Improving AOR Method for a Class of Two-by-Two Linear System

In this paper, the preconditioned accelerated overrelaxation (AOR) method for solving a class of two-by-two linear systems is presented. A new preconditioner is proposed according to the idea of [1] by Wu and Huang. The spectral radii of the iteration matrix of the preconditioned and the original methods are compared. The comparison results show that the convergence rate of the preconditioned AOR methods is indeed better than that of the original AOR methods, whenever the original AOR methods are convergent under certain conditions. Finally, a numerical example is presented to confirm our results.