The Newtonian Operator and Global Convergence Balls for Newton’s Method
We obtain results of restricted global convergence for Newton’s method from ideas based on the Fixed-Point theorem and using the Newtonian operator and auxiliary points. The results are illustrated with a non-linear integral equation of Davis-type and improve the results previously given by the auth...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/7/1074 |
| _version_ | 1827713763211476992 |
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| author | José A. Ezquerro Miguel A. Hernández-Verón |
| author_facet | José A. Ezquerro Miguel A. Hernández-Verón |
| author_sort | José A. Ezquerro |
| collection | DOAJ |
| description | We obtain results of restricted global convergence for Newton’s method from ideas based on the Fixed-Point theorem and using the Newtonian operator and auxiliary points. The results are illustrated with a non-linear integral equation of Davis-type and improve the results previously given by the authors. |
| first_indexed | 2024-03-10T18:43:33Z |
| format | Article |
| id | doaj.art-5f55f6e25bc14acdaebbdd2449c0777c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T18:43:33Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5f55f6e25bc14acdaebbdd2449c0777c2023-11-20T05:38:46ZengMDPI AGMathematics2227-73902020-07-0187107410.3390/math8071074The Newtonian Operator and Global Convergence Balls for Newton’s MethodJosé A. Ezquerro0Miguel A. Hernández-Verón1Department of Mathematics and Computation, University of La Rioja, alle Madre de Dios, 53, 26006 Logroño, La Rioja, SpainDepartment of Mathematics and Computation, University of La Rioja, alle Madre de Dios, 53, 26006 Logroño, La Rioja, SpainWe obtain results of restricted global convergence for Newton’s method from ideas based on the Fixed-Point theorem and using the Newtonian operator and auxiliary points. The results are illustrated with a non-linear integral equation of Davis-type and improve the results previously given by the authors.https://www.mdpi.com/2227-7390/8/7/1074fixed-point theoremNewton’s methodNewtonian operatorglobal convergenceconvergence ballFredholm integral equation |
| spellingShingle | José A. Ezquerro Miguel A. Hernández-Verón The Newtonian Operator and Global Convergence Balls for Newton’s Method Mathematics fixed-point theorem Newton’s method Newtonian operator global convergence convergence ball Fredholm integral equation |
| title | The Newtonian Operator and Global Convergence Balls for Newton’s Method |
| title_full | The Newtonian Operator and Global Convergence Balls for Newton’s Method |
| title_fullStr | The Newtonian Operator and Global Convergence Balls for Newton’s Method |
| title_full_unstemmed | The Newtonian Operator and Global Convergence Balls for Newton’s Method |
| title_short | The Newtonian Operator and Global Convergence Balls for Newton’s Method |
| title_sort | newtonian operator and global convergence balls for newton s method |
| topic | fixed-point theorem Newton’s method Newtonian operator global convergence convergence ball Fredholm integral equation |
| url | https://www.mdpi.com/2227-7390/8/7/1074 |
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