A Comparison of Entropies in the Underdetermined Moment Problem

The problem of function reconstruction from a small number of accurate moments is reviewed and studied numerically. Since this problem is underdetermined, a number of selections have been proposed to pick out a single function. We consider those selections of the \entropic" variety, i.e. those of the form f(x) = Z (x(t))dt for some convex function. We present a summary of our attempts to determine which \entropy" is best for reconstructing x in a variety of model problems. This presumes we have a measure of \best", which in itself is a diicult issue. We include a review of the pertinent theory and the details of our numerical implementation. We give numerous numerical examples to support our conclusions.