The multistage methods for solving symmetric positive definite toeplitz systems

Abstract

The two-stage iterative methods are also called inner/outer iterative methods. The multistage iteration is nested by several two-stage iterations. Those methods are especial- ly suitable for parallel computation, and can be viewed as extensions of classical iterative methods or as preconditioners for conjugate gradient methods. In this paper, we consider the multistage iterative methods for solving symmetric positive definite Toeplitz systems. Based on the Toeplitz structure, we first construct a multistage block Jacobi splitting, then we prove that the corresponding splitting at each level is P-regular, and show that the resulting method is convergent when the number of iteration at each level is even. At the end, we give some numerical examples to illustrate the effectiveness of our methods.