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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 3-8, 2012
Issue: 2012
Pages: 215-222
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: 2015-07-08T06:46:40Z
Last updated: 2015-07-08
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