Hellinger vs. Kullback-Leibler multivariable spectrum approximation

Details Hellinger vs. Kullback-Leibler multivariable spectrum approximation Hellinger vs. Kullback-Leibler multivariable spectrum approximation

2007-02-08

arxiv.org/abs/math/0702212v1

Mathematics

Optimization and Control

32 pages, 1 figure

Scientific paper

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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