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 generalized L-average Lipschitz condition. As applications, we get estimations of radius of co...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/367161 |
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| Summary: | 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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| ISSN: | 1085-3375 1687-0409 |