On a theorem of S. Smale about Newton's method for analytic mappings
type: Item
instance of: scholarly article
title: On a theorem of S. Smale about Newton's method for analytic mappings
zbMATH Open document ID: 0631.65064
DOI: 10.1016/0893-9659(88)90179-6
published in: Applied Mathematics Letters
publication date: 1988-01-01T00:00:00Z
review text: A theorem of \textit{S. Smale} [Proc. Symp. Honor G. S. Young, Laramie/Wyo. 1985, 185-196 (1986; Zbl 0613.65058)] on the convergence of Newton's method for analytic functions holds only for mappings which are analytic on the entire space. The result is generalized to functions which are analytic on an open subset and, for the original case, when this subset is the entire space the controlling constant given by Smale is improved.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 4026700
zbMATH Keywords: analytic mappings
zbMATH Keywords: Banach spaces
zbMATH Keywords: convergence
zbMATH Keywords: Newton's method
author: Werner C. Rheinboldt
MaRDI profile type: Publication
full work available at URL: 0893-9659(88)90179-6
OpenAlex ID: W2069255158
cites work: Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
cites work: Q5791786
cites work: Q5652137
cites work: Q4720691
cites work: A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions
description: scientific article; zbMATH DE number 4026700