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Sparse Gaussian Elimination on High Performance Computers (1996)
BibTeX
@MISC{Charge96sparsegaussian,
author = {Committee In Charge and Katherine A. Yelick and John R. Gilbert and Phillip Colella and Xiaoyes S. Li and Xiaoye S. Li and James W. Demmel},
title = {Sparse Gaussian Elimination on High Performance Computers},
year = {1996}
}
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Abstract
Sparse Gaussian Elimination on High Performance Computers by XiaoyeS.Li Doctor of Philosophy in Computer Science University of California at Berkeley James W. Demmel, Chair This dissertation presents new techniques for solving large sparse unsymmetric linear systems on high performance computers, using Gaussian elimination with partial pivoting. The e#ciencies of the new algorithms are demonstrated for matrices from various #elds and for a variety of high performance machines. In the #rst part we discuss optimizations of a sequential algorithm to exploit the memory hierarchies that exist in most RISC-based superscalar computers. We begin with the left-looking supernode-column algorithm by Eisenstat, Gilbert and Liu, which includes Eisenstat and Liu's symmetric structural reduction for fast symbolic factorization. Our key contribution is to develop both numeric and symbolic schemes to perform supernodepanel updates to achieve better data reuse in cache and #oating-point registers...
Keyphrases
high performance computer sparse gaussian elimination fast symbolic factorization symbolic scheme data reuse symmetric structural reduction sequential algorithm large sparse unsymmetric linear system partial pivoting li doctor left-looking supernode-column algorithm oating-point register risc-based superscalar computer high performance machine new technique rst part memory hierarchy berkeley james computer science university supernodepanel update key contribution new algorithm gaussian elimination various eld
