The coefficients of the greatest common divisor of two polynomials $f$ and $g$ (GCD$(f,g)$) can be obtained from the Sylvester subresultant matrix $S_j(f,g)$ transformed to lower triangular form, where $1\le j\le d$ and $d=$ deg(GCD$(f,g)$) needs to be computed. Firstly, it is supposed that the coefficients of polynomials are given exactly. Transformations of $S_j(f,g)$ for an arbitrary allowable $j$ are in details described and an algorithm for the calculation of the GCD$(f,g)$ is formulated. If inexact polynomials are given, then an approximate greatest common divisor (AGCD) is introduced. The considered techniques for an AGCD computations are shortly discussed and numerically compared in the presented paper.

EUDML-ID : urn:eudml:doc:271358
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@article{702730,
     title = {Calculation of the greatest common divisor of perturbed polynomials},
     booktitle = {Programs and Algorithms of Numerical Mathematics},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics AS CR},
     address = {Prague},
     year = {2013},
     pages = {215-222},
     url = {http://dml.mathdoc.fr/item/702730}
}

Zítko, Jan; Eliaš, Ján. Calculation of the greatest common divisor of perturbed polynomials, dans Programs and Algorithms of Numerical Mathematics, GDML_Books,  (2013), pp. 215-222. http://gdmltest.u-ga.fr/item/702730/