On the dynamic solution of an operator inverse problem
type: Item
instance of: scholarly article
title: On the dynamic solution of an operator inverse problem
zbMATH Open document ID: 0924.65050
DOI: 10.1007/BF02358918
author: M. S. Blizorukova
author: Vyacheslav I. Maksimov
published in: Computational Mathematics and Modeling
publication date: 1999-06-15T00:00:00Z
review text: For a given family of linear operators \( B(x): U \to V^*, \;x \in V \), and an operator \( B_1(\cdot): V \to V^* \) where \( U \) and \( V \) are Banach spaces and \( V^* \) denotes the dual space of \( V \), the following equation is considered \[ B(x)u - B_1(x) = f.\tag{1} \] Here \( f \in V^* \) is given, and \( x = x(u) \in V \) in equation (1) depends on \( u \). It is supposed that equation (1) possesses a solution \( u \) in a given set \( P \subset U \), and on the other hand \( x(u) \) is approximately known only, i.e., \( \xi_h \in V \) and \( h > 0 \) are available such that \( \| \xi_h - x(u) \| \leq h \) is satisfied. Some applications are presented, and a Tikhonov-type method is considered for equation (1) which on further conditions on the spaces and operators is shown to be regularizing when a specific a priori parameter choice is applied.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 65J20
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 1283691
zbMATH Keywords: nonlinear ill-posed problems
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: parameter estimation
zbMATH Keywords: operator inverse problem
zbMATH Keywords: Banach spaces
reviewed by: Robert Plato
MaRDI profile type: Publication
cites work: Q3797561
cites work: Q3951472
cites work: Q4203294
cites work: Q3139162
cites work: Q4145478
full work available at URL: https://doi.org/10.1007/bf02358918
OpenAlex ID: W2074623060
description: scientific article; zbMATH DE number 1283691