Local convergence of inexact methods under the Hölder condition
type: Item
instance of: scholarly article
title: Local convergence of inexact methods under the Hölder condition
zbMATH Open document ID: 1181.65082
author: C. Li
author: Weiping Shen
published in: Journal of Computational and Applied Mathematics
publication date: 2008-11-18T00:00:00Z
review text: The convergence properties are studied for some inexact Newton-like methods for solving nonlinear operator equations in Banach spaces. In practice the Newton method has two disadvantages: it requires computing exactly Jacobian matrices and secondly, it requires solving exactly the corresponding linear equations. In this paper such inexact Newton-like methods avoiding both disadvantages are developed using a new type of residual control. Under the assumption that the derivative of the operator defining the equation satisfies the Hölder condition, the radius of the convergence ball of the inexact Newton-like methods with the new type residual control is estimated, and a linear and superlinear convergence rate is proved. A slight modification of the inexact Newton-like method of \textit{R. H. Chan, H. L. Chang} and \textit{S. F. Xu} [BIT 43, No.~1, 7--20 (2003; Zbl 1029.65036)] for solving inverse eigenvalue problems is proposed. A numerical example for illustrating the performance of the latter algorithm is presented.
reviewed by: Otu Vaarmann
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 5368389
zbMATH Keywords: nonlinear operator equation
zbMATH Keywords: inexact Newton-like methods
zbMATH Keywords: Hölder condition
zbMATH Keywords: inverse eigenvalue problem
zbMATH Keywords: Banach spaces
zbMATH Keywords: radius of the convergence ball
zbMATH Keywords: superlinear convergence
zbMATH Keywords: numerical example
zbMATH Keywords: algorithm
MaRDI profile type: Publication
full work available at URL: j.cam.2007.12.001
OpenAlex ID: W2086475550
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DOI: 10.1016/J.CAM.2007.12.001
description: scientific article; zbMATH DE number 5368389