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.

EUDML-ID : urn:eudml:doc:271277
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@article{702765,
     title = {An improvement of Euclid's algorithm},
     booktitle = {Programs and Algorithms of Numerical Mathematics},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics AS CR},
     address = {Prague},
     year = {2010},
     pages = {251-260},
     url = {http://dml.mathdoc.fr/item/702765}
}

Zítko, Jan; Kuřátko, Jan. An improvement of Euclid's algorithm, dans Programs and Algorithms of Numerical Mathematics, GDML_Books,  (2010), pp. 251-260. http://gdmltest.u-ga.fr/item/702765/