A unified convergence analysis for secant-type methods
type: Item
instance of: scholarly article
zbMATH Open document ID: 1320.65082
DOI: 10.4134/JKMS.2014.51.6.1155
published in: Journal of the Korean Mathematical Society
publication date: 2014-11-14T00:00:00Z
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 6369561
zbMATH Keywords: local convergence analysis
zbMATH Keywords: semilocal convergence analysis
zbMATH Keywords: secant-type method
zbMATH Keywords: Banach space
zbMATH Keywords: majorizing sequence
zbMATH Keywords: divided difference
zbMATH Keywords: nonlinear operator equation
zbMATH Keywords: comparison of methods
zbMATH Keywords: error bound
zbMATH Keywords: Newton's method
zbMATH Keywords: numerical example
author: Ioannis Konstantinos Argyros
author: Ángel Alberto Magreñán
MaRDI profile type: Publication
title: A unified convergence analysis for secant-type methods
review text: A unified local and semilocal convergence analysis for secant-type methods for the approximation of a locally unique solution of a nonlinear equation in a Banach space setting is presented. The analysis performed includes the computation of the bounds on the limit points of the majorizing sequences involved. Under the same computational cost the semilocal convergence criteria can be weaker, the error bounds more precise and in the local case the convergence balls can be larger and the error bounds tighter than in existing studies, at least for the cases of Newton's method and the secant method. Three representative numerical examples are used to illustrate the theoretical results.
description: scientific article; zbMATH DE number 6369561