176-4967-0 (hardcover), 0-8176-4968-9 (e-book)",
ISBN-13 = "978-0-8176-4967-8 (hardcover), 978-0-8176-4968-5
(e-book)",
LCCN = "QA188 .S74 2010",
bibdate = "Wed May 28 12:51:20 MDT 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Contemporary mathematicians",
acknowledgement = ack-nhfb,
URL = "http://public.eblib.com/EBLPublic/PublicView.do?ptiID=64586;
http://rave.ohiolink.edu/ebooks/ebc/978081764968;
http://site.ebrary.com/id/1042123",
abstract = "Published in honor of his 70th birthday, this volume
explores and celebrates the work of G. W. (Pete)
Stewart, a world-renowned expert in computational
linear algebra. This volume includes: forty-four of
Stewart's most influential research papers in two
subject areas: matrix algorithms, and rounding and
perturbation theory; a biography of Stewart; a complete
list of his publications, students, and honors;
selected photographs; and commentaries on his works in
collaboration with leading experts in the field.
\booktitle{G. W. Stewart: Selected Works with
Commentaries} will appeal to graduate students,
practitioners.",
subject = "Stewart, G. W (Gilbert W.); Perturbation
(Mathematics); Matrices",
tableofcontents = "Cover \\
G. W. Stewart \\
Contents \\
Foreword \\
List of Contributors \\
Part I: G. W. Stewart \\
1. Biography of G. W. Stewart \\
2. Publications, Honors, and Students \\
2.1 Publications of G. W. Stewart \\
2.2 Major Honors of G. W. Stewart \\
2.3 Ph.D. Students of G. W. Stewart \\
Part II: Commentaries \\
3. Introduction to the Commentaries \\
4. Matrix Decompositions: Linpack and Beyond \\
4.1 The Linpack Project \\
4.2 Some Algorithmic Insights \\
4.3 The Triangular Matrices of Gaussian Elimination and
Related Decompositions \\
4.4 Solving Sylvester Equations \\
4.5 Perturbation Bounds for Matrix Factorizations \\
4.6 Rank Degeneracy \\
4.7 Pivoted $QR$ as an Alternative to SVD \\
4.8 Summary \\
5. Updating and Downdating Matrix Decompositions \\
5.1 Solving Nonlinear Systems of Equations \\
5.2 More General Update Formulas for $QR$ \\
5.3 Effects of Rounding Error on Downdating Cholesky
Factorizations \\
5.4 Stability of a Sequence of Updates and Downdates
\\
5.5 An Updating Algorithm for Subspace Tracking \\
5.6 From the $URV$ to the $ULV$ \\
5.7 Impact \\
6. Least Squares, Projections, and Pseudoinverses \\
6.1 Continuity of the Pseudoinverse \\
6.2 Perturbation Theory \\
6.3 Weighted Pseudoinverses \\
6.4 Impact \\
7. The Eigenproblem and Invariant Subspaces:
Perturbation Theory \\
7.1 Perturbation of Eigenvalues of General Matrices \\
7.2 Further Results for Hermitian Matrices \\
7.3 Stochastic Matrices \\
7.4 Graded Matrices \\
7.5 Rayleigh / Ritz Approximations \\
7.6 Powers of Matrices \\
7.7 Impact \\
8. The SVD, Eigenproblem, and Invariant Subspaces:
Algorithms \\
8.1 Who Invented Subspace Iteration? \\
8.2 Extracting Invariant Subspaces \\
8.3 Approximating the SVD \\
8.4 Impact \\
9. The Generalized Eigenproblem \\
9.1 Perturbation Theory \\
9.2 The $QZ$ Algorithm \\
9.3 Gershgorin's Theorem \\
9.4 Definite Pairs \\
10. Krylov Subspace Methods for the Eigenproblem \\
10.1 A Krylov / Schur Algorithm \\
10.2 Backward Error Analysis of Krylov Subspace Methods
\\
10.3 Adjusting the Rayleigh Quotient in Lanczos Methods
\\
10.4 Impact \\
11. Other Contributions \\
References \\
Index \\
Part III: Reprints \\
12 Papers on Matrix Decompositions \\
12.1 [GWS-B / 2] (with J. J. Dongarra, J. R. Bunch, and
C. B. Moler) Introduction from Linpack Users Guide \\
12.2 [GWS-J / 17] (with R. H. Bartels), ''Algorithm
432: Solution of the Matrix Equation $AX + XB = C$''
\\
12.3 [GWS-J / 32] ''The Economical Storage of Plane
Rotations'' \\
12.4 [GWS-J / 34] ''Perturbation Bounds for the $QR$
Factorization of a Matrix'' \\
12.5 [GWS-J / 42] (with A. K. Cline, C. B. Moler, and
J. H. Wilkinson), ''An Estimate for the Condition
Number of a Matrix'' \\
12.6 [GWS-J / 49] ''Rank Degeneracy'' \\
12.7 [GWS-J / 78] ''On the Perturbation of $LU$,
Cholesky, and $QR$ Factorizations'' \\
