CLC number: O242.23
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
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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.
@article{title="Kantorovich’s theorem for Newton’s method on Lie groups",
author="WANG Jin-hua, LI Chong",
journal="Journal of Zhejiang University Science A",
volume="8",
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pages="978-986",
year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A0978"
}
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%A WANG Jin-hua
%A LI Chong
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A0978
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T1 - Kantorovich’s theorem for Newton’s method on Lie groups
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A1 - LI Chong
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EP - 986
%@ 1673-565X
Y1 - 2007
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2007.A0978
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.
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