On quasioptimum selection of the regularization parameter in M. M. Lavrent'ev's method
type: Item
instance of: scholarly article
title: On quasioptimum selection of the regularization parameter in M. M. Lavrent'ev's method
zbMATH Open document ID: 0874.65043
DOI: 10.1007/BF00975172
published in: Siberian Mathematical Journal
publication date: 1994-11-08T00:00:00Z
review text: The author considers the operator equation of the first kind \(Az=u\), \(z\in Z\), where \(Z\) is a real Hilbert space. Assuming the equation to be solvable, he discusses the question of determining a stable (in \(Z\)) approximation \(z_\eta= z_\eta(H)\), \(\eta=(h,\delta)\) to the normal solution \(\overline{z}: |z_\eta\rightharpoonup \overline{z}|\to 0\), as \(\eta\to 0\), from the approximate data \(H=(A_h, u_\delta,h,\delta)\) which are subject to the conditions \(|A_h- A|\leq h\); \(u_\delta\in Z\), \(|u_\delta-u|\leq \delta\), \(A_h\in S(z)\) (\(S(z)\) denotes the set of nonnegative selfadjoint bounded linear operators acting in \(Z\)). An a posteriori method for selecting the regularization parameters in the Lavrent'ev method is proposed.
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 65J20
Mathematics Subject Classification ID: 47A50
zbMATH DE Number: 652179
zbMATH Keywords: quasioptimum selection of the regularization parameter
zbMATH Keywords: ill-posed problem
zbMATH Keywords: linear operator equation
zbMATH Keywords: error estimates
zbMATH Keywords: Hilbert space
zbMATH Keywords: Lavrent'ev method
author: A. S. Leonov
reviewed by: P. C. Sinha
MaRDI profile type: Publication
cites work: Q3951472
cites work: Q3966999
cites work: Q5566067
cites work: Use of the regularization method in non-linear problems
cites work: Q3343334
cites work: Q5644548
description: scientific article; zbMATH DE number 652179