A class of generalized Newton iterative schemes
type: Item
instance of: scholarly article
title: A class of generalized Newton iterative schemes
zbMATH Open document ID: 1050.65058
DOI: 10.1016/S0893-9659(03)00027-2
author: D. Massart
published in: Applied Mathematics Letters
publication date: 2004-06-11T00:00:00Z
review text: The author studies an \(N\)-step iterative scheme which generalizes several Newton-type schemes that have appeared in the literature. He shows that, under generalized Zabrejko-Nguen conditions, the iterative scheme converges whenever \(1\leq N\leq\infty\). This proves in a unified context the convergence of an infinite number of iterative schemes which include as special cases the classical Newton scheme, the classical chord scheme, and the generalized Newton scheme as has been considered before, e.g., by \textit{E. de Pascale}, \textit{J. V. Lysenko}, \textit{P. P. Zabrejko} and the reviewer [Numer. Funct. Anal. Optimization 18, No. 1--2, 1--17 (1997; Zbl 0881.65048)].
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 2073755
zbMATH Keywords: nonlinear operator equation
zbMATH Keywords: \(N\)-step Newton scheme
zbMATH Keywords: convergence
zbMATH Keywords: Zabrejko-Nguen conditions
zbMATH Keywords: majorant method
reviewed by: Jürgen Appell
MaRDI profile type: Publication
cites work: Improved error bounds for Newton's method under generalized Zabrejko- Nguen-type assumptions
cites work: Q3218622
cites work: The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
cites work: New results on newton-kantorovich approximations with applications to nonlinear integral equations
full work available at URL: s0893-9659(03)00027-2
OpenAlex ID: W2069992515
description: scientific article; zbMATH DE number 2073755