A supernodal out-of-core sparse Gaussian-elimination method

Sivan Toledo, Anatoli Uchitel

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We present an out-of-core sparse direct solver for unsymmetric linear systems. The solver factors the coefficient matrix A into A∈=∈PLU using Gaussian elimination with partial pivoting. It assumes that A fits within main memory, but it stores the L and U factors on disk (that is, in files). Experimental results indicate that on small to moderately-large matrices (whose factors fit or almost fit in main memory), our code achieves high performance, comparable to that of SuperLU. In some of these cases it is somewhat slower than SuperLU due to overheads associated with the out-of-core behavior of the algorithm (in particular the fact that it always writes the factors to files), but not by a large factor. But in other cases it is faster than SuperLU, probably due to more efficient use of the cache. However, it is able to factor matrices whose factors are much larger than main memory, although at lower computational rates.

Original languageEnglish
Title of host publicationParallel Processing and Applied Mathematics - 7th International Conference, PPAM 2007, Revised Selected Papers
PublisherSpringer Verlag
Number of pages10
ISBN (Print)3540681051, 9783540681052
StatePublished - 2008
Event7th International Conference on Parallel Processing and Applied Mathematics, PPAM 2007 - Gdansk, Poland
Duration: 9 Sep 200712 Sep 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4967 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference7th International Conference on Parallel Processing and Applied Mathematics, PPAM 2007


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