Journal of Applied Mathematics
Volume 2012 (2012), Article ID 784620, 13 pages
http://dx.doi.org/10.1155/2012/784620
Research Article

Perturbation Analysis for the Matrix Equation

Xue-Feng Duan1,2 and Qing-Wen Wang3

1School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China
2Research Center on Data Science and Social Computing, Guilin University of Electronic Technology, Guilin 541004, China
3Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 18 September 2012; Accepted 19 November 2012

Academic Editor: Yang Zhang

Copyright © 2012 Xue-Feng Duan and Qing-Wen Wang. 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 perturbation analysis of the matrix equation . Based on the matrix differentiation, we first give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the sharpness of the perturbation bound.