Calculation of the greatest common divisor of perturbed polynomials

• ID: 2626, RIV: 10133744
• ISSN: not specified, ISBN: 978-80-85823-62-2
• source: Programs and Algorithms of Numerical Mathematics 16, Proceedings of Seminar
• keywords: Sylvester matrix; greatest common divisor ; approximate greatest common divisor ;
• authors: Jan Zítko, Ján Eliaš
• authors from KNM: not assigned

Abstract

The coefficients of the greatest common divisor of two univariate polynomials can be obtained from the Sylvester subresultant matrix transformed to lower triangular form. Firstly, it is supposed that the coefficients of polynomials are given exactly. Transformation is in detail described and an algorithm for the calculation of the greatest common divisor 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.