# Parallel Numerical Linear Algebra

### James W. Demmel, Michael T. Heath and Henk A. van der Vorst

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-92-703

October 1992

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1992/CSD-92-703.pdf

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, the singular value decomposition, and generalizations of these to two matrices. We consider dense, band and sparse matrices.

BibTeX citation:

@techreport{Demmel:CSD-92-703, Author = {Demmel, James W. and Heath, Michael T. and van der Vorst, Henk A.}, Title = {Parallel Numerical Linear Algebra}, Institution = {EECS Department, University of California, Berkeley}, Year = {1992}, Month = {Oct}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1992/6255.html}, Number = {UCB/CSD-92-703}, 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, the singular value decomposition, and generalizations of these to two matrices. We consider dense, band and sparse matrices.} }

EndNote citation:

%0 Report %A Demmel, James W. %A Heath, Michael T. %A van der Vorst, Henk A. %T Parallel Numerical Linear Algebra %I EECS Department, University of California, Berkeley %D 1992 %@ UCB/CSD-92-703 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1992/6255.html %F Demmel:CSD-92-703