Advances in Numerical Analysis
Volume 2012 (2012), Article ID 973407, 17 pages
http://dx.doi.org/10.1155/2012/973407
Research Article

Accelerated Circulant and Skew Circulant Splitting Methods for Hermitian Positive Definite Toeplitz Systems

N. Akhondi and F. Toutounian

School of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad 9177948953, Iran

Received 5 August 2011; Revised 26 October 2011; Accepted 26 October 2011

Academic Editor: Ivan Ganchev Ivanov

Copyright © 2012 N. Akhondi and F. Toutounian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the CSCS method for large Hermitian positive definite Toeplitz linear systems, which first appears in Ng's paper published in (Ng, 2003), and CSCS stands for circulant and skew circulant splitting of the coefficient matrix 𝐴 . In this paper, we present a new iteration method for the numerical solution of Hermitian positive definite Toeplitz systems of linear equations. The method is a two-parameter generation of the CSCS method such that when the two parameters involved are equal, it coincides with the CSCS method. We discuss the convergence property and optimal parameters of this method. Finally, we extend our method to BTTB matrices. Numerical experiments are presented to show the effectiveness of our new method.