New preconditioners for systems of linear equations with Toeplitz structure
type: Item
instance of: scholarly article
title: New preconditioners for systems of linear equations with Toeplitz structure
zbMATH Open document ID: 1317.65085
author: Yongjie Shi
author: Xue-Bo Pi
published in: Calcolo
publication date: 2015-03-23T00:00:00Z
review text: The construction of preconditioners for solving systems of linear equations \(T x = b\), where \(T\) is a block Toeplitz matrix with Toeplitz blocks (BTTB matrix) is discussed. At first, level-2 circulant preconditioners based on generalized Jackson kernels are considered. This type of preconditioners are block circulant matrices with circulant blocks. The presented preconditioners are an extension of circulant preconditioners proposed by \textit{R. H. Chan} et al. [SIAM J. Numer. Anal. 38, No. 3, 876--896 (2000; Zbl 0978.65035)] and [Numer. Math. 92, No. 1, 17--40 (2002; Zbl 1007.65033)]. A second kind of preconditioners is derived from a splitting of BTTB matrices. The proposed BTTB preconditioners are applied to solve BTTB least squares problems. For illustrating the efficiency of the presented preconditioners, three numerical examples are given. The new preconditioners are compared with preconditioners known from the literature.
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 15B05
zbMATH DE Number: 6418666
zbMATH Keywords: Toeplitz matrices
zbMATH Keywords: preconditioners
zbMATH Keywords: block circulant matrix with circulant blocks
zbMATH Keywords: generalized Jackson kernels
zbMATH Keywords: block Toeplitz matrix with Toeplitz blocks
zbMATH Keywords: preconditioned conjugate gradient method
zbMATH Keywords: least squares problem
zbMATH Keywords: numerical example
reviewed by: Michael Jung
MaRDI profile type: Publication
full work available at URL: s10092-012-0074-0
OpenAlex ID: W2057287997
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DOI: 10.1007/S10092-012-0074-0
description: scientific article; zbMATH DE number 6418666