Numerical Linear Algebra for High-Performance Computers

by Jack J. Dongarra, Iain S. Duff, Danny C. Sorensen, and Henk A. van der Vorst

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1998 / xviii + 342 pages / Softcover / ISBN: 978-0-898714-28-9 / List Price $69.50 / SIAM Member Price $48.65 / Order Code SE07

This book presents a unified treatment of recently developed techniques and current understanding about solving systems of linear equations and large scale eigenvalue problems on high-performance computers. It provides a rapid introduction to the world of vector and parallel processing for these linear algebra applications.

Topics include major elements of advanced-architecture computers and their performance, recent algorithmic development, and software for direct solution of dense matrix problems, direct solution of sparse systems of equations, iterative solution of sparse systems of equations, and solution of large sparse eigenvalue problems.

This book supercedes the SIAM publication Solving Linear Systems on Vector and Shared Memory Computers, which appeared in 1990. The new book includes a considerable amount of new material in addition to incorporating a substantial revision of existing text.

Contents (abbreviated)
About the Authors; Preface; Introduction; Chapter 1: High Performance Computing; Chapter 2: Overview of Current High-Performance Computers; Chapter 3: Implementation Details and Overhead; Chapter 4: Performance: Analysis, Modeling, and Measurements; Chapter 5: Building Blocks in Linear Algebra; Chapter 6: Direct Solution of Sparse Linear Systems; Chapter 7: Krylov Subspaces: Projection; Chapter 8: Iterative Methods for Linear Systems; Chapter 9: Preconditioning and Parallel Preconditioning; Chapter 10: Linear Eigenvalue Problems Ax=lx; Chapter 11: The Generalized Eigenproblem; Appendix A: Acquiring Mathematical Software; Appendix B: Glossary; Appendix C: Level 1, 2, and 3 BLAS Quick Reference; Appendix D: Operation Counts for Various BLAS and Decompositions; Bibliography; Index.

Royalties from the sale of this book are contributed to the SIAM student travel fund.

ISBN: 9780898714289