Local convergence of Newton's method on the Heisenberg group

被引：2
|
作者：
Dali, Bechir [1 ]
Li, Chong [2 ]
Wang, Jinhua [3 ]
机构：
[1] King Saud Univ, Coll Sci, Dept Math, POB 2455, Riyadh 11451, Saudi Arabia
[2] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China
[3] Zhejiang Univ Technol, Dept Math, Hangzhou 310032, Zhejiang, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2016年 / 300卷
基金：
中国国家自然科学基金;
关键词：
Newton's method; Heisenberg group; Lipschitz condition; RIEMANNIAN-MANIFOLDS; VECTOR-FIELDS; UNIQUENESS; ZEROS;
D O I：
10.1016/j.cam.2015.12.025
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present paper, we study Newton's method on the Heisenberg group for solving the equation f (x) = 0, where f is a mapping from Heisenberg group to its Lie algebra. Under certain generalized Lipschitz condition, we obtain the convergence radius of Newton's method and the estimation of the uniqueness ball of the zero point off. Some applications to special cases including Kantorovich's condition and gamma-condition are provided. The determination of an approximate zero point of an analytic mapping is also presented. Concrete examples are given to illustrate applications of our results. (C) 2016 Elsevier B.V. All rights reserved.
引用
收藏
页码：217 / 232
页数：16
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