On the comparison of a weak variant of the Newton--Kantorovich and Miranda theorems.
type: Item
instance of: scholarly article
title: On the comparison of a weak variant of the Newton--Kantorovich and Miranda theorems.
zbMATH Open document ID: 1074.65062
author: Ioannis Konstantinos Argyros
published in: Journal of Computational and Applied Mathematics
publication date: 2004-03-29T00:00:00Z
review text: The author [J. Comput. Appl. Math. 157, 169--185 (2003; Zbl 1030.65060)] has shown a semi-local convergence theorem under weaker assumptions than those of the Newton-Kantorovich theorem. Operators satisfying the weakened Newton-Kantorovich conditions are shown to satisfy the conditions of the weakened Miranda theorem.
reviewed by: René Lamour
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 2062755
zbMATH Keywords: Newton-Kantorovich theorem
zbMATH Keywords: Miranda theorem
zbMATH Keywords: Center-Lipschitz condition
zbMATH Keywords: Miranda partition/domain/conditions
zbMATH Keywords: Newton-Kantrovich hypothesis
zbMATH Keywords: semi-local convergence
MaRDI profile type: Publication
full work available at URL: j.cam.2003.10.015
OpenAlex ID: W2080269073
cites work: Q2765609
cites work: Local convergence of inexact Newton-like iterative methods and applications
cites work: On The Convergence And Application Of Newton's Method Under Weak HÖlder Continuity Assumptions
cites work: An improved error analysis for Newton-like methods under generalized conditions
cites work: Some notions of nonstationary multistep iteration processes
cites work: Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
cites work: Q3943431
cites work: A GENERALIZED THEOREM OF MIRANDA AND THE THEOREM OF NEWTON–KANTOROVICH
DOI: 10.1016/J.CAM.2003.10.015
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description: scientific article; zbMATH DE number 2062755