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arXiv · 2404.15338

Annealing approach to root-finding

Junghyo Jo·Alexandre Wagemakers·Vipul Periwal
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Abstract

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.

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Junghyo Jo, Alexandre Wagemakers, Vipul Periwal. 2024-08-01. Annealing approach to root-finding. https://arxiv.org/abs/2404.15338

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