2024/04/10 by Jo, Junghyo, Wagemakers, Alexandre, Periwal, Vipul · 1 citation
#Chaotic Dynamics (nlin.CD) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2404.15338
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.