A preconditioned AOR iterative scheme for systems of linear equations with L-matrics

In this paper we investigate theoretically and numerically the new preconditioned method to accelerate over-relaxation (AOR) and succesive over-relaxation (SOR) schemes, which are used to the large sparse linear systems. The iterative method that is usually measured by the convergence rate is an important method for solving large linear equations, so we focus on the convergence rate of the different preconditioned iterative methods. Our results indicate that the proposed new method is highly effective to improve the convergence rate and it is the best one in three preconditioned methods that are revealed in the comparison theorems and numerical experiment.