Synopses & Reviews
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.
Synopsis
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.
Synopsis
Watkins provides readers with a comprehensive introduction to the fundamentals of numerical linear algebra. Updated with the latest material in the field, this second edition now uses MATLAB for many of the exercises and examples. It also covers applications for electrical circuits, mass-spring systems, and simple partial differential equations. New sections are also included on methods of solving large, sparse eigenvalue problems with discussions of the popular implicitly-restarted Arnold and Jacobi-Davidson methods.
About the Author
DAVID S. WATKINS, PhD, is Professor of Mathematics at Washington State University.
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.