FACTORIZED APPROXIMATE INVERSES WITH ADAPTIVE DROPPING

• ID: 2734, RIV: 10331031
• ISSN: 1064-8275, ISBN: not specified
• source: SIAM Journal of Scientific Computing
• keywords: approximate inverses; incomplete factorization; Gram-Schmidt orthogonalization; preconditioned iterative methods
• authors: Jiri Kopal, Miroslav Rozloznik, Miroslav Tůma
• authors from KNM: Tůma Miroslav

Abstract

This paper presents a new approach to constructing factorized approximate inverses for a symmetric and positive definite matrix A. The proposed strategy is based on adaptive dropping that reflects the quality of preserving the relation UZ = I between the direct factor U and the inverse factor Z satisfying A = (UU)-U-T and A(-1) = ZZ(T). An important part of the approach is column pivoting, used to minimize the growth of the condition number of leading principal submatrices of U that occurs explicitly in the dropping criterion. Numerical experiments demonstrate that the resulting approximate inverse factorization is robust as a preconditioner for solving large and sparse systems of linear equations.