Convergence of Newton's Method on Lie Groups

2021 ◽  
pp. 349-360
Author(s):  
Ioannis K. Argyros
Keyword(s):  
Lie Groups ◽  
Newton’S Method ◽  
Newton's Method

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.

scholarly journals Smale’s point estimate theory for Newton’s method on Lie groups

2009 ◽  
Vol 25 (2) ◽  
pp. 128-151 ◽  
Author(s):  
Chong Li ◽  
Jin-Hua Wang ◽  
Jean-Pierre Dedieu
Keyword(s):  
Lie Groups ◽  
Newton’S Method ◽  
Newton's Method ◽  
Point Estimate

Newton’s method on Lie groups

2008 ◽  
Vol 31 (1-2) ◽  
pp. 217-228 ◽  
Author(s):  
Ioannis K. Argyros
Keyword(s):  
Lie Groups ◽  
Newton’S Method ◽  
Newton's Method

Extending the applicability of Newton’s method on Lie groups

2013 ◽  
Vol 219 (20) ◽  
pp. 10355-10365 ◽  
Author(s):  
Ioannis K. Argyros ◽  
Saïd Hilout
Keyword(s):  
Lie Groups ◽  
Newton’S Method ◽  
Newton's Method

Optimal Power Flow Using Newton’s Method

2012 ◽  
Vol 3 (2) ◽  
pp. 167-169
Author(s):  
F.M.PATEL F.M.PATEL ◽  
◽  
N. B. PANCHAL N. B. PANCHAL
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Optimal Power

An Efficient Sixth-Order Convergent Newton-Type Iterative Method for Nonlinear Equations

2012 ◽  
Vol 220-223 ◽  
pp. 2585-2588
Author(s):  
Zhong Yong Hu ◽  
Fang Liang ◽  
Lian Zhong Li ◽  
Rui Chen
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Sixth Order ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present a modified sixth order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives per iteration. Hence the efficiency index of the presented method is 1.43097 which is better than that of classical Newton’s method 1.41421. Several results are given to illustrate the advantage and efficiency the algorithm.

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