12.8 [GWS-J / 89] ''On Graded $QR$ Decompositions of
Products of Matrices'' \\
12.9 [GWS-J / 92] ''On the Perturbation of $LU$ and
Cholesky Factors'' \\
12.10 [GWS-J / 94] ''The Triangular Matrices of
Gaussian Elimination and Related Decompositions'' \\
12.11 [GWS-J / 103] ''Four Algorithms for the the [sic]
Efficient Computation of Truncated Pivoted $QR$
Approximations to a Sparse Matrix'' \\
12.12 GWS-J / 118 (with M. W. Berry and S. A. Pulatova)
''Algorithm 844: Computing Sparse Reduced-Rank
Approximations to Sparse Matrices'' \\
13 Papers on Updating and Downdating Matrix
Decompositions \\
14 Papers on Least Squares, Projections, and
Generalized Inverses \\
15 Papers on the Eigenproblem and Invariant Subspaces:
Perturbation Theory \\
16 Papers on the SVD, Eigenproblem and Invariant
Subspaces: Algorithms \\
17 Papers on the Generalized Eigenproblem \\
18 Papers on Krylov Subspace Methods for the
Eigenproblem",
}
@Book{Stakgold:2011:GFB,
author = "Ivar Stakgold and Michael J. Holst",
title = "{Green}'s Functions and Boundary Value Problems",
volume = "99",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Third",
pages = "xxi + 855",
year = "2011",
ISBN = "0-470-60970-2 (hardcover)",
ISBN-13 = "978-0-470-60970-5 (hardcover)",
LCCN = "QA379 .S72 2011",
bibdate = "Fri Jul 27 19:07:28 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Pure and applied mathematics",
abstract = "This Third Edition includes basic modern tools of
computational mathematics for boundary value problems
and also provides the foundational mathematical
material necessary to understand and use the tools.
Central to the text is a down-to-earth approach that
shows readers how to use differential and integral
equations when tackling significant problems in the
physical sciences, engineering, and applied
mathematics, and the book maintains a careful balance
between sound mathematics and meaningful applications.
A new co-author, Michael J. Holst, has been added to
this new edition, and together he and Ivar Stakgold
incorporate recent developments that have altered the
field of applied mathematics, particularly in the areas
of approximation methods and theory including best
linear approximation in linear spaces; interpolation of
functions in Sobolev Spaces; spectral, finite volume,
and finite difference methods; techniques of nonlinear
approximation; and Petrov-Galerkin and Galerkin methods
for linear equations. Additional topics have been added
including weak derivatives and Sobolev Spaces, linear
functionals, energy methods and A Priori estimates,
fixed-point techniques, and critical and super-critical
exponent problems. The authors have revised the
complete book to ensure that the notation throughout
remained consistent and clear as well as adding new and
updated references. Discussions on modeling, Fourier
analysis, fixed-point theorems, inverse problems,
asymptotics, and nonlinear methods have also been
updated.",
acknowledgement = ack-nhfb,
subject = "Boundary value problems; Green's functions;
Mathematical physics",
tableofcontents = "Green's functions (intuitive ideas) \\
The theory of distributions \\
One-dimensional boundary value problems \\
Hilbert and Banach spaces \\
Operator theory \\
Integral equations \\
Spectral theory of second-order differential operators
\\
Partial differential equations \\
Nonlinear problems \\
Approximation theory and methods",
}
@Book{Gilli:2011:NMO,
editor = "Manfred Gilli and Dietmar Maringer and Enrico
Schumann",
booktitle = "Numerical Methods and Optimization in Finance",
title = "Numerical Methods and Optimization in Finance",
publisher = pub-ELSEVIER-ACADEMIC,
address = pub-ELSEVIER-ACADEMIC:adr,
pages = "xv + 584",
year = "2011",
ISBN = "0-12-375662-6",
ISBN-13 = "978-0-12-375662-6",
LCCN = "HG106 .G55 2011",
bibdate = "Wed Feb 8 07:35:45 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Finance; Mathematical methods",
}
@Book{Govil:2017:PAT,
editor = "Narendra Kumar Govil and Ram Mohapatra and Mohammed A.
