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Abstract and Applied Analysis
Volume 2014, Article ID 137486, 7 pages
http://dx.doi.org/10.1155/2014/137486
Research Article

A Matrix Iteration for Finding Drazin Inverse with Ninth-Order Convergence

1Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa
3Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran

Received 31 January 2014; Accepted 11 March 2014; Published 14 April 2014

Academic Editor: Sofiya Ostrovska

Copyright © 2014 A. S. Al-Fhaid 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

The aim of this paper is twofold. First, a matrix iteration for finding approximate inverses of nonsingular square matrices is constructed. Second, how the new method could be applied for computing the Drazin inverse is discussed. It is theoretically proven that the contributed method possesses the convergence rate nine. Numerical studies are brought forward to support the analytical parts.