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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.6 P.978-986


Kantorovich’s theorem for Newton’s method on Lie groups

Author(s):  WANG Jin-hua, LI Chong

Affiliation(s):  Department of Mathematics, Zhejiang University of Technology, Hangzhou 310032, China; more

Corresponding email(s):   wjh@zjut.edu.cn, cli@zju.edu.cn

Key Words:  Newton&rsquo, s method, Lie group, Kantorovich&rsquo, s theorem, Lipschitz condition

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WANG Jin-hua, LI Chong. Kantorovich’s theorem for Newton’s method on Lie groups[J]. Journal of Zhejiang University Science A, 2007, 8(6): 978-986.

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The convergence criterion of newton&rsquo;s method to find the zeros of a map f from a lie group to its corresponding Lie algebra is established under the assumption that f satisfies the classical lipschitz condition, and that the radius of convergence ball is also obtained. Furthermore, the radii of the uniqueness balls of the zeros of f are estimated. Owren and Welfert (2000) stated that if the initial point is close sufficiently to a zero of f, then newton&rsquo;s method on lie group converges to the zero; while this paper provides a kantorovich&rsquo;s criterion for the convergence of newton&rsquo;s method, not requiring the existence of a zero as a priori.

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