Qazi and Gerhard Schmeisser",
booktitle = "Progress in Approximation Theory and Applicable
Complex Analysis: In Memory of {Q. I. Rahman}",
title = "Progress in Approximation Theory and Applicable
Complex Analysis: In Memory of {Q. I. Rahman}",
volume = "117",
publisher = pub-SV,
address = pub-SV:adr,
pages = "",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-49242-1",
ISBN = "3-319-49240-3 (print), 3-319-49242-X (e-book)",
ISBN-13 = "978-3-319-49240-7 (print), 978-3-319-49242-1
(e-book)",
LCCN = "QA402.5-402.6",
bibdate = "Sat Feb 10 18:46:45 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Springer Optimization and Its Applications",
URL = "https://link.springer.com/chapter/10.1007/978-3-319-49242-1",
abstract = "Current and historical research methods in
approximation theory are presented in this book
beginning with the 1800s and following the evolution of
approximation theory via the refinement and extension
of classical methods and ending with recent techniques
and methodologies. Graduate students, postdocs, and
researchers in mathematics, specifically those working
in the theory of functions, approximation theory,
geometric function theory, and optimization will find
new insights as well as a guide to advanced topics. The
chapters in this book are grouped into four themes; the
first, polynomials (Chapters 1--8), includes
inequalities for polynomials and rational functions,
orthogonal polynomials, and location of zeros. The
second, inequalities and extremal problems are
discussed in Chapters 9--13. The third, approximation
of functions, involves the approximants being
polynomials, rational functions, and other types of
functions and are covered in Chapters 14--19. The last
theme, quadrature, cubature and applications, comprises
the final three chapters and includes an article
coauthored by Rahman. This volume serves as a memorial
volume to commemorate the distinguished career of Qazi
Ibadur Rahman (1934--2013) of the Universit{\'e} de
Montr{\'e}al. Rahman was considered by his peers as one
of the prominent experts in analytic theory of
polynomials and entire functions. The novelty of his
work lies in his profound abilities and skills in
applying techniques from other areas of mathematics,
such as optimization theory and variational principles,
to obtain final answers to countless open problems.",
acknowledgement = ack-nhfb,
series-URL = "https://link.springer.com/bookseries/7393",
tableofcontents = "On the $L_2$ Markov Inequality with Laguerre Weight
\\
Markov-Type Inequalities for Products of Muntz
Polynomials Revisited \\
On Bernstein-Type Inequalities for the Polar Derivative
of a Polynomial \\
On Two Inequalities for Polynomials in the Unit Disk
\\
Inequalities for Integral Norms of Polynomials via
Multipliers \\
Some Rational Inequalities Inspired by Rahman's
Research \\
On an Asymptotic Equality for Reproducing Kernels and
Sums of Squares of Orthonormal Polynomials \\
Two Walsh-Type Theorems for the Solutions of
Multi-Affine Symmetric Polynomials \\
Vector Inequalities for a Projection in Hilbert Spaces
and Applications \\
A Half-Discrete Hardy--Hilbert-Type Inequality with a
Best Possible Constant Factor Related to the Hurwitz
Zeta Function \\
Quantum Integral Inequalities for Generalized Convex
Functions \\
Quantum integral inequalities for generalized preinvex
functions \\
On the Bohr inequality \\
Bernstein-Type Polynomials on Several Intervals \\
Best Approximation by Logarithmically Concave Classes
of Functions \\
Local approximation using Hermite functions \\
Approximating the Riemann Zeta and Related Functions
\\
Overconvergence of Rational Approximants of Meromorphic
Functions \\
Approximation by Bernstein--Faber--Walsh and
Sz{\'a}sz--Mirakjan--Faber--Walsh Operators in Multiply
Connected Compact Sets of $\mathbb{C}$ \\
Summation Formulas of Euler--Maclaurin and Abel--Plana:
Old and New Results and Applications \\
A New Approach to Positivity and Monotonicity for the
Trapezoidal Method and Related Quadrature Methods \\
A Unified and General Framework for Enriching Finite
Element Approximations",
}
@Book{Kneusel:2017:NC,
author = "Ronald T. Kneusel",
title = "Numbers and Computers",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xiii + 346",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-50508-4",
ISBN = "3-319-50507-6, 3-319-50508-4 (e-book)",
ISBN-13 = "978-3-319-50507-7, 978-3-319-50508-4 (e-book)",
LCCN = "????",
bibdate = "Tue Aug 22 05:58:01 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
