Smale's Point Estimate Theory For Newton's Method On Lie Groups

Chong Li; Jin-Hua Wang; Jean-Pierre Dedieu

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Smale's Point Estimate Theory For Newton's Method On Lie Groups

机译：李群上牛顿法的Smale点估计理论

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摘要

We introduce the notion of the (one-parameter subgroup) γ-condition for a map f from a Lie group to its Lie algebra and establish α-theory and γ-theory for Newton's method for a map f satisfying this condition. Applications to analytic maps are provided, and Smale's a-theory and γ-theory are extended and developed. Examples arising from initial value problems on Lie group are presented to illustrate applications of our results.

机译：我们介绍了从李群到李代数的映射f的（一参数子群）γ条件的概念，并为满足该条件的映射f建立了牛顿法的α理论和γ理论。提供了对解析图的应用，并扩展了Smale的a-理论和γ-理论。列举了李群初始值问题引起的例子，以说明我们的结果的应用。

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来源
《Journal of complexity》 |2009年第2期|128-151|共24页
作者
Chong Li; Jin-Hua Wang; Jean-Pierre Dedieu;
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作者单位

Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China;

Department of Mathematics, Zhejiang University of Technology. Hangzhou 310032, PR China;

lnstitut de Mathematiques, Universite Paul Sabatier, 31062 Toulouse Cedex 9, France;

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原文格式 PDF
正文语种 eng
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关键词
newton's method; lie group; the γ-condition; smale's point estimate theory;

机译：牛顿法;李群;γ条件;Smale点估计理论;

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Smale's Point Estimate Theory For Newton's Method On Lie Groups

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