Approximate polynomial GCD

• ID: 2570, RIV: 10133856
• ISSN: not specified, ISBN: 978-80-85823-62-2
• source: Programs and Algorithms of Numerical Mathematics 16, Proceedings of Seminar
• keywords: Greatest common divisor; Euclid's algorithm; Sylvester matrix
• authors: Ján Eliaš, Jan Zítko
• authors from KNM: not assigned

Abstract

The computation of polynomial greatest common divisor (GCD) ranks among basic algebraic problems with many applications. The problem of the GCD computing of two exact polynomials is well defined and can be solved symbolically, for example, by the oldest and comonly used Euclid's algorithm. However, this is an ill-posed problem, particularly, when some unknown noise is applied to the polynomial coefficients. The aim is to overcome the ill-posed sensitivity of the GCD computation in the presence of noise. It is shown that this can be successively done through a TLS formulation of the solved problem.