URL = "http://link.springer.com/10.1007/978-3-319-50508-4",
abstract = "This is a book about numbers and how those numbers are
represented in and operated on by computers. It is
crucial that developers understand this area because
the numerical operations allowed by computers, and the
limitations of those operations, especially in the area
of floating point math, affect virtually everything
people try to do with computers. This book aims to fill
this gap by exploring, in sufficient but not
overwhelming detail, just what it is that computers do
with numbers. Divided into two parts, the first deals
with standard representations of integers and floating
point numbers, while the second examines several other
number representations. Details are explained
thoroughly, with clarity and specificity. Each chapter
ends with a summary, recommendations, carefully
selected references, and exercises to review the key
points. Topics covered include interval arithmetic,
fixed-point numbers, big integers and rational
arithmetic. This new edition has three new chapters:
Pitfalls of Floating-Point Numbers (and How to Avoid
Them), Arbitrary Precision Floating Point, and Other
Number Systems. This book is for anyone who develops
software including software engineers, scientists,
computer science students, engineering students and
anyone who programs for fun.",
acknowledgement = ack-nhfb,
subject = "Number theory; Numerals; Numeration; Computer science;
Mathematics; Mathematics; Number theory; Numerals;
Numeration; Arithmetic and Logic Structures; Numeric
Computing; Arithmetik; Informatik; Software Engineering.",
tableofcontents = "Number Systems \\
Integers \\
Floating Point \\
Pitfalls of Floating-Point Numbers (and How to Avoid
Them) \\
Big Integers and Rational Arithmetic \\
Fixed-Point Numbers \\
Decimal Floating Point \\
Interval Arithmetic \\
Arbitrary Precision Floating-Point \\
Other Number Systems",
}
@Book{Saad:2011:NML,
author = "Youcef Saad",
booktitle = "Numerical Methods for Large Eigenvalue Problems",
title = "Numerical Methods for Large Eigenvalue Problems",
volume = "66",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Second",
pages = "xv + 276",
year = "2011",
ISBN = "1-61197-072-5",
ISBN-13 = "978-1-61197-072-2",
LCCN = "QA188 .S18 2011",
bibdate = "Fri Jun 10 21:37:06 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Classics in applied mathematics",
URL = "http://www.cs.umn.edu/~saad/eig_book_2ndEd.pdf",
acknowledgement = ack-nhfb,
subject = "Nonsymmetric matrices; Eigenvalues",
}
@Proceedings{Blowey:2012:FNA,
editor = "James Blowey and Max Jensen",
booktitle = "{Frontiers in Numerical Analysis --- Durham 2010}",
title = "{Frontiers in Numerical Analysis --- Durham 2010}",
volume = "85",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "xi + 282",
pages = "xi + 282",
year = "2012",
CODEN = "LNCSA6",
DOI = "https://doi.org/10.1007/978-3-642-23914-4",
ISBN = "3-642-23913-7 (print), 3-642-23914-5 (e-book)",
ISBN-13 = "978-3-642-23913-7 (print), 978-3-642-23914-4
(e-book)",
ISSN = "1439-7358",
ISSN-L = "1439-7358",
LCCN = "????",
bibdate = "Thu Dec 20 14:35:54 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/lncse.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
note = "Proceedings of the Twelfth LMS--EPSRC Summer School in
Computational Mathematics and Scientific Computation
held at the University of Durham, UK, 25--31 July
2010.",
series = ser-LNCSE,
URL = "http://link.springer.com/book/10.1007/978-3-642-23914-4;
http://www.springerlink.com/content/978-3-642-23914-4",
acknowledgement = ack-nhfb,
series-URL = "http://link.springer.com/bookseries/3527",
}
@Proceedings{Graham:2012:NAM,
editor = "Ivan G. Graham and Thomas Y. Hou and Omar Lakkis and
Robert Scheichl",
booktitle = "Numerical Analysis of Multiscale Problems",
title = "Numerical Analysis of Multiscale Problems",
volume = "83",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "vii + 363",
pages = "vii + 363",
year = "2012",
CODEN = "LNCSA6",
DOI = "https://doi.org/10.1007/978-3-642-22061-6",
ISBN = "3-642-22060-6 (print), 3-642-22061-4 (e-book)",
ISBN-13 = "978-3-642-22060-9 (print), 978-3-642-22061-6
(e-book)",
ISSN = "1439-7358",
ISSN-L = "1439-7358",
LCCN = "QA297 .N844 2012",
bibdate = "Thu Dec 20 14:35:50 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/lncse.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
note = "Ten invited expository articles from the 91st LMS
Durham Symposium on {\em Numerical Analysis of
Multiscale Problems}, Durham, UK, 5--15 July 2010.",
