Extensions of Certain Graph-based Algorithms for Preconditioning

The original TPABLO algorithms are a collection of algorithms which compute a symmetric permutation of a linear system such that the permuted system has a relatively full block diagonal with relatively large nonzero entries. This block diagonal can then be used as a preconditioner. We propose and an...

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Vydáno v:SIAM journal on scientific computing Ročník 29; číslo 5; s. 2144 - 2161
Hlavní autoři: Fritzsche, David, Frommer, Andreas, Szyld, Daniel B.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 01.01.2007
Témata:
Algorithms
Applied mathematics
Decomposition
Experiments
ISSN:1064-8275, 1095-7197
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Shrnutí:The original TPABLO algorithms are a collection of algorithms which compute a symmetric permutation of a linear system such that the permuted system has a relatively full block diagonal with relatively large nonzero entries. This block diagonal can then be used as a preconditioner. We propose and analyze three extensions of this approach: We incorporate a nonsymmetric permutation to obtain a large diagonal, we use a more general parametrization for TPABLO, and we use a block Gauss-Seidel preconditioner which can be implemented to have the same execution time as the corresponding block Jacobi preconditioner. Experiments are presented showing that for certain classes of matrices, the block Gauss-Seidel preconditioner used with the system permuted with the new algorithm can outperform the best ILUT preconditioners in a large set of experiments.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:1064-8275
1095-7197
DOI:10.1137/060661284