A fast heuristic method for polynomial moment problems with Boltzmann-Shannon Entropy

The authors consider the best entropy estimate to a nonnegative density x̅ on IR^m given some of its algebraic or trigonometric moments. Using the special structure of this kind of problem, a useful linear relationship among the moments is derived. A simple algorithm then provides a fairly good estimate of x̅ by just solving a couple of linear systems. Numerical computations make the algorithm seem reasonable although the theoretical convergence is still an open problem. Some notes about the error bounds are given at the end of the paper.