Symmetric permutations for I-matrices to delay and avoid small pivots during factorization
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Publication Details
Output type: Journal article
Author list: Mayer J
Publisher: Society for Industrial and Applied Mathematics
Publication year: 2007
Journal: SIAM Journal on Scientific Computing (1064-8275)
Volume number: 30
Issue number: 2
Start page: 982
End page: 996
Number of pages: 15
ISSN: 1064-8275
eISSN: 1095-7197
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Open access status: green
Full text URL: https://publikationen.bibliothek.kit.edu/1000005031/246126
Abstract
In this article, we present several new permutations for I-matrices making these more suitable for incomplete LU-factorization preconditioners used in solving linear systems by iterative methods. A general matrix can be transformed by row permutation as well as row and columns scaling into an I-matrix, i.e., a matrix having elements of modulus 1 on the diagonal and elements of modulus of no more than 1 elsewhere. Reordering rows and columns by the same permutation clearly preserves I-matrices. In this article, we consider such reordering techniques which make the permuted matrix more suitable for an incomplete LU-factorization preconditioner than the original I-matrix. We use a multilevel ILUC, an incomplete LU-factorization preconditioner using Grout's implementation of Gaussian elimination without pivoting to test these reorderings. The combination of I-matrix preprocessing with the various algorithms presented here and the multilevel incomplete LU-factorizations forms a powerful preconditioning method for unsymmetric, highly indefinite problems. The C++ code has been made available in the software package ILU++.
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