Numerical Linear Algebra on High-Performance Computers

Provides a rapid introduction to the world of vector and parallel processing for these linear algebra applications.

Jack J. Dongarra (Author), Iain S. Duff (Author), Danny C. Sorensen (Author), Hank A. van der Vorst (Author)

9780898714289, Society for Industrial and Applied Mathematics

Paperback / softback, published 1 January 1987

360 pages
25.5 x 17.5 x 1.8 cm, 0.6 kg

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.

About the authors
Preface
Introduction
1. High performance computing
2. Overview of current high-performance computers
3. Implementation details and overhead
4. Performance: analysis, modeling, and measurements
5. Building blocks in linear algebra
6. Direct solution of sparse linear systems
7. Krylov subspaces: projection
8. Iterative methods for linear systems
9. Preconditioning and parallel preconditioning
10. Linear Eigenvalue problems Ax=lx
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.

Subject Areas: Algebra [PBF]