Spectral Factorization of nD Polynomials

In this paper recent new approaches to the representation of a positive polynomials as a sum of squares are used in order to compute spectral factorizations of nonnegative multivariable polynomials. In principle this problem is solved due to the positive solution of Hilberts 17th problem by Artin. Unfortunately Artins result is not constructive and the denominator polynomials arising have no special structure which can be used to compute stable factorizations. In this paper a recent result of Demanze will be used to compute spectral factorization with nD Hurwitz stable factors. The approach is computationally feasible and the decomposition is computed using recently developed methods for semidefinite programming. We are able to reduce the factorization problem to a feasibility problem for a linear matrix inequality.