series = ser-LNCSE,
URL = "http://link.springer.com/book/10.1007/978-3-642-22061-6;
http://www.springerlink.com/content/978-3-642-22061-6",
acknowledgement = ack-nhfb,
series-URL = "http://link.springer.com/bookseries/3527",
}
@Proceedings{Achdou:2013:HJE,
editor = "Yves Achdou and Guy Barles and Hitoshi Ishii and
Grigory L. Litvinov",
booktitle = "{Hamilton--Jacobi Equations: Approximations, Numerical
Analysis and Applications: Cetraro, Italy 2011}",
title = "{Hamilton--Jacobi Equations: Approximations, Numerical
Analysis and Applications: Cetraro, Italy 2011}",
volume = "2074",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xv + 301",
year = "2013",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/978-3-642-36433-4",
ISBN = "3-642-36432-2 (print), 3-642-36433-0 (e-book)",
ISBN-13 = "978-3-642-36432-7 (print), 978-3-642-36433-4
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
LCCN = "QA3 .L28 no. 2074; QA3 .L28 no. 2074; QA316 .C56
2011",
bibdate = "Tue May 6 14:56:48 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/lnm2010.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = ser-LECT-NOTES-MATH,
URL = "http://link.springer.com/book/10.1007/978-3-642-36433-4;
http://www.springerlink.com/content/978-3-642-36433-4",
acknowledgement = ack-nhfb,
remark = "Editors: Paola Loreti, Nicoletta Anna Tchou",
series-URL = "http://link.springer.com/bookseries/304",
}
@Book{Brezinski:2013:WGV,
author = "Claude Brezinski and Ahmed Sameh",
booktitle = "{Walter Gautschi}, Volume 1: Selected Works with
Commentaries",
title = "{Walter Gautschi}, Volume 1: Selected Works with
Commentaries",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xi + 694 + 50",
year = "2013",
DOI = "https://doi.org/10.1007/978-1-4614-7034-2",
ISBN = "1-4614-7033-1, 1-4614-7034-X",
ISBN-13 = "978-1-4614-7033-5, 978-1-4614-7034-2",
LCCN = "QA297",
bibdate = "Thu Jan 9 19:14:41 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Contemporary Mathematicians",
URL = "http://site.ebrary.com/id/10787871",
abstract = "Walter Gautschi has written extensively on topics
ranging from special functions, quadrature and
orthogonal polynomials to difference and differential
equations, software implementations, and the history of
mathematics. He is world renowned for his pioneering
work in numerical analysis and constructive orthogonal
polynomials, including a definitive textbook in the
former, and a monograph in the latter area.",
acknowledgement = ack-nhfb,
subject = "Gautschi, Walter; Gautschi, Walter,; Mathematical
analysis; Numerical analysis; Mathematical analysis.;
Numerical analysis.",
subject-dates = "1927--",
tableofcontents = "Preface \\
Part I Walter Gautschi \\
Biography of Walter Gautschi \\
A brief summary of my scientific work and highlights of
my career \\
Publications \\
Part II Commentaries \\
Numerical conditioning \\
Special functions \\
Interpolation and approximation \\
Part III Reprints \\
Numerical conditioning \\
Special functions \\
Interpolation and approximation",
}
@Book{Trefethen:2013:ATA,
author = "Lloyd N. Trefethen",
title = "Approximation Theory and Approximation Practice",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "viii + 305",
year = "2013",
ISBN = "1-61197-239-6 (paperback)",
ISBN-13 = "978-161-197-2-39-9 (paperback)",
LCCN = "QA221 .T73 2013",
MRclass = "41-01 (41-04 65-06)",
MRnumber = "3012510",
MRreviewer = "Ana Cristina Matos",
bibdate = "Fri Jun 21 15:10:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
acknowledgement = ack-nhfb,
tableofcontents = "1. Introduction \\
2. Chebyshev Points and Interpolants \\
3. Chebyshev Polynomials and Series \\
4. Interpolants, Projections, and Aliasing \\
5. Barycentric Interpolation Formula \\
6. Weierstrass Approximation Theorem \\
7. Convergence for Differentiable Functions \\
8. Convergence for Analytic Functions \\
9. Gibbs Phenomenon \\
10. Best Approximation \\
11. Hermite Integral Formula \\
12. Potential Theory and Approximation \\
13. Equispaced Points, Runge Phenomenon \\
14. Discussion of High-Order Interpolation \\
15. Lebesgue Constants \\
16. Best and Near-Best \\
17. Orthogonal Polynomials \\
18. Polynomial Roots and Colleague Matrices \\
19. Clenshaw--Curtis and Gauss Quadrature \\
20. Carath{\'e}odory--Fej{\'e}r Approximation \\
21. Spectral Methods \\
22. Linear Approximation: Beyond Polynomials \\
23. Nonlinear Approximation: Why Rational Functions \\
24. Rational Best Approximation \\
25. Two Famous Problems \\
26. Rational Interpolation and Linearized Least-Squares
\\
