A Newton method for canonical Wiener-Hopf and spectral factorization of matrix polynomials
Albrecht Boettcher, Martin Halwaß · Electronic Journal of Linear Algebra · 2013
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.