Journal of Applied Mathematics
Volume 2013 (2013), Article ID 827826, 4 pages
http://dx.doi.org/10.1155/2013/827826
Research Article

Comparison Theorems for Single and Double Splittings of Matrices

Cui-Xia Li, Qun-Fa Cui, and Shi-Liang Wu

School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China

Received 5 February 2013; Accepted 14 March 2013

Academic Editor: Giuseppe Marino

Copyright © 2013 Cui-Xia Li 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

Some comparison theorems for the spectral radius of double splittings of different matrices under suitable conditions are presented, which are superior to the corresponding results in the recent paper by Miao and Zheng (2009). Some comparison theorems between the spectral radius of single and double splittings of matrices are established and are applied to the Jacobi and Gauss-Seidel double SOR method.