The problem of reconstructing a distribution with bounded support from its moments is practically relevant in many fields, such as chemical engineering, electrical engineering, and image analysis. The problem is closely related to a classical moment problem, called the truncated Hausdorff moment problem (THMP). We call a method that finds or approximates a solution to the THMP a Hausdorff moment transform (HMT). In practice, selecting the right HMT for specific objectives remains a challenge. This study introduces a systematic and comprehensive method for comparing HMTs based on accuracy, computational complexity, and precision requirements. To enable fair comparisons, we present approaches for generating representative moment sequences. The study also enhances existing HMTs by reducing their computational complexity. Our findings show that the performances of the approximations differ significantly in their convergence, accuracy, and numerical complexity and that the decay order of the moment sequence strongly affects the accuracy requirement.

In this note we examine the relationships between a subnormal shift, the measure its moment sequence generates, and those of a large family of weighted shifts associated with the original shift. We examine the effects on subnormality of adding a new weight or changing a weight. We also obtain formulas for evaluating point mass at the origin for the measure associated with the shift. In addition, we examine the relationship between the measure associated with a subnormal shift and those of a family of shifts substantially different from the original shift.