A note on the Kantorovich theorem for Newton iteration
type: Item
instance of: scholarly article
title: A note on the Kantorovich theorem for Newton iteration
zbMATH Open document ID: 0782.65071
DOI: 10.1016/0377-0427(93)90004-U
author: Zhengda Huang
published in: Journal of Computational and Applied Mathematics
publication date: 1993-10-10T00:00:00Z
review text: The paper discusses the convergence of the Newton method for a nonsingular solution of the nonlinear equation \(f(x) = 0\) with \(f: X \to Y\) two times differentiable and \(X\), \(Y\) are Banach spaces. Based on the information of the second derivatives of \(f\) at the initial point, the author gives a new criterion for the convergence of the Newton iteration.
reviewed by: Zhen Mei
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 428536
zbMATH Keywords: convergence
zbMATH Keywords: Newton method
zbMATH Keywords: Banach spaces
MaRDI profile type: Publication
cites work: Optimal Error Bounds for the Newton–Kantorovich Theorem
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cites work: A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions
full work available at URL: 0377-0427(93)90004-u
OpenAlex ID: W1999858920
description: scientific article; zbMATH DE number 428536