Convergence of Halley's method under centered Lipschitz condition on the second Fréchet derivative
We present a semi-local as well as a local convergence analysis of Halley's method for approximating a locally unique solution of a nonlinear equation in a Banach space setting. We assume that the second Fréchet-derivative satisfies a centered Lipschitz condition. Numerical examples are us...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2013-02-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/979 |
| _version_ | 1818109631349653504 |
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| author | Ioannis K. Argyros Hongmin Ren |
| author_facet | Ioannis K. Argyros Hongmin Ren |
| author_sort | Ioannis K. Argyros |
| collection | DOAJ |
| description | We present a semi-local as well as a local convergence analysis of Halley's method for approximating a locally unique solution of a nonlinear equation in a Banach space setting.
We assume that the second Fréchet-derivative satisfies a centered Lipschitz condition.
Numerical examples are used to show that the new convergence criteria are satisfied but earlier ones are not satisfied. |
| first_indexed | 2024-12-11T02:34:19Z |
| format | Article |
| id | doaj.art-557847a8d1b144ad947be200c176f42a |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-11T02:34:19Z |
| publishDate | 2013-02-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-557847a8d1b144ad947be200c176f42a2022-12-22T01:23:45ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2013-02-01421Convergence of Halley's method under centered Lipschitz condition on the second Fréchet derivativeIoannis K. Argyros0Hongmin Ren1Cameron UniversityHangzhou PolytechnicWe present a semi-local as well as a local convergence analysis of Halley's method for approximating a locally unique solution of a nonlinear equation in a Banach space setting. We assume that the second Fréchet-derivative satisfies a centered Lipschitz condition. Numerical examples are used to show that the new convergence criteria are satisfied but earlier ones are not satisfied.https://ictp.acad.ro/jnaat/journal/article/view/979Halley's methodFréchet-derivativeBanach spacesemi-local convergenceFrechet derivativecentered Lipschitz condition |
| spellingShingle | Ioannis K. Argyros Hongmin Ren Convergence of Halley's method under centered Lipschitz condition on the second Fréchet derivative Journal of Numerical Analysis and Approximation Theory Halley's method Fréchet-derivative Banach space semi-local convergence Frechet derivative centered Lipschitz condition |
| title | Convergence of Halley's method under centered Lipschitz condition on the second Fréchet derivative |
| title_full | Convergence of Halley's method under centered Lipschitz condition on the second Fréchet derivative |
| title_fullStr | Convergence of Halley's method under centered Lipschitz condition on the second Fréchet derivative |
| title_full_unstemmed | Convergence of Halley's method under centered Lipschitz condition on the second Fréchet derivative |
| title_short | Convergence of Halley's method under centered Lipschitz condition on the second Fréchet derivative |
| title_sort | convergence of halley s method under centered lipschitz condition on the second frechet derivative |
| topic | Halley's method Fréchet-derivative Banach space semi-local convergence Frechet derivative centered Lipschitz condition |
| url | https://ictp.acad.ro/jnaat/journal/article/view/979 |
| work_keys_str_mv | AT ioanniskargyros convergenceofhalleysmethodundercenteredlipschitzconditiononthesecondfrechetderivative AT hongminren convergenceofhalleysmethodundercenteredlipschitzconditiononthesecondfrechetderivative |