On Wiener - Hopf factorization of scalar polynomial

In the work we propose an algorithm for a Wiener – Hopf factorization of scalar polynomials based on notions of indices and essential polynomials. The algorithm uses computations with finite Toeplitz matrices and permits to obtain coefficients of both factorization factors simultaneously. Computation aspects of the algorithm are considered. An a priory estimate for the condition number of the used Toeplitz matrices is obtained. Upper bounds for the accuracy of the factorization factors are established. All estimates are effective.