Resumen de Computing the polynomial remainder sequence via Bézout matrices
In this paper, we address the task of computing the polynomial remainder sequence appearing in the Euclidean algorithm applied to two polynomials u(x) and v(x) of degree n and m, respectively, m < n via renewed approach based on the approximate block diagonalization of a Bézout matrix B (u, v). More specifically, this algorithm consists of using the efficient Schur complementation method given in terms of a Bézout matrix B(u, v) associated with the input polynomials. We also compare the proposed approach to the approximate block diagonalization of a Hankel matrix H(u, v) in which the successive transformation matrices are upper triangular Toeplitz matrices. All algorithms have been implemented in Matlab. Numerical experiments performed with a wide variety of test problems show the effectiveness of this algorithm in terms of efficiency, stability and robustness.
