Copyright © 2009 Davod Khojasteh Salkuyeh and Hadi Roohani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The approximate inverse (AINV) and the factored approximate inverse (FAPINV) are two known algorithms in the field of preconditioning of linear systems of equations. Both of these algorithms compute a sparse approximate inverse of matrix A in the factored form and are based on computing two sets of vectors which are A-biconjugate. The AINV algorithm computes the inverse factors W and Z of a matrix independently of each other, as opposed to the AINV algorithm, where the computations of the inverse factors are done independently. In this paper, we show that, without any dropping, removing the dependence of the computations of the inverse factors in the FAPINV algorithm results in the AINV algorithm.