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：已经提出了各种方法来近似解决Hausdorf短时间问题的办法。 在本文中,我们为近似值的性能制定了一种比较方法。 讨论并应用了三种生成随机时间序列的方法。 另外,一些近似值随着线性变换和详细的准确性要求分析而被重新改写。 我们的发现表明,近似值的性能在它们的趋同性、准确性和数字复杂性方面差异很大,时间序列的衰变类型对准确性要求产生了强烈的影响。