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Annealing approach to root finding.

Junghyo Jo^1,2,3, Alexandre Wagemakers⁴, Vipul Periwal⁵

¹Department of Physics Education, <a href="https://ror.org/04h9pn542">Seoul National University</a>, Seoul 08826, Korea.

Physical Review. E

|September 19, 2024

Summary

This summary is machine-generated.

This study introduces a new parameterized Newton-Raphson method for faster and more robust root-finding. Inspired by physics, it offers an annealing approach for numerical methods.

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Area of Science:

Numerical Analysis
Computational Physics

Background:

The Newton-Raphson method is a cornerstone for solving equations numerically.
Its applications span various scientific disciplines, including physics.
Enhancing its convergence and robustness remains an active research area.

Purpose of the Study:

To introduce a novel parameterized variant of the Newton-Raphson method.
To leverage physical principles for improved numerical root-finding.
To explore connections with series expansion methods.

Main Methods:

Development of a parameterized Newton-Raphson algorithm.
Analytical validation of the method's properties.
Empirical testing for convergence and robustness.
Establishing links to the Adomian series method.

Main Results:

The parameterized method demonstrates enhanced robustness.
Faster convergence rates were observed in root-finding iterations.
A novel annealing approach was enabled by the introduced parameter.
Connections to the Adomian series were mathematically established.

Conclusions:

The parameterized Newton-Raphson method offers significant improvements over the standard technique.
The physics-inspired parameter provides a new dimension for numerical optimization.
This work opens avenues for advanced iterative root-finding algorithms.