27. Pad{\'e} Approximation \\
28. Analytic Continuation and Convergence Acceleration
\\
Appendix: Six Myths of Polynomial Interpolation and
Quadrature \\
References \\
Index",
}
@Book{Wartak:2013:CPI,
author = "Marek S. Wartak",
title = "Computational photonics: an introduction with
{MATLAB}",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xiii + 452",
year = "2013",
ISBN = "1-107-00552-3 (hardcover)",
ISBN-13 = "978-1-107-00552-5 (hardcover)",
LCCN = "TK8304 .W37 2013",
bibdate = "Mon Feb 29 05:42:22 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://assets.cambridge.org/97811070/05525/cover/9781107005525.jpg",
abstract = "A comprehensive manual on the efficient modeling and
analysis of photonic devices through building numerical
codes, this book provides graduate students and
researchers with the theoretical background and MATLAB
programs necessary for them to start their own
numerical experiments. Beginning by summarizing topics
in optics and electromagnetism, the book discusses
optical planar waveguides, linear optical fiber, the
propagation of linear pulses, laser diodes, optical
amplifiers, optical receivers, finite-difference
time-domain method, beam propagation method and some
wavelength division devices, solitons, solar cells and
metamaterials. Assuming only a basic knowledge of
physics and numerical methods, the book is ideal for
engineers, physicists and practicing scientists. It
concentrates on the operating principles of optical
devices, as well as the models and numerical methods
used to describe them.",
acknowledgement = ack-nhfb,
subject = "Optoelectronic devices; Mathematical models;
Photonics; Mathematics; MATLAB; SCIENCE / Optics",
tableofcontents = "1. Introduction \\
2. Basic facts from optics \\
3. Basic facts from electromagnetism \\
4. Slab waveguides \\
5. Linear optical fibre and signal degradation \\
6. Propagation of linear pulses \\
7. Optical sources \\
8. Optical amplifiers and EDFA \\
9. Semiconductor optical amplifiers (SOA) \\
10. Optical receivers \\
11. Finite difference time domain (FDTD) formulation
\\
12. Solar cells \\
13. Metamaterials \\
Appendices \\
Index",
}
@Book{Arfken:2013:MMP,
author = "George B. (George Brown) Arfken and Hans-J{\"u}rgen
Weber and Frank E. Harris",
booktitle = "Mathematical Methods for Physicists: a Comprehensive
Guide",
title = "Mathematical Methods for Physicists: a Comprehensive
Guide",
publisher = pub-ELSEVIER-ACADEMIC,
address = pub-ELSEVIER-ACADEMIC:adr,
edition = "Seventh",
pages = "xiii + 1205",
year = "2013",
ISBN = "0-12-384654-4 (hardcover)",
ISBN-13 = "978-0-12-384654-9 (hardcover)",
LCCN = "QA37.3 .A74 2013",
bibdate = "Thu May 3 08:02:53 MDT 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
jenson.stanford.edu:2210/unicorn",
acknowledgement = ack-nhfb,
subject = "Mathematical analysis; Mathematical physics",
tableofcontents = "Preface / xi--xiii \\
1: Mathematical Preliminaries / 1--82 \\
2: Determinants and Matrices / 83--121 \\
3: Vector Analysis / 123--203 \\
4: Tensors and Differential Forms / 205--249 \\
5: Vector Spaces / 251--297 \\
6: Eigenvalue Problems / 299--328 \\
7: Ordinary Differential Equations / 329--380 \\
8: Sturm--Liouville Theory / 381--399 \\
9: Partial Differential Equations / 401--445 \\
10: Green's Functions / 447--467 \\
11: Complex Variable Theory / 469--550 \\
12: Further Topics in Analysis / 551--598 \\
13: Gamma Function / 599--641 \\
14: Bessel Functions / 643--713 \\
15: Legendre Functions / 715--772 \\
16: Angular Momentum / 773--814 \\
17: Group Theory / 815--870 \\
18: More Special Functions / 871--933 \\
19: Fourier Series / 935--962 \\
20: Integral Transforms / 963--1046 \\
21: Integral Equations / 1047--1079 \\
22: Calculus of Variations / 1081--1124 \\
23: Probability and Statistics / 1125--1179 \\
Index / 1181--1205",
}
@Book{Brezinski:2014:WGVa,
editor = "Claude Brezinski and Ahmed Sameh",
booktitle = "{Walter Gautschi}. Volume 2: selected works with
commentaries",
title = "{Walter Gautschi}. Volume 2: selected works with
commentaries",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xiii + 914 + 33",
year = "2014",
DOI = "https://doi.org/10.1007/978-1-4614-7049-6",
ISBN = "1-4614-7048-X, 1-4614-7049-8 (e-book)",
ISBN-13 = "978-1-4614-7048-9, 978-1-4614-7049-6 (e-book)",
LCCN = "QA404.5",
bibdate = "Thu Jan 9 19:16:48 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Contemporary mathematicians",
URL = "http://link.springer.com/10.1007/978-1-4614-7049-6",
abstract = "Walter Gautschi has written extensively on topics
