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2013 Local Convergence of Newton’s Method on Lie Groups and Uniqueness Balls
Jinsu He, Jinhua Wang, Jen-Chih Yao
Abstr. Appl. Anal. 2013(SI45): 1-9 (2013). DOI: 10.1155/2013/367161


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.


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Jinsu He. Jinhua Wang. Jen-Chih Yao. "Local Convergence of Newton’s Method on Lie Groups and Uniqueness Balls." Abstr. Appl. Anal. 2013 (SI45) 1 - 9, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1307.65079
MathSciNet: MR3129324
Digital Object Identifier: 10.1155/2013/367161

Rights: Copyright © 2013 Hindawi


Vol.2013 • No. SI45 • 2013
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