Calculation of the greatest common divisor of perturbed polynomials

Zítko, Jan, and Eliaš, Ján. "Calculation of the greatest common divisor of perturbed polynomials." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics AS CR, 2013. 215-222. <http://eudml.org/doc/271358>.

@inProceedings{Zítko2013,
abstract = {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.},
author = {Zítko, Jan, Eliaš, Ján},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {polynomial greatest common divisor; approximate greatest common divisor; Sylvester subresultant matrix; singular value; structured total least norm method},
location = {Prague},
pages = {215-222},
publisher = {Institute of Mathematics AS CR},
title = {Calculation of the greatest common divisor of perturbed polynomials},
url = {http://eudml.org/doc/271358},
year = {2013},
}

TY - CLSWK
AU - Zítko, Jan
AU - Eliaš, Ján
TI - Calculation of the greatest common divisor of perturbed polynomials
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2013
CY - Prague
PB - Institute of Mathematics AS CR
SP - 215
EP - 222
AB - 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.
KW - polynomial greatest common divisor; approximate greatest common divisor; Sylvester subresultant matrix; singular value; structured total least norm method
UR - http://eudml.org/doc/271358
ER -