On the preconditioned AOR iterative method for Z-matrices

Several preconditioned AOR methods have been proposed to solve system of linear equations $Ax=b$, where $A\in {\mathbb{R}}^{n\times n}$ is a unit Z-matrix. The aim of this paper is to give a comparison result for a class of preconditioners $P$, where $P\in {\mathbb{R}}^{n\times n}$ is nonsingular, nonnegative and has unit diagonal entries. Numerical results for corresponding preconditioned GMRES methods are given to illustrate the theoretical results.