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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 685753, 7 pages
http://dx.doi.org/10.1155/2013/685753
Research Article

On the Iterative Method for the System of Nonlinear Matrix Equations

Faculty of Science and Arts, Qassim University, Buraydah 51431, P.O. Box 1162, Saudi Arabia

Received 15 November 2012; Accepted 20 February 2013

Academic Editor: Mohammad T. Darvishi

Copyright © 2013 Asmaa M. Al-Dubiban. 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 positive definite solutions for the system of nonlinear matrix equations are considered, where are two positive integers and A, B are nonsingular complex matrices. Some sufficient conditions for the existence of positive definite solutions for the system are derived. Under some conditions, an iterative algorithm for computing the positive definite solutions for the system is proposed. Also, the estimation of the error is obtained. Finally, some numerical examples are given to show the efficiency of the proposed iterative algorithm.