  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.
