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Introduction to parallel and vector solution of linear systems / James M. Ortega.

By: Ortega, James M, 1932-.
Material type: TextTextSeries: Frontiers of computer science: Publisher: New York : Plenum Press, c1988Description: xi, 305 p. : ill. ; 24 cm.ISBN: 0306428628; 9780306428623.Subject(s): Equations -- Numerical solutions -- Data processing | Parallel processing (Electronic computers) | Supercomputers | Algebra Linear equations Numerical solutionDDC classification: 515/.252 Other classification: 31.76 | *65F05 | 65-02 | 65F10 | 65Y05 | 68N25
Contents:
Introduction: Vector and parallel computers -- Basic concepts of parallelism and vectorization -- Matrix multiplication -- Direct methods for linear equations: Direct methods for vector computers -- Direct methods for parallel computers -- Banded systems -- Iterative methods for linear equations: Jacobi's method -- The Gauss-Seidel and SOR iterations -- Minimization methods -- The preconditioned conjugate gradient method -- Appendix 1. The ijk forms of LU and Choleski decomposition -- Appendix 2. Convergence of iterative methods -- Appendix 3. The conjugate gradient algorithm -- Appendix 4. Basic linear algebra.
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Item type Current location Call number Status Date due Barcode
Book University of Texas At Tyler
Stacks - 3rd Floor
QA218 .O78 1988 (Browse shelf) Available 0000000360974

Includes bibliographical references (p. 285-298) and index.

Introduction: Vector and parallel computers -- Basic concepts of parallelism and vectorization -- Matrix multiplication -- Direct methods for linear equations: Direct methods for vector computers -- Direct methods for parallel computers -- Banded systems -- Iterative methods for linear equations: Jacobi's method -- The Gauss-Seidel and SOR iterations -- Minimization methods -- The preconditioned conjugate gradient method -- Appendix 1. The ijk forms of LU and Choleski decomposition -- Appendix 2. Convergence of iterative methods -- Appendix 3. The conjugate gradient algorithm -- Appendix 4. Basic linear algebra.

Reviews provided by Syndetics

CHOICE Review

Ortega's is one of the more serious books dealing with parallel computing. In the first chapter he describes the salient features of the pipelined-vector and parallel computers, and provides a very good introduction to many of the standard measures of performance and factors that affect them. Ortega then discusses direct methods, covering the three standard techniques for factoring a matrix--LU, Cholesky, and orthogonal factorizations. He concentrates in large part on how to organize the computations that would exploit the structure of parallel and vector machines. He finishes with an in-depth coverage of parallel iterative techniques, contained in Chapter 3. Appendixes cover the basic facts from linear algebra, conjugate gradient method, and proof of convergence of iterative techniques. This book would be suitable for a second-level college course on numerical methods. It includes a number of exercise problems and an extensive bibliography. A welcome and a timely addition to the growing literature on parallel computing for college and university libraries. -S. Lakshmivarahan, University of Oklahoma

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