QR-factorization method for computing the greatest common divisorof polynomials with inexact coefficients

Authors:
C.J. Zarowski;Xiaoyan Ma;F.W. Fairman
Affiliations:
Dept. of Electr. & Comput. Eng., Queen's Univ., Kingston, Ont.;-;-
Venue:
IEEE Transactions on Signal Processing
Year:
2000

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Abstract

This paper presents a novel means of computing the greatest common divisor (GCD) of two polynomials with real-valued coefficients that have been perturbed by noise. The method involves the QR-factorization of a near-to-Toeplitz matrix derived from the Sylvester matrix of the two polynomials. It turns out that the GCD to within a constant factor is contained in the last nonzero row of the upper triangular matrix R in the QR-factorization of the near-to-Toeplitz matrix. The QR-factorization is efficiently performed by an algorithm due to Chun et al. (1987). A condition number estimator due to Bischof (1990) and an algorithm for rank estimation due to Zarowski (1998) are employed to account for the effects of noise