LOCAL CONVERGENCE RESULTS FOR NEWTON'S METHOD

2012 ◽  
Vol 25 (2) ◽  
pp. 267-275
Author(s):  
Ioannis K. Argyros ◽  
Said Hilout
Keyword(s):  
Newton’S Method ◽  
Local Convergence ◽  
Newton's Method ◽  
Convergence Results

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

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jinsu He ◽  
Jinhua Wang ◽  
Jen-Chih Yao
Keyword(s):  
Lie Groups ◽  
Lipschitz Condition ◽  
Lie Group ◽  
Newton’S Method ◽  
Local Convergence ◽  
Newton's Method ◽  
Zero Point ◽  
Radius Of Convergence ◽  
Convergence Ball

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 generalizedL-average Lipschitz condition. As applications, we get estimations of radius of convergence ball under the Kantorovich condition and theγ-condition, respectively. In particular, under theγ-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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