A new semilocal convergence theorem for Newton's method involving twice Fréchet-differen\-tiabil\-ity at only one point
type: Item
instance of: scholarly article
title: A new semilocal convergence theorem for Newton's method involving twice Fréchet-differen\-tiabil\-ity at only one point
zbMATH Open document ID: 1075.65081
author: Zhongyong Hu
published in: Journal of Computational and Applied Mathematics
publication date: 2005-06-30T00:00:00Z
review text: This paper is concerned with the problem of approximating a locally unique solution of the equation \( F(x)=0\) , where \(F\) is defined an open convex subset of a Banach space \(X\) with values in a Banach space \(Y\). It is assumed that an operator \(F\) is twice continuously Fréchet-differentiability at only one point. The author provide a new semilocal convergence theorem for Newton's method. Error estimates are derived. A simple numerical example is given.
reviewed by: Karel Najzar
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 2183976
zbMATH Keywords: Newton's method
zbMATH Keywords: Fréchet-differentiability
zbMATH Keywords: error estimates
zbMATH Keywords: semilocal convergence
zbMATH Keywords: Banach space
zbMATH Keywords: numerical example
zbMATH Keywords: nonlinear operator equation
MaRDI profile type: Publication
full work available at URL: j.cam.2004.12.005
OpenAlex ID: W2052766026
cites work: A Newton-Kantorovich theorem for equations involving \(m\)-Fréchet differentiable operators and applications in radiative transfer
cites work: A new semilocal convergence theorem for Newton's method in Banach space using hypotheses on the second Fréchet-derivative
cites work: On a theorem of L.V. Kantorovich concerning Newton's method.
cites work: The theory of Newton's method
cites work: A new semilocal convergence theorem for Newton's method
cites work: Accessibility Of Solutions By Newton's Method
cites work: A note on the Kantorovich theorem for Newton iteration
cites work: Q3943431
cites work: Newton's method under mild differentiability conditions with error analysis
DOI: 10.1016/J.CAM.2004.12.005
description: scientific article; zbMATH DE number 2183976