Algorithm of Polynomial Factorization and Its Implementation in Maple
Victor Mikhailovich Adukov · Bulletin of the South Ural State University Series Mathematical Modelling Programming and Computer Software · 2018
In the work we propose an algorithm for a WienerHopf factorization of scalar polynomials.The algorithm based on notions of indices and essential polynomials allows to nd the factorization factors of the polynomial with the guaranteed accuracy.The method uses computations with nite Toeplitz matrices and permits to obtain coecients 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 found.Formulas for computation of the Laurent coecients with the given accuracy for functions that analytical and non-vanishing in an annular neighborhood of the unit circle are obtained.Stability of the factorization factors is studied.Upper bounds for the accuracy of the factorization factors are established.All estimates are eective.The proposed algorithm is implemented in Maple computer system as module "PolynomialFactorization". Numerical experiments with the module show a good agreement with the theoretical studies.