On preconditioned AOR method for solving linear systems

Abstract

In this paper, we investigate the preconditioned AOR method for solving linear systems. We study two general preconditioners and propose some lower triangular, upper triangular and combination preconditioners. For $A$ being an L-matrix, a nonsingular M-matrix, an irreducible L-matrix and an irreducible nonsingular M-matrix, four types of comparison theorems are presented, respectively. They contain a general comparison result, a strict comparison result and two Stein-Rosenberg type comparison results. Our theorems include and are better than almost all known corresponding results.