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International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 179481, 6 pages
Research Article

On the Relation between the AINV and the FAPINV Algorithms

Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran

Received 26 July 2009; Accepted 3 November 2009

Academic Editor: Victor Nistor

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.


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.