  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.
