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Article

Eckstein, Jiří ; Zítko, Jan
Comparison of algorithms for calculation of the greatest common divisor of several polynomials. (English). In: Chleboun, J., Přikryl, P., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 8-13, 2014. Institute of Mathematics AS CR, Prague, 2015. pp. 64-70
MSC: 11A05, 11C08, 65F30
Keywords:
greatest common divisor of polynomials; Sylvester matrix; Bezout matrix
Summary:
The computation of the greatest common divisor (GCD) has many applications in several disciplines including computer graphics, image deblurring problem or computing multiple roots of inexact polynomials. In this paper, Sylvester and Bézout matrices are considered for this purpose. The computation is divided into three stages. A rank revealing method is shortly mentioned in the first one and then the algorithms for calculation of an approximation of GCD are formulated. In the final stage the coefficients are improved using Gauss-Newton method. Numerical results show the efficiency of proposed last two stages.
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