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Journal of Applied Mathematics
Volume 2014, Article ID 731562, 8 pages
http://dx.doi.org/10.1155/2014/731562
Research Article

Approximating the Inverse of a Square Matrix with Application in Computation of the Moore-Penrose Inverse

1Department of Mathematics, Zahedan Branch, Islamic Azad University, Zahedan, Iran
2Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Received 3 January 2014; Revised 13 February 2014; Accepted 27 February 2014; Published 31 March 2014

Academic Editor: Juan R. Torregrosa

Copyright © 2014 F. Soleymani et al. 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

This paper presents a computational iterative method to find approximate inverses for the inverse of matrices. Analysis of convergence reveals that the method reaches ninth-order convergence. The extension of the proposed iterative method for computing Moore-Penrose inverse is furnished. Numerical results including the comparisons with different existing methods of the same type in the literature will also be presented to manifest the superiority of the new algorithm in finding approximate inverses.