Two-step Newton-Tikhonov method for Hammerstein-type equations: finite-dimensional realization
type: Item
instance of: scholarly article
title: Two-step Newton-Tikhonov method for Hammerstein-type equations: finite-dimensional realization
zbMATH Open document ID: 1264.65214
DOI: 10.5402/2012/783579
author: Santhosh George
author: Monnanda E. Shobha
published in: ISRN Applied Mathematics
publication date: 2013-06-11T00:00:00Z
review text: Summary: Finite-dimensional realization of a two-Step Newton-Tikhonov method is considered for obtaining a stable approximate solution to nonlinear ill-posed Hammerstein-type operator equations \(KF(x) = f\). Here \(F : D(F) \subseteq X \to X\) is nonlinear monotone operator, \(K : X \to X\) is a bounded linear operator, \(X\) is a real Hilbert space, and \(Y\) is a Hilbert space. The error analysis for this method is done under two general source conditions, the first one involves the operator \(K\) and the second one involves the Fréchet derivative of \(F\) at an initial approximation \(x_0\) of the the solution \(\hat{x}\): balancing principle of \textit{S. Pereverzev} and \textit{E. Schock} [SIAM J. Numer. Anal. 43, No.~5, 2060--2076 (2005; Zbl 1103.65058)] is employed in choosing the regularization parameter and order optimal error bounds are established. Numerical illustration is given to confirm the reliability of our approach.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 6172986
zbMATH Keywords: two-Step Newton-Tikhonov method
zbMATH Keywords: nonlinear ill-posed Hammerstein-type operator equations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2012/783579
OpenAlex ID: W2119249490
Wikidata QID: Q58692358
cites work: A Quadratic Convergence Yielding Iterative Method for Nonlinear Ill-posed Operator Equations
cites work: Iterative regularization methods for nonlinear ill-posed problems
cites work: Newton–Tikhonov regularization of ill-posed Hammerstein operator equation
cites work: A modified Newton-Lavrentiev regularization for nonlinear ill-posed Hammerstein-type operator equations
cites work: A simplified generalized Gauss-Newton method for nonlinear ill-posed problems
cites work: Lavrentiev regularization and balancing principle for solving ill-posed problems with monotone operators
cites work: An iterative regularization method for ill-posed Hammerstein type operator equation
cites work: On the Adaptive Selection of the Parameter in Regularization of Ill-Posed Problems
cites work: A convergence analysis for directional two-step Newton methods
cites work: Regularized Versions of Continuous Newton's Method and Continuous Modified Newton's Method Under General Source Conditions
cites work: Continuous modified Newton's-type method for nonlinear operator equations
description: scientific article; zbMATH DE number 6172986