Lasha Ephremidze and Ilya Spitkovsky
abstract:
A necessary condition for the existence of spectral factorization is positive
definiteness a.e. on the unit circle of a matrix function which is being
factorized. Correspondingly, the existing methods of approximate computation of
the spectral factor can be applied only in the case where the matrix function is
positive definite. However, in many practical situations an empirically
constructed matrix spectral densities may lose this property. In the present
paper we consider possibilities of approximate spectral factorization of matrix
functions by their known perturbation which might not be positive definite on
the unit circle.
Mathematics Subject Classification: 47A68
Key words and phrases: Matrix spectral factorization, positive definite matrix functions