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Parallel numerical linear algebra

Published online by Cambridge University Press:  07 November 2008

James W. Demmel ,
Michael T. Heath  and
Henk A. van der Vorst
James W. Demmel
Affiliation:
Computer Science Division and Mathematics DepartmentUniversity of California at BerkeleyBerkeley, CA 94720USA E-mail: [email protected]
Michael T. Heath
Affiliation:
Department of Computer Science and National Center for Supercomputing ApplicationsUniversity of IllinoisUrbana, IL 61801USA E-mail: [email protected]
Henk A. van der Vorst
Affiliation:
Mathematical InstituteUtrecht UniversityUtrecht, The Netherlands E-mail: [email protected]
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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 paralled 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.

Type
Research Article
Information
Acta Numerica , Volume 2 , January 1993 , pp. 111 - 197
Copyright
Copyright © Cambridge University Press 1993

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