New algorithm for polynomial spectral factorization with quadratic convergence. II

It is known that two cases of the polynomial spectral factorization are used in applications: the polynomial "discrete" spectral factorization (s) cp( — s) and all roots of the polynomial cp(s) have nonpositive real parts. It is supposed that b(s) = b0 + b1s + ... ... + bks , cp(s) = cp0 + <pjS + ... + cpks k are polynomials with real coefficients. This spectral factorization is used in quadratic continuous optimality problems. There are known three numerical methods for the computation of the spectral factorization cp(s) (p(-s) of a(s) = b(s) b( — s): (i) computation of the roots of a(s) and their suitable selection, (ii) mapping the "continuous" variable s into the "discrete" variable £ by