Hellinger vs. Kullback-Leibler multivariable spectrum approximation

2007/02/08 by A. Ferrante, Augusto Ferrante, Michele Pavon +6
Chemistry · Computer Science · Mathematics · #Blind Source Separation Techniques #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Spectroscopy and Laser Applications #math.OC

paper · pdf · doi:10.48550/arxiv.math/0702212

32 pages, 1 figure

arxiv created 2007/02/08 · openalex publication_date 2007/02/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a matricial version of the Byrnes-Georgiou-Lindquist generalized moment problem with complexity constraint. We introduce a new metric on multivariable spectral densities induced by the family of their spectral factors which, in the scalar case, reduces to the Hellinger distance. We solve the corresponding constrained optimization problem via duality theory. A highly nontrivial existence theorem for the dual problem is established in the Byrnes-Lindquist spirit. A matricial Newton-type algorithm is finally provided for the numerical solution of the dual problem. Simulation indicates that the algorithm performs effectively and reliably.

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