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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 367161, 9 pages
http://dx.doi.org/10.1155/2013/367161
Research Article

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

1Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
2Department of Mathematics, Zhejiang University of Technology, Hangzhou 310032, China
3Department of Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan
4Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 80702, Taiwan
5Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 20 August 2013; Accepted 1 October 2013

Academic Editor: Antonio M. Peralta

Copyright © 2013 Jinsu He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.