Computing a Hurwitz factorization of a polynomial

摘要

A polynomial is called a Hurwitz polynomial (sometimes, when the coefficients are real, a stable polynomial) if all its roots have real part strictly less than zero. In this paper we present a numerical method for computing the coefficients of the Hurwitz factor f(z) of a polynomial p(z). It is based on a polynomial description of the classical LR algorithm for solving the matrix eigenvalue problem. Similarly with the matrix iteration, it turns out that the proposed scheme has a global linear convergence and, moreover, the convergence rate can be improved by considering the technique of shifting. Our numerical experiments, performed with several test polynomials, indicate that the algorithm has good stability properties since the computed approximation errors are generally in accordance with the estimated condition numbers of the desired factors.