Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Approximate inverse-free preconditioners for Toeplitz matrices

Language

English

Abstract

In this paper, we propose approximate inverse-free preconditioners for solving Toeplitz systems. The preconditioners are constructed based on the famous Gohberg-Semencul formula. We show that if a Toeplitz matrix is generated by a positive bounded function and its entries enjoys the off-diagonal decay property, then the eigenvalues of the preconditioned matrix are clustered around one. Experimental results show that the proposed preconditioners are superior to other existing preconditioners in the literature. © 2011 Elsevier Inc. All rights reserved.

Keywords

Approximate inverse-free preconditioners, Gohberg-Semencul formula, Preconditioned conjugate gradient method, Toeplitz matrices

Publication Date

2011

Source Publication Title

Applied Mathematics and Computation

Volume

217

Issue

16

Start Page

6856

End Page

6867

Publisher

Elsevier

DOI

10.1016/j.amc.2011.01.030

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.amc.2011.01.030

ISSN (print)

00963003

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