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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 124979, 7 pages
http://dx.doi.org/10.1155/2013/124979
Research Article

Iterative Solution 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 17 May 2013; Accepted 21 September 2013

Academic Editor: Masoud Hajarian

Copyright © 2013 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

An efficient iterative algorithm is presented to solve a system of linear matrix equations , with real matrices and . By this iterative algorithm, the solvability of the system can be determined automatically. When the system is consistent, for any initial matrices and , a solution can be obtained in the absence of roundoff errors, and the least norm solution can be obtained by choosing a special kind of initial matrix. In addition, the unique optimal approximation solutions and to the given matrices and in Frobenius norm can be obtained by finding the least norm solution of a new pair of matrix equations , where , . The given numerical example demonstrates that the iterative algorithm is efficient. Especially, when the numbers of the parameter matrices are large, our algorithm is efficient as well.