Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems
type: Item
instance of: scholarly article
title: Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems
zbMATH Open document ID: 0842.65036
author: Otmar Scherzer
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-03-24T00:00:00Z
review text: The author considers the convergence of iterative methods for solving a nonlinear operator equation \(F(x)= y\) by using the method of Landweber iteration, which is defined by the iterative scheme \[ x_{k+ 1}= x_k- f'(x_k)^* [f(x_k)- y]\equiv U(x_k). \] The author shows that if the functions \(U\) and \(f\) satisfy some conditions then the iterative schemes (weakly or strongly) converge to a solution of the original equation. Moreover, the author gives conditions guaranteeing that the iterative scheme is convergent in the case of inexact data \(y\) and gives the convergence rates for ill-posed problems. Finally, the author applies the results to an inverse problem for identifying the diffusion coefficient in a boundary-valued problem of an ordinary differential equation of order two.
reviewed by: Yu Wenhuan
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 65J20
zbMATH DE Number: 859240
zbMATH Keywords: nonlinear ill-posed problem
zbMATH Keywords: convergence
zbMATH Keywords: iterative methods
zbMATH Keywords: nonlinear operator equation
zbMATH Keywords: Landweber iteration
zbMATH Keywords: inverse problem
zbMATH Keywords: diffusion coefficient
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1335
OpenAlex ID: W2058204667
DOI: 10.1006/JMAA.1995.1335
description: scientific article; zbMATH DE number 859240