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Advances in Numerical Analysis
Volume 2013 (2013), Article ID 512084, 7 pages
http://dx.doi.org/10.1155/2013/512084
Research Article

Some Results on Preconditioned Mixed-Type Splitting Iterative Method

1Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061, China
2Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 20 June 2013; Revised 14 September 2013; Accepted 27 September 2013

Academic Editor: Zhong-Zhi Bai

Copyright © 2013 Guangbin Wang and Fuping Tan. 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

We present a preconditioned mixed-type splitting iterative method for solving the linear system , where is a Z-matrix. And we give some comparison theorems to show that the rate of convergence of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give one numerical example to illustrate our results.