On an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems
type: Item
instance of: scholarly article
title: On an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems
zbMATH Open document ID: 0932.65065
author: Qinian Jin
author: Zongyi Hou
published in: Numerische Mathematik
publication date: 2000-03-15T00:00:00Z
review text: For solving the nonlinear ill-posed problem \(F(x)= y\), where \(F\) is a weakly closed, continuous and Fréchet differentiable operator between Hilbert spaces, Tikhonov's regularization is well known. \textit{O. Scherzer}, \textit{H. W. Engl} and \textit{K. Kunisch} [SIAM J. Numer. Anal. 30, No. 6, 1796-1838 (1993; Zbl 0799.65060)] proposed an a posteriori technique to find optimal regularization parameters. Unfortunately, assumptions for proving optimally were too restrictive to cover a larger set of problems. In this paper, the authors proceed with the study of the technique proposed and prove optimality under less restrictive conditions. Moreover, convergence rates could be improved.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 65J20
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 1355489
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: a posteriori parameter choice
zbMATH Keywords: nonlinear ill-posed problem
zbMATH Keywords: optimal regularization parameters
zbMATH Keywords: convergence
reviewed by: Etienne Emmrich
MaRDI profile type: Publication
full work available at URL: s002110050442
OpenAlex ID: W2315941165
DOI: 10.1007/S002110050442
description: scientific article; zbMATH DE number 1355489