With the standard conditions on a mapping, the authors develop convergence criteria for Newton’s method in a Lie environment. This work extends the previous results of B. Owren
and B. Welfert
[BIT 40, No. 1, 121–145 (2000; Zbl 0957.65054
)] and J.-H. Wang
and C. Li
[J. Zhejiang Univ. Sci. A, 8, 978–986 (2006)]. The main results develop a L-Lipschitz condition under which a sequence generated by Newton’s method is both well-defined and convergent. These results are independent of the metrics defined on the groups. Furthermore, they provide a number of illustrations indicating the advantage of their technique over earlier works.