In this thesis we study the computation of the greatest common divisor of two polynomials. Firstly, properties of Sylvester matrices are considered as well as their role in computation. We then note, that this approach can be naturally generalized for several polynomials. In the penultimate section, Bézout matrices are studied as an analogy to the Sylvester ones, providing necessary comparison. Extension for more than polynomials is presented here as well. Algorithms corresponding to the individual approaches are presented as well. Finally, the algorithms are implemented in MATLAB and are compared in numerical experiments. Powered by TCPDF (www.tcpdf.org)

In this work, the analysis of the computation of the greatest common divisor of univariate and bivariate polynomials is presented. The whole process is split into three stages. In the first stage, data preprocessing is explained and the resulting better numerical behavior is demonstrated. Next stage is concerned with the problem of the computation of the numerical rank of the Sylvester matrix, from which the degree of the greatest common divisor is obtained. The last stage is the actual algorithm for calculating the greatest common divisor of two polynomials. Furthermore, the underlying theory behind the computation of the greatest common divisor is explained and illustrated on many examples. 1