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.
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页码：758 / 761
页数：4
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