An improvement of Euclid's algorithm

• ID: 2542, RIV: 10080852
• ISSN: not specified, ISBN: 978-80-85823-57-8
• source: Programs and Algorithms of Numerical Mathematics 15
• keywords: Euclid's algorithm; greatest common divisor; numerical experiments
• authors: Jan Zítko, Jan Kuřátko
• authors from KNM: not assigned

Abstract

The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid's algorithm is simulated by the reduction of the Sylvester matrix to an upper triangular form by using c-s transformation and QR-factorization method. Both procedures are described and numerically compared with classical Euclid's algorithm. The new procedures yield more precise results.