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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| Format: | Article |
| Language: | English |
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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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| author | Jinsu He Jinhua Wang Jen-Chih Yao |
| author_facet | Jinsu He Jinhua Wang Jen-Chih Yao |
| author_sort | Jinsu He |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a6e582bfe5dd455b8b9a9925361065ab |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a6e582bfe5dd455b8b9a9925361065ab2025-02-03T05:54:30ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/367161367161Local Convergence of Newton’s Method on Lie Groups and Uniqueness BallsJinsu He0Jinhua Wang1Jen-Chih Yao2Department of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Mathematics, Zhejiang University of Technology, Hangzhou 310032, ChinaCenter for Fundamental Science, Kaohsiung Medical University, Kaohsiung 80702, TaiwanAn 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.http://dx.doi.org/10.1155/2013/367161 |
| spellingShingle | Jinsu He Jinhua Wang Jen-Chih Yao Local Convergence of Newton’s Method on Lie Groups and Uniqueness Balls Abstract and Applied Analysis |
| title | Local Convergence of Newton’s Method on Lie Groups and Uniqueness Balls |
| title_full | Local Convergence of Newton’s Method on Lie Groups and Uniqueness Balls |
| title_fullStr | Local Convergence of Newton’s Method on Lie Groups and Uniqueness Balls |
| title_full_unstemmed | Local Convergence of Newton’s Method on Lie Groups and Uniqueness Balls |
| title_short | Local Convergence of Newton’s Method on Lie Groups and Uniqueness Balls |
| title_sort | local convergence of newton s method on lie groups and uniqueness balls |
| url | http://dx.doi.org/10.1155/2013/367161 |
| work_keys_str_mv | AT jinsuhe localconvergenceofnewtonsmethodonliegroupsanduniquenessballs AT jinhuawang localconvergenceofnewtonsmethodonliegroupsanduniquenessballs AT jenchihyao localconvergenceofnewtonsmethodonliegroupsanduniquenessballs |