2009/11/02 by Augusto Ferrante, Ferrante, Augusto, Federico Ramponi +3
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Control Systems and Identification #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #math.OC #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.0911.0434
arxiv created 2009/11/02 · openalex publication_date 2009/11/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.