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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 461407, 15 pages
http://dx.doi.org/10.1155/2012/461407
Research Article

Iterative Algorithm for Solving a System of Nonlinear Matrix Equations

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

Received 15 August 2012; Accepted 7 November 2012

Academic Editor: Abdel-Maksoud A. Soliman

Copyright © 2012 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

We discuss the positive definite solutions for the system of nonlinear matrix equations and , where , are two positive integers. Some properties of solutions are studied, and the necessary and sufficient conditions for the existence of positive definite solutions are given. An iterative algorithm for obtaining positive definite solutions of the system is proposed. Moreover, the error estimations are found. Finally, some numerical examples are given to show the efficiency of the proposed iterative algorithm.