Local convergence for an eighth order method for solving equations and systems of equations
The aim of this study is to extend the applicability of an eighth convergence order method from the k−dimensional Euclidean space to a Banach space setting. We use hypotheses only on the first derivative to show the local convergence of the method. Earlier studies use hypotheses up to the eighth der...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2019-01-01
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| Series: | Nonlinear Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/nleng-2017-0105 |
| _version_ | 1818598217106849792 |
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| author | Argyros Ioannis K. George Santhosh |
| author_facet | Argyros Ioannis K. George Santhosh |
| author_sort | Argyros Ioannis K. |
| collection | DOAJ |
| description | The aim of this study is to extend the applicability of an eighth convergence order method from the k−dimensional Euclidean space to a Banach space setting. We use hypotheses only on the first derivative to show the local convergence of the method. Earlier studies use hypotheses up to the eighth derivative although only the first derivative and a divided difference of order one appear in the method. Moreover, we provide computable error bounds based on Lipschitz-type functions. |
| first_indexed | 2024-12-16T12:00:11Z |
| format | Article |
| id | doaj.art-ac8bc00d297b42d9bf1f9fdedf03e954 |
| institution | Directory Open Access Journal |
| issn | 2192-8010 2192-8029 |
| language | English |
| last_indexed | 2024-12-16T12:00:11Z |
| publishDate | 2019-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonlinear Engineering |
| spelling | doaj.art-ac8bc00d297b42d9bf1f9fdedf03e9542022-12-21T22:32:27ZengDe GruyterNonlinear Engineering2192-80102192-80292019-01-0181747910.1515/nleng-2017-0105nleng-2017-0105Local convergence for an eighth order method for solving equations and systems of equationsArgyros Ioannis K.0George Santhosh1Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USADepartment of Mathematical and Computational Sciences, NITMangaluruKarnataka, India-575 025The aim of this study is to extend the applicability of an eighth convergence order method from the k−dimensional Euclidean space to a Banach space setting. We use hypotheses only on the first derivative to show the local convergence of the method. Earlier studies use hypotheses up to the eighth derivative although only the first derivative and a divided difference of order one appear in the method. Moreover, we provide computable error bounds based on Lipschitz-type functions.https://doi.org/10.1515/nleng-2017-0105banach spacelocal convergenceconvergence orderlipschitz condition65h1065g9947h1749m15 |
| spellingShingle | Argyros Ioannis K. George Santhosh Local convergence for an eighth order method for solving equations and systems of equations Nonlinear Engineering banach space local convergence convergence order lipschitz condition 65h10 65g99 47h17 49m15 |
| title | Local convergence for an eighth order method for solving equations and systems of equations |
| title_full | Local convergence for an eighth order method for solving equations and systems of equations |
| title_fullStr | Local convergence for an eighth order method for solving equations and systems of equations |
| title_full_unstemmed | Local convergence for an eighth order method for solving equations and systems of equations |
| title_short | Local convergence for an eighth order method for solving equations and systems of equations |
| title_sort | local convergence for an eighth order method for solving equations and systems of equations |
| topic | banach space local convergence convergence order lipschitz condition 65h10 65g99 47h17 49m15 |
| url | https://doi.org/10.1515/nleng-2017-0105 |
| work_keys_str_mv | AT argyrosioannisk localconvergenceforaneighthordermethodforsolvingequationsandsystemsofequations AT georgesanthosh localconvergenceforaneighthordermethodforsolvingequationsandsystemsofequations |