A family of modified regularizing circulant preconditioners for two-levels Toeplitz systems

被引：5

作者：

Bini, DA

Favati, P

Menchi, O

机构：

[1] Univ Pisa, Dipartmento Matemat, I-56127 Pisa, Italy

[2] IIT, CNR, I-56124 Pisa, Italy

[3] Univ Pisa, Dipartimento Informat, I-56127 Pisa, Italy

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2004年 / 48卷 / 5-6期

关键词：

Toeplitz matrices; circulant matrices; regularizing preconditioners; iterative methods;

D O I：

10.1016/j.camwa.2004.03.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Customary circulant preconditioners of Chan, Strang, and inverse-Toeplitz type are modified for the regularized solution of ill-conditioned Toeplitz systems. Given a symmetric two-level Toeplitz matrix A, and two parameters tau and sigma, consider the customary preconditioner C and modify it by replacing its eigenvalues with-modulus less than tau with the value alpha. The circulant matrix obtained in this way is used as a preconditioner. We analyze the distribution of the eigenvalues of the preconditioned matrix and the regularization properties. Numerical experiments, shown for the image restoration problem, validate the theoretical results. (C) 2004 Elsevier Ltd. All rights reserved.

引用

页码：755 / 768

页数：14

共 15 条

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Bertero M., 1998, Introduction to Inverse Problems in Imaging (Advanced Lectures in Mathematics)

[2]

Bini D., 1994, POLYNOMIAL MATRIX CO, V1

[3] CIRCULANT PRECONDITIONERS FOR HERMITIAN TOEPLITZ-SYSTEMS [J].