Heuristic solutions to polynomial moment problems with some convex entropic objectives

We are asking to estimate a nonnegative density (x) over bar on R(m), given some of its algebraic or trigonometric moments. The maximum entropy method is to introduce an entropy-like objective function and then solve a convex minimization programming with some linear constraints. In the existing literature, Newton's method or some other iteration methods are used to solve its dual problem. In this paper, special structures of the problem have been discovered when we use some particular entropies, which include Boltzmann-Shannon entropy and Burg's entropy. Useful linear relationships among the moments help us to set up very fast and effective algorithms. Numerical computations and comparison are also presented.