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Parallel Numerical Linear Algebra (1993)
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| Citations: | 769 - 23 self |
BibTeX
@MISC{Demmel93parallelnumerical,
author = {James W. Demmel and Michael T. Heath and Henk A. van der Vorst},
title = {Parallel Numerical Linear Algebra},
year = {1993}
}
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Abstract
We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We illustrate these principles using current architectures and software systems, and by showing how one would implement matrix multiplication. Then, we present direct and iterative algorithms for solving linear systems of equations, linear least squares problems, the symmetric eigenvalue problem, the nonsymmetric eigenvalue problem, and the singular value decomposition. We consider dense, band and sparse matrices.
Keyphrases
parallel numerical linear algebra square problem singular value decomposition basic operation nonsymmetric eigenvalue problem parallel architecture current architecture open problem basic principle parallel processing survey general technique numerical linear algebra parallel machine software system iterative algorithm efficient algorithm symmetric eigenvalue problem matrix multiplication linear system sparse matrix general principle
