A total least squares method for Toeplitz systems of equations
type: Item
instance of: scholarly article
title: A total least squares method for Toeplitz systems of equations
zbMATH Open document ID: 0918.65028
DOI: 10.1007/BF02510260
author: Julie Kamm
author: James G. Nagy
published in: BIT
publication date: 1999-08-17T00:00:00Z
review text: The Newton method is used to solve the total least squares (TLS) problem for Toeplitz systems (a Toeplitz matrix has constant entries on each diagonal). TLS differs from the usual \(\text{LS} (Tf\approx g)\) in that both \(T\) and \(g\) are corrupted by errors. The Newton method requires the solution of a linear system and the authors present a preconditioned conjugate gradient method for this; either \(LDL^T\) factorization, or a circulant approximation, are suggested for the preconditioner. When Newton's method is coupled with a bisection scheme, it is shown that global convergence can be guaranteed. The paper concludes with some numerical tests comparing results of three variants of the basic scheme.
reviewed by: Adrian Swift
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 1228555
zbMATH Keywords: total least squares method
zbMATH Keywords: Newton method
zbMATH Keywords: Toeplitz systems
zbMATH Keywords: preconditioned conjugate gradient method
zbMATH Keywords: global convergence
zbMATH Keywords: numerical tests
describes a project that uses: VanHuffel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1228555