A simplified proof of the Kantorovich theorem for solving equations using telescopic series
We extend the applicability of the Kantorovich theorem (KT) for solving nonlinear equations using Newton-Kantorovich method in a Banach space setting. Under the same information but using elementary scalar telescopic majorizing series, we provide a simpler proof for the (KT) [2], [7]. Our results p...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2015-12-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/1084 |
| _version_ | 1818108512155205632 |
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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 extend the applicability of the Kantorovich theorem (KT) for solving nonlinear equations using Newton-Kantorovich method in a Banach space setting. Under the same information but using elementary scalar telescopic majorizing series, we provide a simpler proof for the (KT) [2], [7]. Our results provide at least as precise information on the location of the solution. Numerical examples are also provided in this study.
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| first_indexed | 2024-12-11T02:16:32Z |
| format | Article |
| id | doaj.art-ecd655ed8b2540bb9012a7bb75c214e1 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-11T02:16:32Z |
| publishDate | 2015-12-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-ecd655ed8b2540bb9012a7bb75c214e12022-12-22T01:24:11ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2015-12-01442A simplified proof of the Kantorovich theorem for solving equations using telescopic seriesIoannis K. Argyros0Hongmin Ren1Cameron UniversityHangzhou Polytechnic We extend the applicability of the Kantorovich theorem (KT) for solving nonlinear equations using Newton-Kantorovich method in a Banach space setting. Under the same information but using elementary scalar telescopic majorizing series, we provide a simpler proof for the (KT) [2], [7]. Our results provide at least as precise information on the location of the solution. Numerical examples are also provided in this study. https://ictp.acad.ro/jnaat/journal/article/view/1084Newton-Kantorovich methodBanach spacemajorizing seriestelescopic seriesKantorovich theorem |
| spellingShingle | Ioannis K. Argyros Hongmin Ren A simplified proof of the Kantorovich theorem for solving equations using telescopic series Journal of Numerical Analysis and Approximation Theory Newton-Kantorovich method Banach space majorizing series telescopic series Kantorovich theorem |
| title | A simplified proof of the Kantorovich theorem for solving equations using telescopic series |
| title_full | A simplified proof of the Kantorovich theorem for solving equations using telescopic series |
| title_fullStr | A simplified proof of the Kantorovich theorem for solving equations using telescopic series |
| title_full_unstemmed | A simplified proof of the Kantorovich theorem for solving equations using telescopic series |
| title_short | A simplified proof of the Kantorovich theorem for solving equations using telescopic series |
| title_sort | simplified proof of the kantorovich theorem for solving equations using telescopic series |
| topic | Newton-Kantorovich method Banach space majorizing series telescopic series Kantorovich theorem |
| url | https://ictp.acad.ro/jnaat/journal/article/view/1084 |
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