Computing the polynomial remainder sequence via Bézout matrices

• Autores: Skander Belhaj
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 250, Nº 1, 2013, págs. 244-255
• Idioma: inglés
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• Resumen

  • 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.