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.

翻译：针对截断Hausdorff矩问题的近似求解，已有多种方法被提出。本文建立了一种比较各类近似方法性能的评估框架，讨论并应用了三种生成随机矩序列的方式。此外，部分近似方法被改写为线性变换形式，并对其精度要求进行了详细分析。研究结果表明，不同近似方法在收敛特性、精度和数值复杂度方面存在显著差异，且矩序列的衰减类型对精度要求具有重要影响。