Mathematical Properties of Frost's Local-Energy Method

Frost's local-energy method is analyzed in two different ways. An exact, trigonometric solution is carried out for the two-dimensional problem. The more general problem is treated by perturbation theory. It is shown that not all solutions of the local-energy equations correspond to minimum variance. Some correspond to maximum variance, others to a saddle point on the variance hypersurface. The number of minimum variance solutions is equal to the number of basis functions when the latter are well chosen, but may otherwise be smaller.