Extending the applicability of secant methods and nondiscrete induction
type: Item
instance of: scholarly article
title: Extending the applicability of secant methods and nondiscrete induction
zbMATH Open document ID: 1251.65080
author: Ioannis Konstantinos Argyros
author: Saïd Hilout
published in: Applied Mathematics and Computation
publication date: 2012-06-11T00:00:00Z
review text: Nondiscrete mathematical induction is used to extend the applicability of secant methods for solving nonlinear operator equations in a Banach space setting. This approach has the following advantages over earlier works under the same information: weaker sufficient convergence conditions; tighter error bounds on the distances involved and more information on the location of the solution. Numerical examples where these results apply but earlier ones fail to solve nonlinear operator equations as well as tighter error bounds are also provided in this study.
reviewed by: Juri M. Rappoport
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 6045151
zbMATH Keywords: secant methods
zbMATH Keywords: Banach space
zbMATH Keywords: nondiscrete mathematical induction
zbMATH Keywords: semilocal convergence
zbMATH Keywords: consistent approximation
zbMATH Keywords: rate of convergence
zbMATH Keywords: Chandrasekhar integral equation
zbMATH Keywords: numerical examples
zbMATH Keywords: error bounds
describes a project that uses: NewtonLib
MaRDI profile type: Publication
full work available at URL: j.amc.2011.08.064
OpenAlex ID: W2107201039
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DOI: 10.1016/J.AMC.2011.08.064
description: scientific article; zbMATH DE number 6045151