Copyright © 2010 Qingbing Liu and Guoliang Chen. 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.
-(-)matrices appear in many areas of science and engineering, for example, in the solution of the
linear complementarity problem (LCP) in optimization theory and in the solution of large systems
for real-time changes of data in fluid analysis in car industry. Classical (stationary) iterative
methods used for the solution of linear systems have been shown to convergence for this class of
matrices. In this paper, we present some comparison theorems on the preconditioned AOR iterative
method for solving the linear system. Comparison results show that the rate of convergence of the
preconditioned iterative method is faster than the rate of convergence of the classical iterative
method. Meanwhile, we apply the preconditioner to -matrices and obtain the convergence result.
Numerical examples are given to illustrate our results.