Local Convergence and Radius of Convergence for Modified Newton Method
We investigate the local convergence of modified Newton method, i.e., the classical Newton method in which the derivative is periodically re-evaluated. Based on the convergence properties of Picard iteration for demicontractive mappings, we give an algorithm to estimate the local radius of convergen...
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Sciendo
2017-12-01
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| Series: | Annals of the West University of Timisoara: Mathematics and Computer Science |
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| Online Access: | https://doi.org/10.1515/awutm-2017-0020 |
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doaj-0469427f516842289c8f9249144a67ad2021-09-06T19:40:24ZengSciendoAnnals of the West University of Timisoara: Mathematics and Computer Science1841-33072017-12-0155215716910.1515/awutm-2017-0020awutm-2017-0020Local Convergence and Radius of Convergence for Modified Newton MethodMăruşter Ştefan0Department of Computer Science, West University of Timisoara, B-l V. Parvan nr. 4, Timisoara, RomaniaWe investigate the local convergence of modified Newton method, i.e., the classical Newton method in which the derivative is periodically re-evaluated. Based on the convergence properties of Picard iteration for demicontractive mappings, we give an algorithm to estimate the local radius of convergence for considered method. Numerical experiments show that the proposed algorithm gives estimated radii which are very close to or even equal with the best ones.https://doi.org/10.1515/awutm-2017-0020modified newton methodlocal convergencelocal convergence radius45g1047h1765j1565g99 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Măruşter Ştefan |
| spellingShingle |
Măruşter Ştefan Local Convergence and Radius of Convergence for Modified Newton Method Annals of the West University of Timisoara: Mathematics and Computer Science modified newton method local convergence local convergence radius 45g10 47h17 65j15 65g99 |
| author_facet |
Măruşter Ştefan |
| author_sort |
Măruşter Ştefan |
| title |
Local Convergence and Radius of Convergence for Modified Newton Method |
| title_short |
Local Convergence and Radius of Convergence for Modified Newton Method |
| title_full |
Local Convergence and Radius of Convergence for Modified Newton Method |
| title_fullStr |
Local Convergence and Radius of Convergence for Modified Newton Method |
| title_full_unstemmed |
Local Convergence and Radius of Convergence for Modified Newton Method |
| title_sort |
local convergence and radius of convergence for modified newton method |
| publisher |
Sciendo |
| series |
Annals of the West University of Timisoara: Mathematics and Computer Science |
| issn |
1841-3307 |
| publishDate |
2017-12-01 |
| description |
We investigate the local convergence of modified Newton method, i.e., the classical Newton method in which the derivative is periodically re-evaluated. Based on the convergence properties of Picard iteration for demicontractive mappings, we give an algorithm to estimate the local radius of convergence for considered method. Numerical experiments show that the proposed algorithm gives estimated radii which are very close to or even equal with the best ones. |
| topic |
modified newton method local convergence local convergence radius 45g10 47h17 65j15 65g99 |
| url |
https://doi.org/10.1515/awutm-2017-0020 |
| work_keys_str_mv |
AT marusterstefan localconvergenceandradiusofconvergenceformodifiednewtonmethod |
| _version_ |
1717768538896203776 |