Publikace na Matematicko-fyzikální fakulta |
2012
Abstrakt
The Euclid's algorithm for calculation of the greatest common divisor of two univariate polynomials can be implemented as a series of elementary transformations applied to the Sylvester resultant matrix. The theory is explained for the case that the calculations are performed symbolically.
For the calculation in computer environment, the approximate greatest common divisor (AGCD) is defined. The finding of AGCD is not an ill-posed problem and is connected with the determination of the numerical rank of the Sylvester matrix.
Techniques for the calculation of the AGCD based on the least square computation are presented together with nontrivial numerical experiments.