English

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

Optimization and Control 2009-11-04 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0911.0434,
  title  = {On the convergence of an efficient algorithm for Kullback-Leibler approximation of spectral densities},
  author = {Augusto Ferrante and Federico Ramponi and Francesco Ticozzi},
  journal= {arXiv preprint arXiv:0911.0434},
  year   = {2009}
}