Maximal-entropy driven determination of weights in least-square approximation

TL;DR

This paper introduces a novel maximal-entropy approach to determine weights and coefficients simultaneously in least-square approximation, demonstrating promising results with polynomial test cases.

Contribution

It presents a new method leveraging maximal-entropy principles to optimize weights and coefficients in least-square approximation within a single framework.

Findings

Effective weight and coefficient determination in polynomial approximation

Demonstrated method's potential through representative test cases

Provides a foundation for future improvements in the approach

Abstract

We exploit the idea to use the maximal-entropy method, successfully tested in information theory and statistical thermodynamics, to determine approximating function's coefficients and squared errors' weights simultaneously as output of one single problem in least-square approximation. We provide evidence of the method's capabilities and performance through its application to representative test cases by working with polynomials as a first step. We conclude by formulating suggestions for future work to improve the version of the method we present in this paper.