On a Steffensen-Hermite type method for approximating the solutions of nonlinear equations
It is well known that the Steffensen and Aitken-Steffensen type methods are obtained from the chord method, using controlled nodes. The chord method is an interpolatory method, with two distinct nodes. Using this remark, the Steffensen and Aitken-Steffensen methods have been generalized using interp...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2006-02-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
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| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/1015 |
| _version_ | 1828462120914649088 |
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| author | Ion Păvăloiu |
| author_facet | Ion Păvăloiu |
| author_sort | Ion Păvăloiu |
| collection | DOAJ |
| description | It is well known that the Steffensen and Aitken-Steffensen type methods are obtained from the chord method, using controlled nodes. The chord method is an interpolatory method, with two distinct nodes. Using this remark, the Steffensen and Aitken-Steffensen methods have been generalized using interpolatory methods obtained from the inverse interpolation polynomial of Lagrange or Hermite type. In this paper we study the convergence and efficiency of some Steffensen type methods which are obtained from the inverse interpolatory polynomial of Hermite type with two controlled nodes. |
| first_indexed | 2024-12-11T02:30:50Z |
| format | Article |
| id | doaj.art-7995b06dc7d749358e98b928694e096d |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-11T02:30:50Z |
| publishDate | 2006-02-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-7995b06dc7d749358e98b928694e096d2022-12-22T01:23:50ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2006-02-01351On a Steffensen-Hermite type method for approximating the solutions of nonlinear equationsIon Păvăloiu0Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian AcademyIt is well known that the Steffensen and Aitken-Steffensen type methods are obtained from the chord method, using controlled nodes. The chord method is an interpolatory method, with two distinct nodes. Using this remark, the Steffensen and Aitken-Steffensen methods have been generalized using interpolatory methods obtained from the inverse interpolation polynomial of Lagrange or Hermite type. In this paper we study the convergence and efficiency of some Steffensen type methods which are obtained from the inverse interpolatory polynomial of Hermite type with two controlled nodes.https://ictp.acad.ro/jnaat/journal/article/view/1015nonlinear equations in \({\mathbb R}\)Steffensen and Aitken-Steffensen methodsinverse interpolatory polynomial of Hermite type |
| spellingShingle | Ion Păvăloiu On a Steffensen-Hermite type method for approximating the solutions of nonlinear equations Journal of Numerical Analysis and Approximation Theory nonlinear equations in \({\mathbb R}\) Steffensen and Aitken-Steffensen methods inverse interpolatory polynomial of Hermite type |
| title | On a Steffensen-Hermite type method for approximating the solutions of nonlinear equations |
| title_full | On a Steffensen-Hermite type method for approximating the solutions of nonlinear equations |
| title_fullStr | On a Steffensen-Hermite type method for approximating the solutions of nonlinear equations |
| title_full_unstemmed | On a Steffensen-Hermite type method for approximating the solutions of nonlinear equations |
| title_short | On a Steffensen-Hermite type method for approximating the solutions of nonlinear equations |
| title_sort | on a steffensen hermite type method for approximating the solutions of nonlinear equations |
| topic | nonlinear equations in \({\mathbb R}\) Steffensen and Aitken-Steffensen methods inverse interpolatory polynomial of Hermite type |
| url | https://ictp.acad.ro/jnaat/journal/article/view/1015 |
| work_keys_str_mv | AT ionpavaloiu onasteffensenhermitetypemethodforapproximatingthesolutionsofnonlinearequations |