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Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods

Richard Barrett, Michael W. Berry, Tony F. Chan, James Demmel, June Donato, Jack Dongarra, Victor Eijkhout, Roldan Pozo, Charles Romine, and Henk van der Vorst

In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist. Templates, a description of a general algorithm rather than the executable object or source code more commonly found in a conventional software library, offer whatever degree of customization the user may desire.

Templates offer three distinct advantages: they are general and reusable; they are not language specific; and they exploit the expertise of both the numerical analyst, who creates a template reflecting in-depth knowledge of a specific numerical technique, and the computational scientist, who then provides "value-added" capability to the general template description, customizing it for specific needs.

For each template that is presented, the authors provide: a mathematical description of the flow of algorithm; discussion of convergence and stopping criteria to use in the iteration; suggestions for applying a method to special matrix types; advice for tuning the template; tips on parallel implementations; and hints as to when and why a method is useful.

Partial Contents

Chapter 1: Introduction, Why Use Templates?, What Methods Are Covered? Chapter 2: Iterative Methods, Overview of the Methods, Stationary Iterative Methods, Nonstationary Iterative Methods, Summary of the Methods, A Short History of Krylov Methods, Survey of Recent Krylov Methods; Chapter 3: Preconditioners, The Why and How, Jacobi Preconditioning, SSOR Preconditioning, Incomplete Factorization Preconditioners, Polynomial Preconditioners, Other Preconditioners; Chapter 4: Related Issues, Complex Systems, Stopping Criteria, Data Structures, Parallelism; Chapter 5: Remaining Topics, The Lanczos Connection, Block Iterative Methods, Reduced System Preconditioning, Domain Decomposition Methods, Multigrid Methods, Row Projection Methods; Appendix A: Obtaining the Software; Appendix B: Overview of the BLAS; Appendix C: Glossary.

Royalties from the sale of this book are contributed to the SIAM Student Travel Fund.

1993 / xiii + 112 pages / Softcover / ISBN-13: 978-0-898713-28-2 / ISBN-10: 0-89871-328-5 /
List Price $43.00 / SIAM Member Price $30.10 / Order Code OT43
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