On the preconditioned AOR iterative method for Z-matrices

TL;DR

This paper analyzes the effectiveness of preconditioned AOR iterative methods for solving linear systems with Z-matrices, providing theoretical comparison results and numerical experiments to demonstrate their performance.

Contribution

It introduces a comparison framework for a class of preconditioners in AOR methods applied to Z-matrices, including numerical validation.

Findings

Preconditioners improve convergence of AOR methods.

Numerical results confirm theoretical predictions.

Preconditioned GMRES methods show enhanced performance.

Abstract

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.