Nested-dissection orderings for sparse LU with partial pivoting

Igor Brainman, Sivan Toledo

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

1 Scopus citations

Abstract

We describe the implementation and performance of a novel fill-minimization ordering technique for sparse LU factorization with partial pivoting. The technique was proposed by Gilbert and Schreiber in 1980 but never implemented and tested. Like other techniques for ordering sparse matrices for LU with partial pivoting, our new method preorders the columns of the matrix (the row permutation is chosen by the pivoting sequence during the numerical factorization). Also like other methods, the column permutation Q that we select is a permutation that minimizes the fill in the Cholesky factor of QTATAQ. Unlike existing column-ordering techniques, which all rely on minimum-degree heuristics, our new method is based on a nested-dissection ordering of ATA. Our algorithm, however, never computes a representation of ATA, which can be expensive. We only work with a representation of A itself. Our experiments demonstrate that the method is efficient and that it can reduce fill significanly relative to the best existing methods. The method reduces the LU running time on some very large matrices (tens of millions of nonzeros in the factors) by more than a factor of 2.

Original languageEnglish
Title of host publicationNumerical Analysis and Its Applications - 2nd International Conference, NAA 2000, Revised Papers
EditorsLubin Vulkov, Plamen Yalamov, Jerzy Waniewski
PublisherSpringer Verlag
Pages125-133
Number of pages9
ISBN (Print)9783540418146
DOIs
StatePublished - 2001
Event2nd International Conference on Numerical Analysis and Its Applications, NAA 2000 - Rousse, Bulgaria
Duration: 11 Jun 200015 Jun 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1988
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference2nd International Conference on Numerical Analysis and Its Applications, NAA 2000
Country/TerritoryBulgaria
CityRousse
Period11/06/0015/06/00

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