Annealing approach to root-finding
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916342030925824 |
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| author | Jo, Junghyo Wagemakers, Alexandre Periwal, Vipul |
| author_facet | Jo, Junghyo Wagemakers, Alexandre Periwal, Vipul |
| contents | The Newton-Raphson method is a fundamental root-finding technique with numerous applications in physics. In this study, we propose a parameterized variant of the Newton-Raphson method, inspired by principles from physics. Through analytical and empirical validation, we demonstrate that this novel approach offers increased robustness and faster convergence during root-finding iterations. Furthermore, we establish connections to the Adomian series method and provide a natural interpretation within a series framework. Remarkably, the introduced parameter, akin to a temperature variable, enables an annealing approach. This advancement sets the stage for a fresh exploration of numerical iterative root-finding methodologies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15338 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Annealing approach to root-finding Jo, Junghyo Wagemakers, Alexandre Periwal, Vipul Numerical Analysis Chaotic Dynamics The Newton-Raphson method is a fundamental root-finding technique with numerous applications in physics. In this study, we propose a parameterized variant of the Newton-Raphson method, inspired by principles from physics. Through analytical and empirical validation, we demonstrate that this novel approach offers increased robustness and faster convergence during root-finding iterations. Furthermore, we establish connections to the Adomian series method and provide a natural interpretation within a series framework. Remarkably, the introduced parameter, akin to a temperature variable, enables an annealing approach. This advancement sets the stage for a fresh exploration of numerical iterative root-finding methodologies. |
| title | Annealing approach to root-finding |
| topic | Numerical Analysis Chaotic Dynamics |
| url | https://arxiv.org/abs/2404.15338 |