A new semilocal convergence theorem for the secant method under Hölder continuous divided differences
type: Item
instance of: scholarly article
title: A new semilocal convergence theorem for the secant method under Hölder continuous divided differences
zbMATH Open document ID: 1112.65050
author: Hongmin Ren
author: Shijun Yang
author: Qingbiao Wu
published in: Applied Mathematics and Computation
publication date: 2007-01-09T00:00:00Z
review text: A new Kantorovitch type convergence theorem is provided for the secant method in Banach spaces for the nonlinear operator equation \(F(x)=0\). Here \(F\) is defined on an open convex domain \(\Omega\) of a Banach space \(X\) with values in a Banach space \(Y\). The results are of interest since they apply to cases in which the known conditions failed or they were more complicated. Two examples are presented, in which the authors' conditions work, while the earlier ones fail.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 5083662
zbMATH Keywords: recurrence relations
zbMATH Keywords: numerical examples
zbMATH Keywords: Banach spaces
zbMATH Keywords: nonlinear operator equation
MaRDI profile type: Publication
full work available at URL: j.amc.2006.03.034
OpenAlex ID: W2049807595
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cites work: The secant method and divided differences Hölder continuous
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DOI: 10.1016/J.AMC.2006.03.034
description: scientific article; zbMATH DE number 5083662