A New Preconditioner for Toeplitz Matrices

被引：3

作者：

Dominguez-Jimenez, Maria Elena ^{[1
]}

Ferreira, Paulo J. S. G. ^{[2
]}

机构：

[1] Univ Politecn Madrid, Dept Matemat Aplicada, ETSII, GI TACA, E-28006 Madrid, Spain

[2] Univ Aveiro, Signal Proc Lab, DETI IEETA, P-3810193 Aveiro, Portugal

来源：

IEEE SIGNAL PROCESSING LETTERS | 2009年 / 16卷 / 09期

关键词：

PCG; preconditioners; Toeplitz matrices; CIRCULANT PRECONDITIONERS;

D O I：

10.1109/LSP.2009.2024735

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

In this paper we introduce and analyze a new preconditioner for Toeplitz matrices that exhibits excellent spectral properties: the eigenvalues of the preconditioned matrix are highly clustered around the unity. As a result, it yields very rapid convergence when used to solve Toeplitz equations via the preconditioned conjugate gradient method. The new preconditioner can be regarded as a refinement of preconditioners built by embedding the Toeplitz matrix in a positive definite circulant. Necessary and sufficient conditions that ensure that the positive definite embedding is possible are given.

引用

页码：758 / 761

页数：4

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