Relaxing convergence conditions for Newton's method
type: Item
instance of: scholarly article
title: Relaxing convergence conditions for Newton's method
zbMATH Open document ID: 0965.65082
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-08-02T00:00:00Z
review text: The author considers a Newton method to solve the equation \(F(x)\in 0\), where \(F\) is a nonlinear Fréchet differentiable operator from Banach space \(X\) to Banach space \(Y\). The classical Lipschitz condition for the first derivative is replaced a weakened condition. Then the convergence is proved and an error estimate is given. The presented theory is illustrated by a nonlinear equation of Hammerstein type.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 1533178
zbMATH Keywords: Kantorovich theorem
zbMATH Keywords: Lipschitz condition
zbMATH Keywords: nonlinear operator equation
zbMATH Keywords: nonlinear Hammerstein equation
zbMATH Keywords: Newton method
zbMATH Keywords: Banach space
zbMATH Keywords: convergence
zbMATH Keywords: error estimate
author: M. A. Hernández
reviewed by: Lechoslaw Hącia
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6900
OpenAlex ID: W1993169050
cites work: The Newton-Kantorovich method under mild differentiability conditions and the Ptâk error estimates
cites work: Q4034594
cites work: Q4220542
cites work: On the convergence of a certain class of iterative procedures under relaxed conditions with applications
cites work: Q3292729
cites work: A new semilocal convergence theorem for Newton's method
cites work: A note on the Kantorovich theorem for Newton iteration
cites work: Q3943431
cites work: Q5652137
cites work: Q4191521
cites work: Newton's method under mild differentiability conditions with error analysis
DOI: 10.1006/JMAA.2000.6900
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description: scientific article; zbMATH DE number 1533178