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Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2007, Vol. 8 Issue (6): 978-986    DOI: 10.1631/jzus.2007.A0978
Computational Mathematics     
Kantorovich’s theorem for Newton’s method on Lie groups
WANG Jin-hua, LI Chong
Department of Mathematics, Zhejiang University of Technology, Hangzhou 310032, China; Department of Mathematics, Zhejiang University, Hangzhou 310027, China
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Abstract  The convergence criterion of Newton’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’s method on Lie group converges to the zero; while this paper provides a Kantorovich’s criterion for the convergence of Newton’s method, not requiring the existence of a zero as a priori.

Key wordsNewton’s method      Lie group      Kantorovich’s theorem      Lipschitz condition     
Received: 20 September 2006     
CLC:  O242.23  
Cite this article:

WANG Jin-hua, LI Chong. Kantorovich’s theorem for Newton’s method on Lie groups. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(6): 978-986.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2007.A0978     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2007/V8/I6/978

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