On the Georgiou–Lindquist Approach to Constrained Kullback–Leibler Approximation of Spectral Densities

We consider the Georgiou-Lindquist constrained approximation of spectra in the Kullback-Leibler sense. We propose an alternative iterative algorithm to solve the corresponding convex optimization problem. The Lagrange multiplier is computed as a fixed point of a nonlinear matricial map. Simulation indicates that the algorithm is extremely effective.