A note on the stability of Toeplitz matrix inversion formulas.
type: Item
instance of: scholarly article
title: A note on the stability of Toeplitz matrix inversion formulas.
zbMATH Open document ID: 1069.15007
author: You-Wei Wen
author: Wai-Ki Ching
author: Hong Liu
author: Michael Ng
published in: Applied Mathematics Letters
publication date: 2005-03-07T00:00:00Z
review text: It is shown that the algorithms of \textit{A. Ben-Artzi} and \textit{T. Shalom} [Linear Algebra Appl. 75, 173--192 (1986; Zbl 0586.15005)], \textit{G. Labahn} and \textit{T. Shalom} [ibid. 175, 143--158 (1992; Zbl 0760.15005)] and \textit{M. K. Ng, K. Rost} and \textit{Y.-W. Wen} [ibid. 348, No. 1--3, 145--151 (2002; Zbl 0998.15031)] for the inversion of a well conditioned Toeplitz matrix are forward stable. I.e., the difference between the computed inverse and the exact inverse has a finite \(2\)-norm.
reviewed by: Adhemar Bultheel
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 65F05
zbMATH DE Number: 2140761
zbMATH Keywords: Toeplitz matrix
zbMATH Keywords: inversion formulas
zbMATH Keywords: stability
zbMATH Keywords: forward stable
MaRDI profile type: Publication
full work available at URL: j.aml.2003.11.002
OpenAlex ID: W2153813320
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DOI: 10.1016/J.AML.2003.11.002
description: scientific article; zbMATH DE number 2140761