Local Convergence of Newton’s Method on Lie Groups and Uniqueness Balls
Copyright policy )Local Convergence of Newton’s Method on Lie Groups and Uniqueness Balls
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.
- Zhejiang University of Technology China (People's Republic of)
- National Sun Yat-sen University Taiwan
- King Abdulaziz University Saudi Arabia
- Kaohsiung Medical University Taiwan
- Zhejiang Normal University China (People's Republic of)
convergence, Numerical solutions to equations with nonlinear operators, Lie algebra, Implicit function theorems; global Newton methods on manifolds, Lie group, Analysis on real and complex Lie groups, Newton method, QA1-939, Kantorovich condition, exponential mapping, nonlinear equation, Mathematics
convergence, Numerical solutions to equations with nonlinear operators, Lie algebra, Implicit function theorems; global Newton methods on manifolds, Lie group, Analysis on real and complex Lie groups, Newton method, QA1-939, Kantorovich condition, exponential mapping, nonlinear equation, Mathematics
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