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Article

Zítko, Jan ; Kuřátko, Jan
An improvement of Euclid's algorithm. (English). In: Chleboun, J., Přikryl, P., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 6-11, 2010. Institute of Mathematics AS CR, Prague, 2010. pp. 251-260
MSC: 11A05, 13P05, 65F30
Keywords:
Euclid's algorithm; greatest common divisor; Sylvester matrix
Summary:
The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid's algorithm can be easily simulated by the reduction of the Sylvester matrix to an upper triangular form. This is performed by using $c$-$s$ transformation and $QR$-factorization methods. Both procedures are described and numerically compared. Computations are performed in the floating point environment.
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