Circulant And Skew Circulant Matrix Splitting Iterative Methods For Toeplitz Linear Systems

Toeplitz matrix as a very important matrix in recent years, scholars have been extensively studied, Toeplitz matrix has a special structure, in engineering terms, physics, astrophysics science,it has a wide range of applications. Therefore, the composition of the matrix equation for solving Toeplitz matrix calculation became a hot topic, we know that solving Toeplitz equations method are direct method and iterative method,we known the direct method a lot,and the iterative method is splitting the coefficient matrix,as we known,the splitting methods include HS (Hermitian and skew hermitian matrix) method,CS (Circulant and skew circulant matrix) method.This paper we will focus more on the iterative method.This paper introduces two circulant and skew circulant matrix splitting method for Toeplitz matrix,we generalize the CSCS method for Toeplitz matrix in the first methods,and to the second method,we introduce a new splitting scheme for Toeplitz matrix,however this splitting can also guarantee the circulant and the skew circulant matrix form.The first chapter is the introduction, mainly introduces the basis and significance of the topic, and the status of domestic and international research, and some basic knowledge of the basics in this section, we introduce the classical HSS method for non-Hermitian positive definite matrix and CSCS method for Toeplitz linear systems. For this article follow-up study to do the groundwork.Chapter 2, wo introduce the complex parameter CSCS method,this method expand the parameter to the complex field.Finally,we will give the result of the experiment.Chapter 3, we introduce a splitting iterative method for Toeplitz matrix on circulant and skew circulant matrix, which is a new form of splitting, by proving the theorem we only do a certain amount of matrix elements restrictions, iterative scheme can convergence.Conclusion of the paper are the complex parameter CSCS method is convergent; The circulant and skew circulant matrix iterative method for Toeplitz matrix will be convergent if we limit the matrix element.