| Kantorovich’s theorem for Newton’s method on Lie groups |
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| 作者姓名： | WANG Jin-hua LI Chong |
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| 作者单位： | WANG Jin-hua1，LI Chong2 (1Department of Mathematics，Zhejiang University of Technology，Hangzhou 310032，China) (2Department of Mathematics，Zhejiang University，Hangzhou 310027，China) |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (No. 10271025)，the Program for New Century Excellent Talents in University of China |
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| 摘 要： | 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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| 关 键 词： | Newton’s method Lie group Kantorovich’s theorem Lipschitz condition |
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