Hausdorff Moment Transforms and Their Performance

TL;DR

This paper compares different approximation methods for the truncated Hausdorff moment problem, analyzing their convergence, accuracy, and complexity, and highlights how the decay type of moment sequences influences performance.

Contribution

It introduces a comparison framework for approximation methods and examines how various random sequence generation techniques impact their effectiveness.

Findings

Performance varies significantly across methods in convergence and accuracy.

Decay type of moment sequences strongly influences approximation accuracy.

Some methods can be expressed as linear transforms with detailed accuracy analysis.

Abstract

Various methods have been proposed to approximate a solution to the truncated Hausdorff moment problem. In this paper, we establish a method of comparison for the performance of the approximations. Three ways of producing random moment sequences are discussed and applied. Also, some of the approximations have been rewritten as linear transforms, and detailed accuracy requirements are analyzed. Our finding shows that the performance of the approximations differs significantly in their convergence properties, accuracy, and numerical complexity and that the decay type of the moment sequence strongly affects the accuracy requirement.