A unifying local convergence result for Newton's method in Riemannian manifolds
type: Item
instance of: scholarly article
title: A unifying local convergence result for Newton's method in Riemannian manifolds
zbMATH Open document ID: 1147.58008
author: B. E. Eshmatov
published in: Foundations of Computational Mathematics
publication date: 2008-08-20T00:00:00Z
full work available at URL: http://hdl.handle.net/10533/139587
review text: In the problem of singularities of a smooth vector field on a Riemannian manifold, an unified result for the existence and local uniqueness of the solution, and for local covergence of a Riemannian version of Newton's method is proposed. Different specializations of the main result recover Riemannian versions of the theorems of Kantorovich and \textit{S. Smale} [Proc. Symp. Honor G. S. Young, Laramie/Wyo. 1985, 185--196 (1986; Zbl 0613.65058)], and Euclidean self-contact theory of [\textit{Y. Nesterov} and \textit{A. Nemirovskii}, Interior-point polynomial algorithms in convex programming. SIAM Studies in Applied Mathematics. 13. Philadelphia, PA: SIAM (1994; Zbl 0824.90112)]. See also [\textit{J.-P. Dedieu, P. Priouret} and \textit{G. Malajovich}, IMA J. Numer. Anal. 23, No. 3, 395--419 (2003; Zbl 1047.65037)].
reviewed by: Maido Rahula
Mathematics Subject Classification ID: 58C15
Mathematics Subject Classification ID: 49M15
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 90C53
zbMATH DE Number: 5314456
zbMATH Keywords: vector field on Riemannian manifold
zbMATH Keywords: Newton's method
zbMATH Keywords: proximity test
zbMATH Keywords: quadratique rate
Wikidata QID: Q57652231
MaRDI profile type: Publication
OpenAlex ID: W2092736015
DBLP publication ID: journals/focm/AlvarezBM08
DOI: 10.1007/S10208-006-0221-6
description: scientific article; zbMATH DE number 5314456