Further Results on the Byrnes-Georgiou-Lindquist Generalized Moment Problem

In this paper, we consider the problem of finding, among solutions of a moment problem, the best Kullback-Leibler approximation of a given a priori spectral density. We present a new complete existence proof for the dual optimization problem in the Byrnes-Lindquist spirit. We also prove a descent property for a matricial iterative method for the numerical solution of the dual problem. The latter has proven to perform extremely well in simulation testbeds.