This paper deals with a method for the approximation of a spectral density
function among the solutions of a generalized moment problem a` la
Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the
Kullback-Leibler pseudo-distance, which gives rise to a convex optimization
problem. After developing the variational analysis, we discuss the properties
of an efficient algorithm for the solution of the corresponding dual problem,
based on the iteration of a nonlinear map in a bounded subset of the dual
space.