A FAST HEURISTIC METHOD FOR POLYNOMIAL MOMENT PROBLEMS WITH BOLTZMANN-SHANNON ENTROPY

The authors consider the best entropy estimate to a nonnegative density xOBAR on R(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 farily good estimate of xOBAR 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.