The two common numerical methods to approximate the solution of partial differential equations are the finite element method and the finite difference method. They both lead to solving large sparse linear systems. For many applications, it is not unusal that the order of matrix is greater than 10, 000. For this kind of problem, a direct method such as Gaussian elimination can not be used because of the prohibitive cost. To this end, many iterative methods with modest cost have been studied and proposed by numerical analysts.(omitted)