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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 352327, 9 pages
http://dx.doi.org/10.1155/2014/352327
Research Article

Generalized Reflexive and Generalized Antireflexive Solutions to a System of Matrix Equations

1Department of Mathematics, Shanghai University, Shanghai 200444, China
2School of Mathematics and Statistics, Suzhou University, Suzhou 234000, China

Received 23 March 2013; Accepted 30 December 2013; Published 23 February 2014

Academic Editor: Jinyun Yuan

Copyright © 2014 Yong Lin 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

Two efficient iterative algorithms are presented to solve a system of matrix equations + , + over generalized reflexive and generalized antireflexive matrices. By the algorithms, the least norm generalized reflexive (antireflexive) solutions and the unique optimal approximation generalized reflexive (antireflexive) solutions to the system can be obtained, too. For any initial value, it is proved that the iterative solutions obtained by the proposed algorithms converge to their true values. The given numerical examples demonstrate that the iterative algorithms are efficient.