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Parallel Matrix Decompositions: Have we been doing it all wrong?
- Carter Edwards
- Po Geng
- Abani Patra
- Texas Institute for Computational and Applied Mathematics
- University of Texas at Austin
- Austin, TX 78712
- Robert van de Geijn
- Texas Institute for Computational and Applied Mathematics
- and
- Department of Computer Sciences
- University of Texas at Austin
- Austin, TX 78712
Abstract
The basic premise of this essay is that traditional matrix
decompositions for distributing matrices on distributed memory
parallel architectures are in practice too restrictive. The primary
problem lies with the fact that such decompositions start with the
matrix, not with the underlying physical problem. Through a series of
examples, we show how this hampers convenient interfaces between
applications and libraries. In some instances, we show how it hampers
performance in general. We propose a new data decomposition, {\em
Physically Based Matrix Decompositions}, which appear to show
promise for solving the
encountered problems. Some traditionally used distributions are shown
to be a special, but often unnatural, case of this more general class
of decompositions.
C. Edwards, P. Geng, A. Patra, and R. van de Geijn,
"Parallel Matrix Decompositions: have we been doing it all wrong?"
TR-95-39, Department of Computer Sciences, University of
Texas, Oct. 1995.