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
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.
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.
