Convergence of the Newton method and uniqueness of zeros of vector fields on Riemannian manifolds

被引：27

作者：

Li, C ^{[1
]}

Wang, JH ^{[1
]}

机构：

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS | 2005年 / 48卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Riemannian manifold; Newton method; convergence ball; uniqueness ball;

D O I：

10.1360/04ys0147

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The estimates of the radii of convergence balls of the Newton method and uniqueness balls of zeroes of vector fields on the Riemannian manifolds are given under the assumption that the covariant derivatives of the vector fields satisfy some kind of general Lipschitz conditions. Some classical results such as the Kantorovich's type theorem and the Smale's gamma-theory are extended.

引用

页码：1465 / 1478

页数：14

共 20 条

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