ranging from special functions, quadrature and
orthogonal polynomials to difference and differential
equations, software implementations, and the history of
mathematics. He is world renowned for his pioneering
work in numerical analysis and constructive orthogonal
polynomials, including a definitive textbook in the
former, and a monograph in the latter area. This
three-volume set, Walter Gautschi: Selected Works with
Commentaries, is a compilation of Gautschis most
influential papers and includes commentaries by leading
experts. The work begins with a detailed biographical
section and ends with a section commemorating Walters
prematurely deceased twin brother. This title will
appeal to graduate students and researchers in
numerical analysis, as well as to historians of
science. Selected Works with Commentaries, Vol. 1
Numerical Conditioning Special Functions Interpolation
and Approximation Selected Works with Commentaries,
Vol. 2 Orthogonal Polynomials on the Real Line
Orthogonal Polynomials on the Semicircle Chebyshev
Quadrature Kronrod and Other Quadratures Gauss-type
Quadrature Selected Works with Commentaries, Vol. 3
Linear Difference Equations Ordinary Differential
Equations Software History and Biography Miscellanea
Works of Werner Gautschi.",
acknowledgement = ack-nhfb,
subject = "Gautschi, Walter; Orthogonal polynomials; Numerical
integration; Mathematics; Numerical Analysis",
subject-dates = "1927--",
tableofcontents = "Part I: Commentaries \\
Orthogonal polynomials on the real line / Gradimir V.
Milovanovi{\'c} \\
Polynomials orthogonal on the semicircle / Lothar
Reichel \\
Chebyshev quadrature / Jaap Korevaar \\
Kronrod and other quadratures / Giovanni Monegato \\
Gauss-type quadrature / Walter Van Assche \\
Part II: Reprints \\
Papers on Orthogonal Polynomials on the Real Line /
Walter Gautschi \\
Papers on Orthogonal Polynomials on the Semicircle /
Walter Gautschi \\
Papers on Chebyshev Quadrature / Walter Gautschi \\
Papers on Kronrod and Other Quadratures / Walter
Gautschi \\
Papers on Gauss-type Quadrature / Walter Gautschi",
}
@Book{Brezinski:2014:WGVb,
editor = "Claude Brezinski and Ahmed Sameh",
booktitle = "{Walter Gautschi}. Volume 3: selected works with
commentaries",
title = "{Walter Gautschi}. Volume 3: selected works with
commentaries",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xi + 767 + 91 + 29",
year = "2014",
DOI = "https://doi.org/10.1007/978-1-4614-7132-5",
ISBN = "1-4614-7131-1, 1-4614-7132-X (e-book)",
ISBN-13 = "978-1-4614-7131-8, 978-1-4614-7132-5 (e-book)",
LCCN = "QA431",
bibdate = "Thu Jan 9 19:20:40 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Contemporary mathematicians",
URL = "http://link.springer.com/10.1007/978-1-4614-7132-5",
abstract = "Walter Gautschi has written extensively on topics
ranging from special functions, quadrature and
orthogonal polynomials to difference and differential
equations, software implementations, and the history of
mathematics. He is world renowned for his pioneering
work in numerical analysis and constructive orthogonal
polynomials, including a definitive textbook in the
former, and a monograph in the latter area. This
three-volume set, Walter Gautschi: Selected Works with
Commentaries, is a compilation of Gautschis most
influential papers and includes commentaries by leading
experts. The work begins with a detailed biographical
section and ends with a section commemorating Walters
prematurely deceased twin brother. This title will
appeal to graduate students and researchers in
numerical analysis, as well as to historians of
science. Selected Works with Commentaries, Vol. 1
Numerical Conditioning Special Functions Interpolation
and Approximation Selected Works with Commentaries,
Vol. 2 Orthogonal Polynomials on the Real Line
Orthogonal Polynomials on the Semicircle Chebyshev
Quadrature Kronrod and Other Quadratures Gauss-type
Quadrature Selected Works with Commentaries, Vol. 3
Linear Difference Equations Ordinary Differential
Equations Software History and Biography Miscellanea
Works of Werner Gautschi.",
acknowledgement = ack-nhfb,
subject = "Gautschi, Walter; Gautschi, Walter,; Difference
equations; Differential equations; Mathematical
Computing; MATHEMATICS; Calculus.; Mathematical
Analysis.; Difference equations.; Differential
equations.",
subject-dates = "1927--",
tableofcontents = "Part I: Commentaries \\
Linear recurrence relations / Lisa Lorentzen \\
Ordinary differential equations / John Butcher \\
Computer algorithms and software packages / Gradimir V.
