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 -condition, respectively. In particular, under the -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.
"Local Convergence of Newton’s Method on Lie Groups and Uniqueness Balls." Abstr. Appl. Anal. 2013 (SI45) 1 - 9, 2013. https://doi.org/10.1155/2013/367161