Year: 2001
Author: Li-Zhi Cheng
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 2 : pp. 167–176
Abstract
In recent papers, some authors studied the solutions of symmetric positive definite (SPD) Toeplitz systems $T_nx=b$ by the conjugate gradient method (CG) with different sine transforms based preconditioners. In this paper, we first discuss the properties of eigenvalues for the main known circulant, skew circulant and sine transform based preconditioners. A counter example shows that E. Boman's preconditioner is only positive semi-definite for the banded Toeplitz matrix. To use preconditioner effectively, then we propose a modified Boman's preconditioner and a new Cesaro sum type sine transform based preconditioner. Finally, the results of numerical experimentation with these two preconditioners are presented.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2001-JCM-8969
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 2 : pp. 167–176
Published online: 2001-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Preconditioner Toeplitz systems The fast sine transform Conjugate gradient algorithm.