Journal of Applied Mathematics
Volume 2013 (2013), Article ID 676978, 6 pages
http://dx.doi.org/10.1155/2013/676978
Research Article

On the Positive Definite Solutions of a Nonlinear Matrix Equation

Panpan Liu,1 Shugong Zhang,1 and Qingchun Li2

1School of Mathematics, Key Laboratory of Symbolic Computation and Knowledge Engineering (Ministry of Education), Jilin University, Changchun 130012, China
2Department of Mathematics, Beihua University, Jilin 132013, China

Received 28 November 2012; Revised 19 April 2013; Accepted 21 April 2013

Academic Editor: J. Biazar

Copyright © 2013 Panpan Liu 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 positive definite solutions of the nonlinear matrix equation are discussed. A necessary and sufficient condition for the existence of positive definite solutions for this equation is derived. Then, the uniqueness of the Hermitian positive definite solution is studied based on an iterative method proposed in this paper. Lastly the perturbation analysis for this equation is discussed.