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

Jinsu He, Jinhua Wang and Jen-Chih Yao

Abstract and Applied Analysis, 2013, vol. 2013, 1-9

Abstract:

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:367161

DOI: 10.1155/2013/367161

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