Local convergence of Newton's method using Kantorovich convex majorants
We are concerned with the problem of approximating a solution of an operator equation using Newton's method. Recently in the elegant work by Ferreira and Svaiter [6] a semilocal convergence analysis was provided which makes clear the relationship of the majorant function with the operator invo...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2010-08-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
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| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/1029 |
| _version_ | 1818199372758777856 |
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| author | Ioannis K. Argyros |
| author_facet | Ioannis K. Argyros |
| author_sort | Ioannis K. Argyros |
| collection | DOAJ |
| description | We are concerned with the problem of approximating a solution of an operator equation using Newton's method. Recently in the elegant work by Ferreira and Svaiter [6] a semilocal convergence analysis was provided which makes clear the relationship of the majorant function with the operator involved. However these results cannot provide information about the local convergence of Newton's method in their present form. Here we have rectified this problem by using two flexible majorant functions. The radius of convergence is also found. Finally, under the same computational cost, we show that our radius of convergence is larger, and the error estimates on the distances involved is finer than the corresponding ones [1], [11]-[13]. |
| first_indexed | 2024-12-12T02:20:43Z |
| format | Article |
| id | doaj.art-b7eb44ab1519499fb8ed11978750775c |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-12T02:20:43Z |
| publishDate | 2010-08-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-b7eb44ab1519499fb8ed11978750775c2022-12-22T00:41:41ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2010-08-01392Local convergence of Newton's method using Kantorovich convex majorantsIoannis K. Argyros0Cameron UniversityWe are concerned with the problem of approximating a solution of an operator equation using Newton's method. Recently in the elegant work by Ferreira and Svaiter [6] a semilocal convergence analysis was provided which makes clear the relationship of the majorant function with the operator involved. However these results cannot provide information about the local convergence of Newton's method in their present form. Here we have rectified this problem by using two flexible majorant functions. The radius of convergence is also found. Finally, under the same computational cost, we show that our radius of convergence is larger, and the error estimates on the distances involved is finer than the corresponding ones [1], [11]-[13].https://www.ictp.acad.ro/jnaat/journal/article/view/1029Newton's methodBanach spaceKantorovich's majorantsconvex functionlocal/semilocal convergenceFréchet-derivative |
| spellingShingle | Ioannis K. Argyros Local convergence of Newton's method using Kantorovich convex majorants Journal of Numerical Analysis and Approximation Theory Newton's method Banach space Kantorovich's majorants convex function local/semilocal convergence Fréchet-derivative |
| title | Local convergence of Newton's method using Kantorovich convex majorants |
| title_full | Local convergence of Newton's method using Kantorovich convex majorants |
| title_fullStr | Local convergence of Newton's method using Kantorovich convex majorants |
| title_full_unstemmed | Local convergence of Newton's method using Kantorovich convex majorants |
| title_short | Local convergence of Newton's method using Kantorovich convex majorants |
| title_sort | local convergence of newton s method using kantorovich convex majorants |
| topic | Newton's method Banach space Kantorovich's majorants convex function local/semilocal convergence Fréchet-derivative |
| url | https://www.ictp.acad.ro/jnaat/journal/article/view/1029 |
| work_keys_str_mv | AT ioanniskargyros localconvergenceofnewtonsmethodusingkantorovichconvexmajorants |