Maximum entropy and the problem of moments: A stable algorithm

TL;DR

This paper introduces a stable, iterative algorithm for entropy optimization to reconstruct distributions from moments, demonstrating its effectiveness through numerical tests and an application to electronic density of states in amorphous silica.

Contribution

The paper presents a novel stable algorithm for entropy maximization from moments, with demonstrated numerical stability and application to electronic structure problems.

Findings

Algorithm shows high stability in numerical tests

Effective in reconstructing distributions from moments

Converges well in electronic density of states application

Abstract

We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an optimal solution can be constructed iteratively. We demonstrate the performance and stability of our algorithm with several tests on numerically difficult functions. We then consider an electronic structure application, the electronic density of states of amorphous silica and study the convergence of Fermi level with increasing number of moments.