Table of Contents
International Journal of Computational Mathematics
Volume 2014, Article ID 727093, 8 pages
http://dx.doi.org/10.1155/2014/727093
Research Article

Hermitian Positive Definite Solution of the Matrix Equation

1College of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China
2College of Mathematics and Econometrics, Hunan University, Changsha 410082, China

Received 26 May 2014; Revised 10 August 2014; Accepted 9 September 2014; Published 24 September 2014

Academic Editor: Asai Asaithambi

Copyright © 2014 Chun-Mei Li and Jing-Jing Peng. 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 consider the Hermitian positive definite solution of the nonlinear matrix equation . Some new sufficient conditions and necessary conditions for the existence of Hermitian positive definite solutions are derived. An iterative method is proposed to compute the Hermitian positive definite solution. In the end, an example is used to illustrate the correctness and application of our results.