# Comparison of algorithms for calculation of the greatest common divisor of several polynomials

- Programs and Algorithms of Numerical Mathematics, Publisher: Institute of Mathematics AS CR(Prague), page 64-70

## Access Full Article

top## Abstract

top## How to cite

topEckstein, Jiří, and Zítko, Jan. "Comparison of algorithms for calculation of the greatest common divisor of several polynomials." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics AS CR, 2015. 64-70. <http://eudml.org/doc/269925>.

@inProceedings{Eckstein2015,

abstract = {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.},

author = {Eckstein, Jiří, Zítko, Jan},

booktitle = {Programs and Algorithms of Numerical Mathematics},

keywords = {greatest common divisor of polynomials; Sylvester matrix; Bezout matrix},

location = {Prague},

pages = {64-70},

publisher = {Institute of Mathematics AS CR},

title = {Comparison of algorithms for calculation of the greatest common divisor of several polynomials},

url = {http://eudml.org/doc/269925},

year = {2015},

}

TY - CLSWK

AU - Eckstein, Jiří

AU - Zítko, Jan

TI - Comparison of algorithms for calculation of the greatest common divisor of several polynomials

T2 - Programs and Algorithms of Numerical Mathematics

PY - 2015

CY - Prague

PB - Institute of Mathematics AS CR

SP - 64

EP - 70

AB - 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.

KW - greatest common divisor of polynomials; Sylvester matrix; Bezout matrix

UR - http://eudml.org/doc/269925

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.