Journal of Applied Mathematics
Volume 2012 (2012), Article ID 401059, 12 pages
http://dx.doi.org/10.1155/2012/401059
Research Article

A Preconditioned Iteration Method for Solving Sylvester Equations

Jituan Zhou,1 Ruirui Wang,2 and Qiang Niu3

1School of Mathematics and Computational Science, Wuyi University, Guangdong, Jiangmen 529000, China
2College of Science, China University of Mining and Technology, Xuzhou 221116, China
3Mathematics and Physics Centre, Xi’an Jiaotong-Liverpool University, Suzhou 215123, China

Received 25 May 2012; Accepted 20 June 2012

Academic Editor: Jianke Yang

Copyright © 2012 Jituan Zhou 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

A preconditioned gradient-based iterative method is derived by judicious selection of two auxil- iary matrices. The strategy is based on the Newton’s iteration method and can be regarded as a generalization of the splitting iterative method for system of linear equations. We analyze the convergence of the method and illustrate that the approach is able to considerably accelerate the convergence of the gradient-based iterative method.