
Accession Number : ADA326874
Title : An Evaluation of LeftLooking, RightLooking and Multifrontal Approaches to Sparse Cholesky Factorization on HierarchicalMemory Machines,
Corporate Author : STANFORD UNIV CA DEPT OF COMPUTER SCIENCE
Personal Author(s) : Rothberg, Edward ; Gupta, Anoop
PDF Url : ADA326874
Report Date : AUG 1991
Pagination or Media Count : 49
Abstract : In this paper we present a comprehensive analysis of the performance of a variety of sparse Cholesky factorization methods on hierarchicalmemory machines. We investigate methods that vary along two different axel along the first axis, we consider three different highlevel approaches to sparse factorization: leftlooking, rightlooking, and multifrontal. Along the second axis, we consider the implementation of each of these highlevel approaches using different sets of primitives. The primitives vary based on the structures they manipulate. One important structure in sparse Cholesky factorization is a single column of the matrix. We first consider primitives that manipulate single columns. These are the most commonly used primitives for expressing the sparse Cholesky computation. Another important structure is the supemode, a set of columns with identical nonzero structure. We consider sets of primitives that exploit the supemodal structure of the matrix to varying degrees. We find that primitives that manipulate larger structures greatly increase the amount of exploitable data reuse, thus leading to dramatically higher performance on hierarchicalmemory machines.
Descriptors : *DISTRIBUTED DATA PROCESSING, *SYSTEMS ANALYSIS, ALGORITHMS, DATA MANAGEMENT, COMPUTER COMMUNICATIONS, MULTIPROCESSORS, SPARSE MATRIX, STRUCTURED PROGRAMMING, COMPUTER BENCHMARKING.
Subject Categories : Computer Systems
Computer Programming and Software
Distribution Statement : APPROVED FOR PUBLIC RELEASE