polynomial greatest common divisor; approximate greatest common divisor; Sylvester subresultant matrix; singular value; total least squares problem
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].