NDLI: Efficient Sparse Cholesky Factorization on a Massively Parallel SIMD Computer

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Manne, Fredrik Hafsteinsson, Hjlmtr
Copyright Year	1995
Abstract	We investigate the effect of load balancing when performing Cholesky factorization on a massively parallel SIMD computer. In particular we describe a supernodal algorithm for performing sparse Cholesky factorization. The way the matrix is mapped onto the processors has significant effect on its efficiency. We show that this assignment problem can be modeled as a graph coloring problem in a weighted graph. By a simple greedy algorithm, we obtain substantial speedup compared with previously suggested data mapping schemes. Experimental runs have been made on a 16K processor MasPar MP-2 parallel computer using symmetric test matrices with irregular sparsity structure. On these problems our implementation achieves performance rates of well above 200 Mflops in double precision arithmetic.
Starting Page	934
Ending Page	950
Page Count	17
File Format	PDF
ISSN	10648275
DOI	10.1137/0916054
e-ISSN	10957197
Issue Number	4
Volume Number	16
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-13
Access Restriction	Subscribed
Subject Keyword	MasPar systems of linear equations Factorization of matrices Direct methods for linear systems and matrix inversion graph coloring data parallel algorithms Graph algorithms sparse matrix algorithms Sparse matrices parallel computing Cholesky factorization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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