Premium
Symmetric Permutations for I‐Matrices to Avoid Small Pivots During Incomplete Factorization
Author(s) -
Mayer Jan
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810821
Subject(s) - row , mathematics , factorization , diagonal , combinatorics , permutation (music) , permutation matrix , row and column spaces , matrix (chemical analysis) , diagonally dominant matrix , preconditioner , block matrix , algorithm , iterative method , pure mathematics , computer science , invertible matrix , geometry , circulant matrix , eigenvalues and eigenvectors , physics , materials science , database , quantum mechanics , acoustics , composite material
Incomplete LU–factorizations have been very successful as preconditioners for solving sparse linear systems iteratively. However, for unsymmetric, indefinite systems small pivots (or even zero pivots) are often very detrimental to the quality of the preconditioner. A fairly recent strategy to deal with this problem has been to permute the rows of the matrix and to scale rows and columns to produce an I–matrix, a matrix having elements of modulus one on the diagonal and elements of at most modulus one elsewhere. These matrices are generally more suited for incomplete LU–factorization. I–matrices are preserved by symmetric permutation, i.e. by applying the same permutation to rows and columns of a matrix. We discuss different approaches for constructing such permutations which aim at improving the sparsity and diagonal dominance of an initial block. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)