Comparative Analysis of Numerical Methods for Parameter Determination

TL;DR

This paper compares various numerical optimization methods, analyzing their computational efficiency and applicability to complex functions, with a case study on the eclipsing binary system AM Leo.

Contribution

It provides a comparative analysis of multiple numerical methods for multidimensional optimization, highlighting their advantages and limitations for complex functions.

Findings

Monte Carlo method applied to AM Leo system

Analysis of computational costs for different methods

Identification of suitable methods for complex functions

Abstract

We made a comparative analysis of numerical methods for multidimensional optimization. The main parameter is a number of computations of the test function to reach necessary accuracy, as it is computationally "slow". For complex functions, analytic differentiation by many parameters can cause problems associated with a significant complication of the program and thus slowing its operation. For comparison, we used the methods: "brute force" (or minimization on a regular grid), Monte Carlo, steepest descent, conjugate gradients, Brent's method (golden section search), parabolic interpolation etc. The Monte-Carlo method was applied to the eclipsing binary system AM Leo.