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Mathematical Problems in Engineering
Volume 2017, Article ID 1624969, 8 pages
https://doi.org/10.1155/2017/1624969
Research Article

The Relaxed Gradient Based Iterative Algorithm for the Symmetric (Skew Symmetric) Solution of the Sylvester Equation

1School of Information and Computer, Anhui Agricultural University, Hefei 230036, China
2School of Mathematics and Statistics, Fuyang Normal College, Anhui 236037, China

Correspondence should be addressed to Xingping Sheng; moc.361@gnehsgnipgnix

Received 26 February 2017; Accepted 23 March 2017; Published 3 April 2017

Academic Editor: Jean Jacques Loiseau

Copyright © 2017 Xiaodan Zhang and Xingping Sheng. 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

In this paper, we present two different relaxed gradient based iterative (RGI) algorithms for solving the symmetric and skew symmetric solution of the Sylvester matrix equation . By using these two iterative methods, it is proved that the iterative solution converges to its true symmetric (skew symmetric) solution under some appropriate assumptions when any initial symmetric (skew symmetric) matrix is taken. Finally, two numerical examples are given to illustrate that the introduced iterative algorithms are more efficient.