Semilocal convergence for Halley's method under weak Lipschitz condition
type: Item
instance of: scholarly article
title: Semilocal convergence for Halley's method under weak Lipschitz condition
zbMATH Open document ID: 1187.65059
author: Xiubin Xu
author: Yonghui Ling
published in: Applied Mathematics and Computation
publication date: 2010-01-08T00:00:00Z
review text: Let \(X,Y\) be Banach spaces, \(D\) be an open convex part of \(X\) and \(F:D\to Y\) be a continuous, twice Fréchet differentiable operator. The semilocal convergence of the Halley's method \[ x_{k+1}=x_k-(I-L_F(x_k))^{-1} F'(x_k)^{-1}F(x_k), \quad k\geq 0, \] towards the unique solution \(x^*\) of \(F(u)=0\) is established, under Lipschitz type assumptions involving the second derivative of \(F\).
reviewed by: Mihai Turinici
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 5655295
zbMATH Keywords: Halley's method
zbMATH Keywords: weak Lipschitz condition
zbMATH Keywords: semilocal convergence
zbMATH Keywords: affine invariant
zbMATH Keywords: Hammerstein integral equation
zbMATH Keywords: Banach spaces
describes a project that uses: NewtonLib
MaRDI profile type: Publication
full work available at URL: j.amc.2009.09.055
OpenAlex ID: W2082505363
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DOI: 10.1016/J.AMC.2009.09.055
description: scientific article; zbMATH DE number 5655295