A convergence rate result for a steepest descent method and a minimal error method for the solution of nonlinear ill-posed problems
type: Item
instance of: scholarly article
title: A convergence rate result for a steepest descent method and a minimal error method for the solution of nonlinear ill-posed problems
zbMATH Open document ID: 0826.65053
DOI: 10.4171/ZAA/679
author: Otmar Scherzer
author: Andreas Neubauer
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1995-11-26T00:00:00Z
review text: The paper is devoted to the study of the convergence of a steepest descent method as well as the minimal error method applied to a nonlinear operator equation of the form \(F(x) = y\) for which the solution (which need not be unique) does not depend continuously on the right-hand side data \(y\). Assuming \(F\) is Lipschitz continuously differentiable and that certain additional conditions are satisfied, a convergence rate result is obtained in the noise free case. Finally, these conditions are illustrated for a parameter estimation problem.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 65J20
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 761127
zbMATH Keywords: nonlinear ill-posed problems
zbMATH Keywords: convergence
zbMATH Keywords: steepest descent method
zbMATH Keywords: minimal error method
zbMATH Keywords: nonlinear operator equation
zbMATH Keywords: parameter estimation
reviewed by: Vasile Berinde
MaRDI profile type: Publication
cites work: On the Landweber iteration for nonlinear ill-posed problems
cites work: Iterative solution methods for inconsistent linear equations with nonself-adjoint operators
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cites work: Steepest descent for singular linear operators with nonclosed range
cites work: A uniform approach to gradient methods for linear operator equations
cites work: A convergence analysis of a method of steepest descent and a two–step algorothm for nonlinear ill–posed problems
full work available at URL: https://doi.org/10.4171/zaa/679
OpenAlex ID: W2009666499
description: scientific article; zbMATH DE number 761127