This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section.
Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the JacobióDavidson method, and automatic multilevel substructuring.
This book is intended for researchers in applied mathematics and scientific computing as well as for practitioners interested in understanding the theory of numerical methods used for eigenvalue problems. It also can be used as a supplemental text for an advanced graduate-level course on these methods.
Preface to the Classics Edition;
Chapter One: Background in Matrix Theory and Linear Algebra;
Chapter Two: Sparse Matrices;
Chapter Three: Perturbation Theory and Error Analysis;
Chapter Four: The Tools of Spectral Approximation;
Chapter Five: Subspace Iteration;
Chapter Six: Krylov Subspace Methods;
Chapter Seven: Filtering and Restarting Techniques;
Chapter Eight: Preconditioning Techniques;
Chapter Nine: Non-Standard Eigenvalue Problems;
Chapter Ten: Origins of Matrix Eigenvalue Problems;
About the Author
Yousef Saad is a College of Science and Engineering distinguished professor in the Department of Computer Science at the University of Minnesota. His current research interests include numerical linear algebra, sparse matrix computations, iterative methods, parallel computing, numerical methods for electronic structure, and data analysis. He is a Fellow of SIAM and the AAAS.
To request an examination copy or desk copy of this book, please use our online request form at www.siam.org/catalog/adopt.php.
eigenvalues, sparse matrices, large matrices, Krylov methods, matrix computations
2011 / xvi + 276 pages / Softcover / ISBN 978-1-611970-72-2
List Price $70.00 / Member Price $49.00 / Order Code CL66