An iteratively regularized Gauss-Newton-Halley method for solving nonlinear ill-posed problems
type: Item
instance of: scholarly article
title: An iteratively regularized Gauss-Newton-Halley method for solving nonlinear ill-posed problems
zbMATH Open document ID: 1327.65102
author: Barbara Kaltenbacher
published in: Numerische Mathematik
publication date: 2015-09-14T00:00:00Z
review text: This paper deals with the problem of the convergence of a Halley-type method for regularizing nonlinear inverse problems \(F(x)=y\) defined in Hilbert spaces. The method is based on the regularized Gauss-Newton iterative method but presents the novelty of including second derivatives of the involved operator \(F\). For a wide range of problems, for instance parameter identification problems for partial differential equations (PDEs), the operational cost of the evaluation of the second derivative is similar to the evaluation of the first derivative. This fact justifies the inclusion of second derivatives in the method. The author proves convergence and convergence rates in terms of the derivatives \(F'\) and \(F''\) depending on the regularity of the exact solution. The method can be applied in the ill-posed situation, where a noise level is assumed. The paper finishes with some numerical applications to the problem of identifying coefficients in some particular PDEs.
reviewed by: José Manuel Gutiérrez Jimenez
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 65N20
Mathematics Subject Classification ID: 65J20
Mathematics Subject Classification ID: 47J06
zbMATH DE Number: 6481913
zbMATH Keywords: nonlinear ill-posed problems
zbMATH Keywords: iterative regularization method
zbMATH Keywords: identification problems in PDEs
zbMATH Keywords: numerical examples
zbMATH Keywords: convergence
zbMATH Keywords: Halley-type method
zbMATH Keywords: Hilbert space
zbMATH Keywords: Gauss-Newton iterative method
MaRDI profile type: Publication
full work available at URL: s00211-014-0682-5
OpenAlex ID: W1984665680
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DOI: 10.1007/S00211-014-0682-5
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description: scientific article; zbMATH DE number 6481913