A Study of an Iteratively-Regularized Simplified Landweber Iteration for Nonlinear Inverse Problems in Hilbert Spaces

Lanweber-type methods are a well-known regularization methods to solve linear and nonlinear ill-posed problems. In this article, we consider a simplified form of Landweber method, say, an iteratively-regularized simplified Landweber iteration for solving nonlinear ill-posed problems. We study a deta...

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Bibliographic Details
Published inNumerical functional analysis and optimization Vol. 44; no. 7; pp. 619 - 652
Main Author Dixit, Sharad Kumar
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 19.05.2023
Taylor & Francis Ltd
Subjects
Convergence
Hilbert space
Ill posed problems
Inverse problems
Iterative methods
Iterative regularization methods
Morozov-type stopping rule
nonlinear ill-posed operator equations
nonlinear operators on Hilbert spaces
Nonlinearity
Primary Mathematics subject index: 47A52
Regularization
Secondary Mathematics subject index: 65F22
source conditions
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Summary:Lanweber-type methods are a well-known regularization methods to solve linear and nonlinear ill-posed problems. In this article, we consider a simplified form of Landweber method, say, an iteratively-regularized simplified Landweber iteration for solving nonlinear ill-posed problems. We study a detailed convergence analysis of the method under standard conditions on the nonlinearity and the rate of convergence under a Hölder-type source condition. Finally, numerical simulations are performed to validate the performance of the method.
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ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2023.2183510