A Newton method for canonical Wiener-Hopf and spectral factorization of matrix polynomials

Abstract

The paper presents a novel Newton method for constructing canonical Wiener-Hopf factorizations of complex matrix polynomials and spectral factorizations of positive definite matrix polynomials. The factorizations are the ones needed for discrete-time linear systems and hence with respect to the unit circle. The Jacobi matrix is analyzed, and the convergence of the method is proved and tested numerically. A new class of highly ill-conditioned test polynomials is introduced, and the method is shown to manifest its very good performance also in this critical setting.