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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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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Wang, Jh., Li, C. Kantorovich’s theorem for Newton’s method on Lie groups. J. Zhejiang Univ. - Sci. A 8, 978–986 (2007). https://doi.org/10.1631/jzus.2007.A0978
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DOI: https://doi.org/10.1631/jzus.2007.A0978