Publication at Faculty of Mathematics and Physics |
2016
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.