On the convergence order of some Aitken-Steffensen type methods
In this note we make a comparative study of the convergence orders for the Steffensen, Aitken and Aitken-Steffensen methods. We provide some conditions ensuring their local convergence. We study the case when the auxiliary operators used have convergence orders \(r_{1},r_{2}\in \mathbb{N}\) respecti...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2003-08-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/748 |
| _version_ | 1811217969540235264 |
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| author | Ion Păvăloiu |
| author_facet | Ion Păvăloiu |
| author_sort | Ion Păvăloiu |
| collection | DOAJ |
| description | In this note we make a comparative study of the convergence orders for the Steffensen, Aitken and Aitken-Steffensen methods. We provide some conditions ensuring their local convergence. We study the case when the auxiliary operators used have convergence orders \(r_{1},r_{2}\in \mathbb{N}\) respectively. We show that the Steffensen, Aitken and Aitken-Steffensen methods have the convergence orders \(r_{1}+1\), \(r_{1}+r_{2}\) and \(r_{1}r_{2}+r_{1}\) respectively. |
| first_indexed | 2024-04-12T07:02:06Z |
| format | Article |
| id | doaj.art-fe05ac24e49e4d4dbbaaa3c84afb3199 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-04-12T07:02:06Z |
| publishDate | 2003-08-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-fe05ac24e49e4d4dbbaaa3c84afb31992022-12-22T03:42:59ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2003-08-01322On the convergence order of some Aitken-Steffensen type methodsIon Păvăloiu0Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian AcademyIn this note we make a comparative study of the convergence orders for the Steffensen, Aitken and Aitken-Steffensen methods. We provide some conditions ensuring their local convergence. We study the case when the auxiliary operators used have convergence orders \(r_{1},r_{2}\in \mathbb{N}\) respectively. We show that the Steffensen, Aitken and Aitken-Steffensen methods have the convergence orders \(r_{1}+1\), \(r_{1}+r_{2}\) and \(r_{1}r_{2}+r_{1}\) respectively.https://www.ictp.acad.ro/jnaat/journal/article/view/748SteffensenAitken and Aitken-Steffensen iterations |
| spellingShingle | Ion Păvăloiu On the convergence order of some Aitken-Steffensen type methods Journal of Numerical Analysis and Approximation Theory Steffensen Aitken and Aitken-Steffensen iterations |
| title | On the convergence order of some Aitken-Steffensen type methods |
| title_full | On the convergence order of some Aitken-Steffensen type methods |
| title_fullStr | On the convergence order of some Aitken-Steffensen type methods |
| title_full_unstemmed | On the convergence order of some Aitken-Steffensen type methods |
| title_short | On the convergence order of some Aitken-Steffensen type methods |
| title_sort | on the convergence order of some aitken steffensen type methods |
| topic | Steffensen Aitken and Aitken-Steffensen iterations |
| url | https://www.ictp.acad.ro/jnaat/journal/article/view/748 |
| work_keys_str_mv | AT ionpavaloiu ontheconvergenceorderofsomeaitkensteffensentypemethods |