# 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

top

## Abstract

top
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.

## How to cite

top

Eckstein, 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?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.