On Wiener - Hopf factorization of scalar polynomial

TL;DR

This paper introduces an algorithm for scalar polynomial Wiener-Hopf factorization utilizing Toeplitz matrices, providing effective estimates for accuracy and condition numbers, and enabling simultaneous computation of both factors.

Contribution

The paper presents a novel algorithm for scalar polynomial Wiener-Hopf factorization based on indices and essential polynomials, with comprehensive computational and accuracy analysis.

Findings

Algorithm computes both factors simultaneously.

Provides effective bounds for accuracy and condition numbers.

Uses finite Toeplitz matrices for computations.

Abstract

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.