On the complexity of computing the GCD of two polynomials via Hankel matrices

This paper is devoted to present a revised algorithm that permits to preserve the beautiful relation between the classical Euclidean algorithm and the block diagonalization of Hankel matrices for two noncoprime polynomials. Our algorithm for Greatest Common Divisor (GCD) computation which has a cost of O ( n 2 ) arithmetic operations is tested for several sets of polynomials. A complexity comparison is given with respect to other existing methods based on structured matrix computations.