Conditioning moments of singular measures for entropy maximization II: Numerical examples

TL;DR

This paper demonstrates a numerical framework for conditioning moments of singular measures to ensure the convergence of entropy maximization algorithms, illustrated through simple one-dimensional examples.

Contribution

It extends previous work by providing numerical illustrations of moment conditioning for entropy maximization on bounded, one-dimensional measures.

Findings

Conditioned moments lead to successful entropy maximization convergence.

Unconditioned moments may cause optimization algorithms to fail.

Numerical comparisons show improved approximation accuracy with conditioning.

Abstract

If moments of singular measures are passed as inputs to the entropy maximization procedure, the optimization algorithm might not terminate. The framework developed in our previous paper demonstrated how input moments of measures, on a broad range of domains, can be conditioned to ensure convergence of the entropy maximization. Here we numerically illustrate the developed framework on simplest possible examples: measures with one-dimensional, bounded supports. Three examples of measures are used to numerically compare approximations obtained through entropy maximization with and without the conditioning step.