Refining an approximate inverse

Direct methods have made remarkable progress in the computational efficiency of factorization algorithms during the last three decades. The advances in graph theoretic algorithms have not received enough attention from the iterative methods community. For example, we demonstrate how symbolic factori...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2000-11, Vol.123 (1), p.293-306
Main Authors: Bridson, Robert, Tang, Wei-Pai
Format: Article
Language:English
Subjects:
Approximate inverse
Cache
Ordering
Preconditioner
Symbolic factorization
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Summary:Direct methods have made remarkable progress in the computational efficiency of factorization algorithms during the last three decades. The advances in graph theoretic algorithms have not received enough attention from the iterative methods community. For example, we demonstrate how symbolic factorization algorithms from direct methods can accelerate the computation of a factored approximate inverse preconditioner. For very sparse preconditioners, however, a reformulation of the algorithm with outer products can exploit even more zeros to good advantage. We also explore the possibilities of improving cache efficiency in the application of the preconditioner through reorderings. The article ends by proposing a block version of the algorithm for further gains in efficiency and robustness.
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(00)00399-X