Milovanovi{\'c} \\
History and biography / Gerhard Wanner \\
Miscellanea / Martin J. Gander \\
Part II: Reprints \\
Papers on Linear Recurrence Relations / Walter Gautschi
\\
Papers on Ordinary Differential Equations / Walter
Gautschi \\
Papers on Computer Algorithms and Software Packages /
Walter Gautschi \\
Papers on History and Biography / Walter Gautschi \\
Papers on Miscellanea / Walter Gautschi \\
Part III: Werner Gautschi \\
Publications / Werner Gautschi \\
Obituaries \\
Recording / Trout Quintet",
}
@Proceedings{Reich:2015:IPO,
editor = "Simeon Reich and Alexander J. Zaslavski",
booktitle = "{Infinite products of operators and their
applications: a research workshop of the Israel Science
Foundation: May 21--24, 2012, Haifa, Israel: Israel
mathematical conference proceedings}",
title = "{Infinite products of operators and their
applications: a research workshop of the Israel Science
Foundation: May 21--24, 2012, Haifa, Israel: Israel
mathematical conference proceedings}",
volume = "636",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "xi + 266",
year = "2015",
DOI = "https://doi.org/10.1090/conm/636",
ISBN = "1-4704-1480-5 (paperback)",
ISBN-13 = "978-1-4704-1480-1 (paperback)",
LCCN = "QA329 .I54 2015",
MRclass = "15-XX; 40-XX; 41-XX; 46-XX; 47-XX; 49-XX; 54-XX;
58-XX; 62-XX; 65-XX; 90-XX",
bibdate = "Fri Aug 12 19:13:19 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
series = "Contemporary mathematics",
URL = "http://www.ams.org/books/conm/636/",
acknowledgement = ack-nhfb,
subject = "Operator theory; Congresses; Operator spaces; Ergodic
theory; Mathematics; Linear and multilinear algebra;
matrix theory; Sequences, series, summability;
Approximations and expansions; Functional analysis;
Operator theory; Calculus of variations and optimal
control; optimization; General topology; Global
analysis, analysis on manifolds; Statistics; Numerical
analysis; Operations research, mathematical
programming.",
}
@Proceedings{Greuel:2016:MSI,
editor = "Gert-Martin Greuel",
booktitle = "{Mathematical Software --- ICMS 2016: 5th
International Conference, Berlin, Germany, July 11--14,
2016: proceedings}",
title = "{Mathematical Software --- ICMS 2016: 5th
International Conference, Berlin, Germany, July 11--14,
2016: proceedings}",
volume = "9725",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxiv + 532",
year = "2016",
DOI = "https://doi.org/10.1007/978-3-319-42432-3",
ISBN = "3-319-42431-9 (print), 3-319-42432-7 (electronic)",
ISBN-13 = "978-3-319-42431-6 (print), 978-3-319-42432-3
(electronic)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "QA76.9.M35",
bibdate = "Mon Feb 5 08:28:37 MST 2018",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = ser-LNCS # "\slash " # ser-LNAI,
URL = "http://zbmath.org/?q=an:1342.68017",
abstract = "This book constitutes the proceedings of the 5th
International Conference on Mathematical Software, ICMS
2015, held in Berlin, Germany, in July 2016. The 68
papers included in this volume were carefully reviewed
and selected from numerous submissions. The papers are
organized in topical sections named: univalent
foundations and proof assistants; software for
mathematical reasoning and applications; algebraic and
toric geometry; algebraic geometry in applications;
software of polynomial systems; software for
numerically solving polynomial systems; high-precision
arithmetic, effective analysis, and special functions;
mathematical optimization; interactive operation to
scientific artwork and mathematical reasoning;
information services for mathematics: software,
services, models, and data; semDML: towards a semantic
layer of a world digital mathematical library;
miscellanea.",
acknowledgement = ack-nhfb,
}