On the convergence of an efficient algorithm for Kullback-Leibler approximation of spectral densities

Details On the convergence of an efficient algorithm for Kullback-Leibler approximation of spectral densities On the convergence of an efficient algorithm for Kullback-Leibler approximation of spectral densities

2009-11-02

arxiv.org/abs/0911.0434v1

Mathematics

Optimization and Control

Scientific paper

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. Our main result is the proof of local convergence of the latter, established as a consequence of the Central Manifold Theorem. Supported by numerical evidence, we conjecture that, in the mentioned bounded set, the convergence is actually global.

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