Title:

Calculation of the greatest common divisor of perturbed polynomials (English) 
Author:

Zítko, Jan 
Author:

Eliaš, Ján 
Language:

English 
Journal:

Programs and Algorithms of Numerical Mathematics 
Volume:

Proceedings of Seminar. Dolní Maxov, June 38, 2012 
Issue:

2012 
Year:


Pages:

215222 
. 
Category:

math 
. 
Summary:

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 $1 \leq j \leq d$ 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. (English) 
Keyword:

polynomial greatest common divisor 
Keyword:

approximate greatest common divisor 
Keyword:

Sylvester subresultant matrix 
Keyword:

singular value 
Keyword:

structured total least norm method 
MSC:

11A05 
MSC:

11C08 
MSC:

11Y40 
MSC:

15A18 
. 
Date available:

20150708T06:46:40Z 
Last updated:

20150708 
Stable URL:

http://hdl.handle.net/10338.dmlcz/702730 
. 