Result: Kantorovich's theorems for Newton's method for mappings and optimization problems on Lie groups
Title:
Kantorovich's theorems for Newton's method for mappings and optimization problems on Lie groups
Authors:
Source:
IMA journal of numerical analysis. 31(1):322-347
Publisher Information:
Oxford: Oxford University Press, 2011.
Publication Year:
2011
Physical Description:
print, 1 p.3/4
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Algèbre, Algebra, Algèbres et anneaux non associatifs, Nonassociative rings and algebras, Théorie des groupes, Group theory, Groupes topologiques, groupes de lie, Topological groups, lie groups, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Optimisation et calcul variationnel numériques, Numerical methods in optimization and calculus of variations, Algèbre linéaire, Linear algebra, Algebra lineal, Analyse numérique, Numerical analysis, Análisis numérico, Convergence, Convergencia, Méthode Newton, Newton method, Método Newton, Méthode optimisation, Optimization method, Método optimización, 15XX, 17Bxx, 22Exx, 22XX, 49XX, 58C15, 65K10, 65Kxx, Lie group, Lipschitz condition, Newton's method
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics, Zhejiang University of Technology, Hangzhou 310032, China
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
ISSN:
0272-4979
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.23896564
Database:
PASCAL Archive
Further Information
With the classical assumptions on f, a convergence criterion of Newton's method (independent of affine connections) to find zeros of a mapping f from a Lie group to its Lie algebra is established, and estimates of the convergence domains of Newton's method are obtained, which improve the corresponding results in Owren & Welfert (2000, BIT Numer. Math., 40, 121-145) and Wang & Li (2006, J. Zhejiang Univ. Sci. A, 8, 978-986). Applications to optimization are provided and the results due to Mahony (1996, Linear Algebra Appl., 248, 67-89) are extended and improved accordingly.