# Article

 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 Year: 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 Stable URL: http://hdl.handle.net/10338.dmlcz/702730 .

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