| 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： | [1]Department of Mathematics, Zhejiang University of Technology, Hangzhou 310032, China [2]Department 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）, and 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 ofa mapffrom a Lie group to its corresponding Lie algebra is established under the assumption thatfsatisfies 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 fare estimated. Owren and Welfert （2000） stated that if the initial point is close sufficiently to a zero off 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： | 李群 牛顿法 Kantorovich定理 Lipschitz条件 收敛 |
| 收稿时间： | 2006-09-20 |
| 修稿时间： | 2007-01-04 |
Kantorovich’s theorem for Newton’s method on Lie groups |
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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,2007,8(6):978-986. |
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| Authors: | Wang Jin-hua Li Chong |
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| Institution: | (1) Department of Mathematics, Zhejiang University of Technology, Hangzhou, 310032, China;(2) Department of Mathematics, Zhejiang University, Hangzhou, 310027, China |
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| Abstract: | The convergence criterion of Newton's method to find the zeros ofa mapffrom a Lie group to its corresponding Lie algebra is established under the assumption thatfsatisfies 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 fare estimated. Owren and Welfert (2000) stated that ifthe 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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| Keywords: | Newton's method Lie group Kantorovich's theorem Lipschitz condition |
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