Symmetric Permutations for I-matrices to Delay and Avoid Small Pivots During Factorization

Authors:
Jan Mayer
Affiliations:
-
Venue:
SIAM Journal on Scientific Computing
Year:
2008

Citing 0
Cited 3

A numerical evaluation of preprocessing and ILU-type preconditioners for the solution of unsymmetric sparse linear systems using iterative methods

ACM Transactions on Mathematical Software (TOMS)
Parallel algorithms for solving linear systems with sparse triangular matrices

Computing
Combined compact difference scheme for linear second-order partial differential equations with mixed derivative

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

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 Crout'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++.