On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization
type: Item
instance of: scholarly article
title: On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization
zbMATH Open document ID: 1165.47009
author: Stefan Kindermann
author: Andreas Neubauer
published in: Inverse Problems and Imaging
publication date: 2009-01-30T00:00:00Z
review text: The authors study the iterated Tikhonov regularization scheme \(x_{\alpha,n}^{\delta}=(T^*T+\alpha I)^{-1}(T^* y^{\delta}+\alpha x_{\alpha,n-1}^{\delta})\), \(x_{\alpha,0}^{\delta}=0\) for linear ill-posed problems \(Tx=y^{\delta}\), where \(\| y^{\delta}-y \| \leq \delta\), \(T\in L(X,Y)\), and \(X,Y\) are Hilbert spaces. For a special error free parameter choice rule \(\alpha=\alpha(y^{\delta})\), the authors derive conditions on \(y^{\delta}-y\) that ensure the convergence of the approximations \(x_{\alpha(y^{\delta}),n}^{\delta}\) to a solution of the unperturbed equation as \(\delta\to 0\). Estimates of the rate of convergence are also established.
reviewed by: Mikhail Yu. Kokurin
Mathematics Subject Classification ID: 47A52
Mathematics Subject Classification ID: 65J20
zbMATH DE Number: 5500622
zbMATH Keywords: quasi-optimality criterion
zbMATH Keywords: heuristic parameter selection
zbMATH Keywords: iterated Tikhonov regularisation
MaRDI profile type: Publication
full work available at URL: ipi.2008.2.291
OpenAlex ID: W2314826591
DOI: 10.3934/IPI.2008.2.291
description: scientific article; zbMATH DE number 5500622