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Persistent URL http://purl.org/net/epubs/work/30767490
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Record Id 30767490
Title A max-plus approach to incomplete Cholesky factorization preconditioners
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Abstract We present a new method for constructing incomplete Cholesky factorization preconditioners for use in solving large sparse symmetric positive-definite linear systems. This method uses max-plus algebra to predict the positions of the largest entries in the Cholesky factor and then uses these positions as the sparsity pattern for the preconditioner. Our method builds on the max-plus incomplete LU factorization preconditioner recently proposed in [J. Hook and F. Tisseur, Incomplete LU preconditioner based on max-plus approximation of LU factorization, MIMS Eprint2016.47, Manchester, 2016] but applied to symmetric positive-definite matrices, which comprise an important special case for the method and its application. An attractive feature of our approach is that the sparsity pattern of each column of the preconditioner can be computed in parallel. Numerical comparisons are made with other incomplete Cholesky factorization preconditioners using problems from a range of practical applications. We demonstrate that the new preconditioner can outperform traditional level-based preconditioners and offer a based approach.
Organisation STFC , SCI-COMP , SCI-COMP-CM
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Language English (EN)
Type Details URI(s) Local file(s) Year
Preprint RAL Preprints RAL-P-2016-009, SIAM J Sci Comput 2016. RAL-P-2016-009.pdf 2016