Local Convergence of Newton’s Method on Lie Groups and Uniqueness Balls

Abstract EN

An estimation of uniqueness ball of a zero point of a mapping on Lie group is established.

Furthermore, we obtain a unified estimation of radius of convergence ball of Newton’s method on Lie groups under a generalized L-average Lipschitz condition.

As applications, we get estimations of radius of convergence ball under the Kantorovich condition and the γ-condition, respectively.

In particular, under the γ-condition, our results improve the corresponding results in (Li et al.

2009, Corollary 4.1) as showed in Remark 17.

Finally, applications to analytical mappings are also given.