Kantorovich's theorem on Newton's method in Riemannian manifolds
type: Item
instance of: scholarly article
title: Kantorovich's theorem on Newton's method in Riemannian manifolds
zbMATH Open document ID: 1003.65057
published in: Journal of Complexity
publication date: 2003-01-08T00:00:00Z
review text: This paper is concerned with the problem of finding a singularity of a vector field in a Riemannian manifold. The authors present an extension of Kantorovich's theorem on Newton's method for this problem in finite dimensional Riemannian manifolds.
reviewed by: Karel Najzar
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 58K45
zbMATH DE Number: 1750228
zbMATH Keywords: Newton's method
zbMATH Keywords: Kantorovich's theorem
zbMATH Keywords: Riemannian manifolds
zbMATH Keywords: singularity
zbMATH Keywords: vectorial field
author: O. P. Ferreira
author: B. F. Svaiter
MaRDI profile type: Publication
full work available at URL: jcom.2001.0582
OpenAlex ID: W2066214692
Wikidata QID: Q115395639
cites work: New results on newton-kantorovich approximations with applications to nonlinear integral equations
cites work: A unified approach for constructing fast two-step Newton-like methods
cites work: On the Kantorovich Hypothesis for Newton’s Method
cites work: Q4003026
cites work: The Geometry of Algorithms with Orthogonality Constraints
cites work: Minimizing a differentiable function over a differential manifold
cites work: Shadowing orbits and Kantorovich's theorem
cites work: Q3231529
cites work: Q5787268
cites work: Q3265960
cites work: Q5332416
cites work: A NEW TECHNIQUE FOR THE CONSTRUCTION OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS
cites work: The imbedding problem for Riemannian manifolds
cites work: The Newton-Kantorovich Theorem
cites work: Q5652137
cites work: Complexity of Bezout's Theorem I: Geometric Aspects
cites work: Q4720691
cites work: Optimization Techniques on Riemannian Manifolds
cites work: Q5797559
cites work: Q4310716
cites work: A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions
DOI: 10.1006/JCOM.2001.0582
description: scientific article; zbMATH DE number 1750228