Local Convergence of Newton's Method on Lie Groups and Uniqueness Balls. (13th November 2013)

• Record Type: Journal Article
• Authors: He, Jinsu; Wang, Jinhua; Yao, Jen-Chih
• Other Names: Peralta Antonio M. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-11-13
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/367161
• Languages: English
• ISSNs: 1085-3375

Abstract

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 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.