On convergence criteria for approximations to the regularization method
type: Item
instance of: scholarly article
title: On convergence criteria for approximations to the regularization method
zbMATH Open document ID: 0944.47007
DOI: 10.1007/BF02674297
author: Leonid Davidovich Menikhes
author: Vitaly Pavlovich Tanana
published in: Siberian Mathematical Journal
publication date: 2000-04-16T00:00:00Z
review text: Practical implementation of the various regularization methods for unstable problems which are proposed in the articles by N.~A. Tikhonov, M.~M. Lavrent'ev and others involves constructions of some finite-dimensional analogs of the regularization methods. Therefore, the problem arises of studying convergence of solutions to these approximation problems. Mainly, the results in this direction yield sufficient conditions for convergence in the case of bounded operators. In the article under consideration, the authors obtain necessary and sufficient conditions for convergence of approximations for closed operators. The criteria for convergence of approximations are exposed in the general case for an arbitrary approximation scheme as well as in one particular case.
reviewed by: Vladimir N. Grebenev
Mathematics Subject Classification ID: 47A50
Mathematics Subject Classification ID: 47A58
Mathematics Subject Classification ID: 49R50
Mathematics Subject Classification ID: 65J10
zbMATH DE Number: 1432190
zbMATH Keywords: unstable problem
zbMATH Keywords: operator equation
zbMATH Keywords: regularization method
zbMATH Keywords: convergence of approximations
zbMATH Keywords: necessary and sufficient conditions for convergence
MaRDI profile type: Publication
cites work: Q3951472
cites work: Q4092883
cites work: Q4192899
cites work: Q3966999
cites work: Q5613420
cites work: A convergence criterion for approximations in the residual method for linear ill-posed problems
description: scientific article; zbMATH DE number 1432190