EXTENDING THE APPLICABILITY OF NEWTON'S METHOD ON RIEMANNIAN MANIFOLDS WITH VALUES IN A CONE

被引：0

作者：

Argyros, Ioannis K. ^{[1
]}

George, Santhosh ^{[2
]}

机构：

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

[2] Natl Inst Technol Karnataka, Dept Math & Computat Sci, Mangalore 757025, Karnataka, India

来源：

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS | 2013年 / 6卷 / 03期

关键词：

Newton's method; Riemannian manifold; semilocal convergence; L-average Lipschitz condition;

D O I：

10.1142/S1793557113500411

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a new semilocal convergence analysis of Newton's method on Riemannian manifolds with values in a cone in order to solve the inclusion problem. Using more precise majorizing sequences than in earlier studies such as [J. H. Wang, S. Huang and C. Li, Extended Newton's method for mappings on Riemannian manifolds with values in a cone, Taiwanese J. Math. 13(2B) (2009) 633-656] and the concept of L-average Lipschitz condition we provide: weaker sufficient convergence conditions; tighter error analysis on the distances involved and an at least as precise information on the solutions. These advantages are obtained using the same parameters and functions. Applications include the celebrated Newton-Kantorovich theorem.

引用

页数：15

共 35 条

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