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Title: Approximate polynomial GCD (English)
Author: Eliaš, Ján
Author: Zítko, Jan
Language: English
Journal: Programs and Algorithms of Numerical Mathematics
Volume: Proceedings of Seminar. Dolní Maxov, June 3-8, 2012
Issue: 2012
Pages: 63-68
Category: math
Summary: The computation of polynomial greatest common divisor (GCD) ranks among basic algebraic problems with many applications, for example, in image processing and control theory. The problem of the GCD computing of two exact polynomials is well defined and can be solved symbolically, for example, by the oldest and commonly used Euclid’s algorithm. However, this is an ill-posed problem, particularly when some unknown noise is applied to the polynomial coefficients. Hence, new methods for the GCD computation have been extensively studied in recent years. The aim is to overcome the ill-posed sensitivity of the GCD computation in the presence of noise. We show that this can be successively done through a TLS formulation of the solved problem, [1,5,7]. (English)
Keyword: polynomial greatest common divisor
Keyword: approximate greatest common divisor
Keyword: Sylvester subresultant matrix
Keyword: singular value
Keyword: total least squares problem
MSC: 11A05
MSC: 11C08
MSC: 11Y40
MSC: 15A18
Date available: 2015-07-08T06:40:41Z
Last updated: 2023-06-05
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