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Journal of Applied Mathematics
Volume 2014, Article ID 515816, 17 pages
http://dx.doi.org/10.1155/2014/515816
Research Article

Iterative Methods to Solve the Generalized Coupled Sylvester-Conjugate Matrix Equations for Obtaining the Centrally Symmetric (Centrally Antisymmetric) Matrix Solutions

1School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China
2College of Fujian Jiangxia, Fuzhou 350108, China

Received 5 February 2014; Accepted 13 June 2014; Published 8 July 2014

Academic Editor: Sazzad Hossien Chowdhury

Copyright © 2014 Yajun Xie and Changfeng Ma. 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 iterative method is presented for obtaining the centrally symmetric (centrally antisymmetric) matrix pair solutions of the generalized coupled Sylvester-conjugate matrix equations , . On the condition that the coupled matrix equations are consistent, we show that the solution pair can be obtained within finite iterative steps in the absence of round-off error for any initial value given centrally symmetric (centrally antisymmetric) matrix. Moreover, by choosing appropriate initial value, we can get the least Frobenius norm solution for the new generalized coupled Sylvester-conjugate linear matrix equations. Finally, some numerical examples are given to illustrate that the proposed iterative method is quite efficient.