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Mathematical Problems in Engineering
Volume 2014, Article ID 539215, 13 pages
http://dx.doi.org/10.1155/2014/539215
Research Article

(Anti-)Hermitian Generalized (Anti-)Hamiltonian Solution to a System of Matrix Equations

1Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444, China
2Department of Basic Mathematics, China University of Petroleum, Qingdao 266580, China
3School of Mathematics and Science, Shijiazhuang University of Economics, Shijiazhuang 050031, China

Received 12 August 2013; Revised 14 November 2013; Accepted 14 November 2013; Published 25 March 2014

Academic Editor: Masoud Hajarian

Copyright © 2014 Juan Yu 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

We mainly solve three problems. Firstly, by the decomposition of the (anti-)Hermitian generalized (anti-)Hamiltonian matrices, the necessary and sufficient conditions for the existence of and the expression for the (anti-)Hermitian generalized (anti-)Hamiltonian solutions to the system of matrix equations are derived, respectively. Secondly, the optimal approximation solution is obtained, where is the (anti-)Hermitian generalized (anti-)Hamiltonian solution set of the above system and is the given matrix. Thirdly, the least squares (anti-)Hermitian generalized (anti-)Hamiltonian solutions are considered. In addition, algorithms about computing the least squares (anti-)Hermitian generalized (anti-)Hamiltonian solution and the corresponding numerical examples are presented.