Annealing approach to root-finding

TL;DR

This paper introduces a physics-inspired, parameterized variant of the Newton-Raphson method that enhances robustness and convergence speed in root-finding, connecting it to series methods and enabling annealing techniques.

Contribution

It proposes a novel, parameterized Newton-Raphson method inspired by physics, incorporating annealing concepts to improve root-finding performance.

Findings

Increased robustness and faster convergence demonstrated.

Connections established with Adomian series method.

Introduces an annealing-based parameter for iterative root-finding.

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.