Hankel matrices and their applications to the numerical factorization of polynomials

Globally convergent algorithms for the numerical factorization of polynomials are presented. When the zeros of a polynomial are all simple and of different modulus, these procedures are useful in the simultaneous determination of all zeros. These methods are derived based on the algebraic properties of sums of powers of complex numbers and Hankel matrices. The remainder and quotient polynomials which arise from applying the Euclidean and a version of Householder's algorithms are investigated in terms of their convergence properties which turn out to be useful in the splitting of a polynomial into a product of two factors.