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Journal of Applied Mathematics
Volume 2014, Article ID 128249, 8 pages
Research Article

Notes on the Hermitian Positive Definite Solutions of a Matrix Equation

1School of Mathematics and Statistics, Shandong University, Weihai 264209, China
2School of Mathematics, Shandong University, Jinan 250100, China

Received 15 January 2014; Revised 26 March 2014; Accepted 15 April 2014; Published 6 May 2014

Academic Editor: Alexander Timokha

Copyright © 2014 Jing Li and Yuhai Zhang. 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.


The nonlinear matrix equation, with is investigated. A fixed point theorem in partially ordered sets is proved. And then, by means of this fixed point theorem, the existence of a unique Hermitian positive definite solution for the matrix equation is derived. Some properties of the unique Hermitian positive definite solution are obtained. A residual bound of an approximate solution to the equation is evaluated. The theoretical results are illustrated by numerical examples.