The iterated regularization with perturbed operators and noisy data
type: Item
instance of: scholarly article
title: The iterated regularization with perturbed operators and noisy data
zbMATH Open document ID: 0822.65032
published in: Science in China. Series A
publication date: 1995-10-15T00:00:00Z
review text: The method of iterated Tikhonov regularization with perturbed operators and noisy data for solving operator equations of the type \(Tx= y\) in Hilbert spaces is investigated. A crucial problem in Tikhonov's regularization is the choice of the regularization parameter in dependence on the noise. If \(T\) is exactly known Tikhonov's regularization done by \textit{J. T. King} and \textit{D. Chillingworth} [Numer. Funct. Anal. Optimization 1, 499-513 (1979; Zbl 0446.65026)] and Arcangeli's method proposed by \textit{H. W. Engl} and \textit{A. Neubauer} [Notes Rep. Math. Sci. Eng. 4, 97-125 (1987; Zbl 0627.65060)] lead to an optimal convergence rate. This paper is to provide an a posteriori parameter choice and a higher asymptotic convergence rate for the iterated Tikhonov regularization by using a generalized Arcangeli method. Convergence rates are estimated.
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 65J20
Mathematics Subject Classification ID: 47A50
zbMATH DE Number: 722359
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: ill-posed problem
zbMATH Keywords: method of iterated Tikhonov regularization
zbMATH Keywords: perturbed operators
zbMATH Keywords: noisy data
zbMATH Keywords: Hilbert spaces
zbMATH Keywords: choice of the regularization parameter
zbMATH Keywords: Arcangeli's method
zbMATH Keywords: optimal convergence
author: Hong Chen
author: Zongyi Hou
reviewed by: Werner H. Schmidt
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 722359