DocumentCode :
1393290
Title :
QR-factorization method for computing the greatest common divisor of polynomials with inexact coefficients
Author :
Zarowski, Christopher J. ; Ma, Xiaoyan ; Fairman, Frederick W.
Author_Institution :
Dept. of Electr. & Comput. Eng., Queen´´s Univ., Kingston, Ont., Canada
Volume :
48
Issue :
11
fYear :
2000
fDate :
11/1/2000 12:00:00 AM
Firstpage :
3042
Lastpage :
3051
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
Keywords :
Toeplitz matrices; matrix decomposition; noise; polynomial matrices; QR-factorization method; Sylvester matrix; condition number estimator; greatest common divisor; inexact coefficient polynomials; near-to-Toeplitz matrix; noise; quadratic residue; rank estimation; real-valued coefficients; upper triangular matrix; Arithmetic; Convergence; Decoding; Galois fields; Helium; Noise measurement; Partitioning algorithms; Polynomials; Quantization; Reed-Solomon codes;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/78.875462
Filename :
875462
Link To Document :
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