AN IMPROVED UNIFYING CONVERGENCE ANALYSIS OF NEWTON'S METHOD IN RIEMANNIAN MANIFOLDS

被引：11

作者：

Argyros, Ioannis K. ^{[1
]}

机构：

[1] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA

来源：

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2007年 / 25卷 / 1-2期

关键词：

Newton's method; Riemannian manifold; local/semilocal convergence; singularity of a vector field; Newton-Kantorovich method;

D O I：

10.1007/BF02832359

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using more precise majorizing sequences we provide a finer convergence analysis than before [1], [7] of Newton's method in Riemannian manifolds with the following advantages: weaker hypotheses, finer error bounds on the distances involved and a more precise information on the location of the singularity of the vector field.

引用

页码：345 / 351

页数：7

共 9 条

[1] ALVAREZ F, 2004, UNIFYING LOCAL CONVE
[2] Argyros I. K., 2005, ADV NONLINEAR VARIAT, V8, P81
[3] A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
Argyros, IK
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 298 (02) : 374 - 397
[4] An improved convergence analysis and applications for Newton-like methods in Banach space
Argyros, IK
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2003, 24 (7-8) : 653 - 672
[5] Argyros IK, 2005, NEWTON METHODS
[6] Carano M. Do, 1992, RIEMANNIAN GEOMETRY
[7] Kantorovich's theorem on Newton's method in Riemannian manifolds
Ferreira, OP
Svaiter, BF
[J]. JOURNAL OF COMPLEXITY, 2002, 18 (01) : 304 - 329
[8] Kantorovich L. V., 1982, FUNCTIONAL ANAL, VSecond
[9] THE MAJORANT METHOD IN THE THEORY OF NEWTON-KANTOROVICH APPROXIMATIONS AND THE PTAK ERROR-ESTIMATES
ZABREJKO, PP
NGUEN, DF
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1987, 9 (5-6) : 671 - 684

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