Catalogue


Fundamentals of matrix computations /
David S. Watkins.
edition
2nd ed.
imprint
New York : Wiley-Interscience, c2002.
description
xiii, 618 p. : ill. ; 25 cm.
ISBN
0471213942 (acid-free paper)
format(s)
Book
Holdings
Subjects
subject
More Details
imprint
New York : Wiley-Interscience, c2002.
isbn
0471213942 (acid-free paper)
catalogue key
4701131
 
Includes bibliographical references (p. 605-610) and indexes.
A Look Inside
About the Author
Author Affiliation
David S. Watkins, PhD, is Professor of Mathematics at Washington State University.
Reviews
This item was reviewed in:
SciTech Book News, September 2002
To find out how to look for other reviews, please see our guides to finding book reviews in the Sciences or Social Sciences and Humanities.
Summaries
Bowker Data Service Summary
Matrix computations lie at the heart of most scientific computational tasks. This volume explains computations and the accompanying theory clearly providing insight into this complex area.
Back Cover Copy
A significantly revised and improved introduction to a critical aspect of scientific computationMatrix computations lie at the heart of most scientific computational tasks. For any scientist or engineer doing large-scale simulations, an understanding of the topic is essential. Fundamentals of Matrix Computations, Second Edition explains matrix computations and the accompanying theory clearly and in detail, along with useful insights.This Second Edition of a popular text has now been revised and improved to appeal to the needs of practicing scientists and graduate and advanced undergraduate students. New to this edition is the use of MATLAB for many of the exercises and examples, although the Fortran exercises in the First Edition have been kept for those who want to use them. This new edition includes: Numerous examples and exercises on applications including electrical circuits, elasticity (mass-spring systems), and simple partial differential equations Early introduction of the singular value decomposition A new chapter on iterative methods, including the powerful preconditioned conjugate-gradient method for solving symmetric, positive definite systems An introduction to new methods for solving large, sparse eigenvalue problems including the popular implicitly-restarted Arnoldi and Jacobi-Davidson methods With in-depth discussions of such other topics as modern componentwise error analysis, reorthogonalization, and rank-one updates of the QR decomposition, Fundamentals of Matrix Computations, Second Edition will prove to be a versatile companion to novice and practicing mathematicians who seek mastery of matrix computation.
Back Cover Copy
A significantly revised and improved introduction to a critical aspect of scientific computation Matrix computations lie at the heart of most scientific computational tasks. For any scientist or engineer doing large-scale simulations, an understanding of the topic is essential. Fundamentals of Matrix Computations, Second Edition explains matrix computations and the accompanying theory clearly and in detail, along with useful insights. This Second Edition of a popular text has now been revised and improved to appeal to the needs of practicing scientists and graduate and advanced undergraduate students. New to this edition is the use of MATLAB for many of the exercises and examples, although the Fortran exercises in the First Edition have been kept for those who want to use them. This new edition includes: * Numerous examples and exercises on applications including electrical circuits, elasticity (mass-spring systems), and simple partial differential equations * Early introduction of the singular value decomposition * A new chapter on iterative methods, including the powerful preconditioned conjugate-gradient method for solving symmetric, positive definite systems * An introduction to new methods for solving large, sparse eigenvalue problems including the popular implicitly-restarted Arnoldi and Jacobi-Davidson methods With in-depth discussions of such other topics as modern componentwise error analysis, reorthogonalization, and rank-one updates of the QR decomposition, Fundamentals of Matrix Computations, Second Edition will prove to be a versatile companion to novice and practicing mathematicians who seek mastery of matrix computation.
Table of Contents
Prefacep. ix
Acknowledgmentsp. xiii
Gaussian Elimination and Its Variantsp. 1
Matrix Multiplicationp. 1
Systems of Linear Equationsp. 11
Triangular Systemsp. 23
Positive Definite Systems: Cholesky Decompositionp. 32
Banded Positive Definite Systemsp. 54
Sparse Positive Definite Systemsp. 63
Gaussian Elimination and the LU Decompositionp. 70
Gaussian Elimination with Pivotingp. 93
Sparse Gaussian Eliminationp. 106
Sensitivity of Linear Systemsp. 111
Vector and Matrix Normsp. 112
Condition Numbersp. 120
Perturbing the Coefficient Matrixp. 133
A Posteriori Error Analysis Using the Residualp. 137
Roundoff Errors; Backward Stabilityp. 139
Propagation of Roundoff Errorsp. 148
Backward Error Analysis of Gaussian Eliminationp. 157
Scalingp. 171
Componentwise Sensitivity Analysisp. 175
The Least Squares Problemp. 181
The Discrete Least Squares Problemp. 181
Orthogonal Matrices, Rotators, and Reflectorsp. 185
Solution of the Least Squares Problemp. 212
The Gram-Schmidt Processp. 220
Geometric Approachp. 239
Updating the QR Decompositionp. 249
The Singular Value Decompositionp. 261
Introductionp. 262
Some Basic Applications of Singular Valuesp. 266
The SVD and the Least Squares Problemp. 275
Sensitivity of the Least Squares Problemp. 281
Eigenvalues and Eigenvectors Ip. 289
Systems of Differential Equationsp. 289
Basic Factsp. 305
The Power Method and Some Simple Extensionsp. 314
Similarity Transformsp. 334
Reduction to Hessenberg and Tridiagonal Formsp. 349
The QR Algorithmp. 356
Implementation of the QR algorithmp. 372
Use of the QR Algorithm to Calculate Eigenvectorsp. 392
The SVD Revisitedp. 396
Eigenvalues and Eigenvectors IIp. 413
Eigenspaces and Invariant Subspacesp. 413
Subspace Iteration, Simultaneous Iteration, and the QR Algorithmp. 420
Eigenvalues of Large, Sparse Matrices, Ip. 433
Eigenvalues of Large, Sparse Matrices, IIp. 451
Sensitivity of Eigenvalues and Eigenvectorsp. 462
Methods for the Symmetric Eigenvalue Problemp. 476
The Generalized Eigenvalue Problemp. 502
Iterative Methods for Linear Systemsp. 521
A Model Problemp. 521
The Classical Iterative Methodsp. 530
Convergence of Iterative Methodsp. 544
Descent Methods; Steepest Descentp. 559
Preconditionersp. 571
The Conjugate-Gradient Methodp. 576
Derivation of the CG Algorithmp. 581
Convergence of the CG Algorithmp. 590
Indefinite and Nonsymmetric Problemsp. 596
Some Sources of Software for Matrix Computationsp. 603
Referencesp. 605
Indexp. 611
Index of Matlab Termsp. 617
Table of Contents provided by Syndetics. All Rights Reserved.

This information is provided by a service that aggregates data from review sources and other sources that are often consulted by libraries, and readers. The University does not edit this information and merely includes it as a convenience for users. It does not warrant that reviews are accurate. As with any review users should approach reviews critically and where deemed necessary should consult multiple review sources. Any concerns or questions about particular reviews should be directed to the reviewer and/or publisher.

  link to old catalogue

Report a problem