Fundamentals of Matrix Computations / Edition 2

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Overview

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.
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Editorial Reviews

Booknews
A textbook for graduate and advanced undergraduate students who are familiar with elementary linear algebra and conversant in a high-level programming language such as Fortran, Pascal, or C. Concerned with the teaching efficient and accurate matrix computations, which underlie most scientific computer codes. Annotation c. Book News, Inc., Portland, OR (booknews.com)
From The Critics
This text explains matrix computations and the accompanying theory in detail, for practicing scientists and graduate and advanced undergraduate students. This second edition makes use of MATLAB for many of the exercises and examples, although Fortran exercises from the first edition have been retained. The new edition contains a new chapter on iterative methods, and an introduction to new methods for solving large, sparse eigenvalue problems including the popular implicitly-restarted Arnoldi and Jacobi-Davidson methods. Watkins teaches mathematics at Washington State University. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Meet the Author

DAVID S. WATKINS, PhD, is Professor of Mathematics at Washington State University.
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Table of Contents

Preface.

Acnowledgments.

Gaussian Elimination and its Variants.

Sensitivity of Linear Systems.

The Least Squares Problem.

The Singular Value Decomposition.

Eigenvalues and Eigenvectors I.

Eigenvalues and Eigenvectors II.

Iterative Methods for Linear Systems.

Appendix: Some Sources of Software for Matrix Computations.

References.

Index.

Index of MATLAB Terms.

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