An iteration method for solving the linear system Ax=b

In this paper, based on a convergence splitting of the matrix A, we present an inner-outer iteration method for solving the linear system Ax=b. We analyze the overall convergence of this method without any other restriction on its parameters. Moreover, we give the accelerated inner-outer iteration method, and discuss how to apply the inner-outer iterations as a preconditioner for the Krylov subspace methods. The inner-outer iteration method can also be used for the solution of AXB=C. Finally, several numerical examples are given to validate the performance of our proposed algorithms.