Smale's point estimate theory for Newton's method on Lie groups

Authors:
Chong Li;Jin-Hua Wang;Jean-Pierre Dedieu
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China;Department of Mathematics, Zhejiang University of Technology, Hangzhou 310032, PR China;Institut de Mathématiques, Université Paul Sabatier, 31062 Toulouse Cedex 9, France
Venue:
Journal of Complexity
Year:
2009

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Abstract

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