This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem 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.
On the convergence of an efficient algorithm for Kullback-Leibler approximation of spectral densities
RAMPONI, Federico Alessandro;
2011-01-01
Abstract
This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
