On the accessibility of Newton's method under a Hölder condition on the first derivative
type: Item
instance of: scholarly article
title: On the accessibility of Newton's method under a Hölder condition on the first derivative
zbMATH Open document ID: 1461.65103
author: J. A. Ezquerro
author: Miguel A. Hernández Verón
published in: Algorithms
publication date: 2019-03-26T00:00:00Z
review text: Summary: We see how we can improve the accessibility of Newton's method for approximating a solution of a nonlinear equation in Banach spaces when a center Hölder condition on the first derivative is used to prove its semi-local convergence.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 7042266
zbMATH Keywords: Newton's method
zbMATH Keywords: semi-local convergence
zbMATH Keywords: recurrence relations
zbMATH Keywords: domain of parameters
zbMATH Keywords: nonlinear system
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a8030514
OpenAlex ID: W1929906732
cites work: Q3943431
cites work: Über die Lösung der im Banachschen Raume definierten nichtlinearen Gleichungen
cites work: Q4034594
cites work: The Newton method for operators with Hölder continuous first derivative
cites work: Newton's method under mild differentiability conditions with error analysis
cites work: On the Newton-Kantorovich hypothesis for solving equations
cites work: Q5342116
cites work: Q3932219
DOI: 10.3390/A8030514
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description: scientific article; zbMATH DE number 7042266