On the Relation between the AINV and the FAPINV AlgorithmsReport as inadecuate




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International Journal of Mathematics and Mathematical SciencesVolume 2009 2009, Article ID 179481, 6 pages

Research ArticleDepartment 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.

Abstract

The approximate inverse AINV and the factored approximate inverse FAPINVare two known algorithms in the field of preconditioning of linear systems of equations. Both of these algorithms compute a sparse approximate inverse of matrix in the factored form and are based on computing two sets of vectors which are -biconjugate. The AINV algorithm computes the inverse factors and 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 thedependence of the computations of the inverse factors in the FAPINV algorithm results in the AINV algorithm.





Author: Davod Khojasteh Salkuyeh and Hadi Roohani

Source: https://www.hindawi.com/



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