A note on Tikhonov regularization of large linear problems
type: Item
instance of: scholarly article
title: A note on Tikhonov regularization of large linear problems
zbMATH Open document ID: 1043.65064
DOI: 10.1023/A:1026091804076
author: Martin Hanke
published in: BIT
publication date: 2003-12-04T00:00:00Z
review text: This short note completes the analysis of bounds of Tikhonov residual \(\varphi(\alpha)=\| b-Ax_\alpha\| _2^2\) given in the paper of \textit{D. Calvetti} and \textit{L. Reichel} [ibid. 43, No. 2, 263--283 (2003; Zbl 1038.65048)], where \(x_\alpha\) is a solution of Tikhonov regularization of the large linear problem \(Ax=b\). The lower and upper bounds for \(\varphi(\alpha)\) are given by the \(l\)-point Gauss and Gaus-Radau quadratures, respectively. The author proves that these bounds depend monotonically on \(l\), i.e. the upper bound is decreasing monotonically, while the lower bound is increasing monotonically with respect to \(l\). The last statement was proved by Calvetti and Reichel [loc. cit.] on the another way.
reviewed by: Teresa Regińska
Mathematics Subject Classification ID: 65F22
Mathematics Subject Classification ID: 65D32
zbMATH DE Number: 2012835
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: norm of residual
zbMATH Keywords: Stieltjes integral
zbMATH Keywords: Gauss and Gauss-Radau quadratures
describes a project that uses: Regularization tools
MaRDI profile type: Publication
full work available at URL: a:1026091804076
OpenAlex ID: W102068913
description: scientific article; zbMATH DE number 2012835