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

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3 Author(s)
Zarowski, C.J. ; Dept. of Electr. & Comput. Eng., Queen''s Univ., Kingston, Ont., Canada ; Xiaoyan Ma ; Fairman, Frederick W.

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

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Signal Processing, IEEE Transactions on  (Volume:48 ,  Issue: 11 )