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Journal of Applied Mathematics
Volume 2014, Article ID 681605, 7 pages
http://dx.doi.org/10.1155/2014/681605
Research Article

Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation

1School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China
2Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061, China
3College of Science, China University of Mining and Technology, Jiangsu 221116, China

Received 19 October 2013; Revised 30 March 2014; Accepted 13 April 2014; Published 7 May 2014

Academic Editor: Zhi-Hong Guan

Copyright © 2014 Zhigang Jia 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 solvability theory of an important self-adjoint polynomial matrix equation is presented, including the boundary of its Hermitian positive definite (HPD) solution and some sufficient conditions under which the (unique or maximal) HPD solution exists. The algebraic perturbation analysis is also given with respect to the perturbation of coefficient matrices. An efficient general iterative algorithm for the maximal or unique HPD solution is designed and tested by numerical experiments.