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 38, 2012 
Issue:

2012 
Year:


Pages:

6368 
. 
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 illposed 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 illposed 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:

20150708T06:40:41Z 
Last updated:

20230605 
Stable URL:

http://hdl.handle.net/10338.dmlcz/702708 
. 