Geodesic
On the computation of the GCD of 2-D polynomials
International Journal of Applied Mathematics and Computer Science, Tome 17 (2007) no. 4, pp. 463-470

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The main contribution of this work is to provide an algorithm for the computation of the GCD of 2-D polynomials, based on DFT techniques. The whole theory is implemented via illustrative examples.
Keywords: greatest common divisor, discrete Fourier transform, two-variable polynomial
Mots-clés : największy wspólny dzielnik, dyskretne przekształcenie Fouriera, wielomian dwuzmienny 
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Tzekis, P.; Karampetakis, N. P.; Terzidis, H. K. On the computation of the GCD of 2-D polynomials. International Journal of Applied Mathematics and Computer Science, Tome 17 (2007) no. 4, pp. 463-470. http://geodesic.mathdoc.fr/item/IJAMCS_2007_17_4_a3/

[1] Karampetakis N. P., Tzekis P., (2005): On the computation of the minimal polynomial of a polynomial matrix. International Journal of Applied Mathematics and Computer Science, Vol. 15, No. 3, pp. 339-349.

[2] Karcanias N. and Mitrouli M., (2004): System theoretic based characterisation and computation of the least common multiple of a set of polynomials. Linear Algebra and Its Applications, Vol. 381, pp. 1-23.

[3] Karcanias N. and Mitrouli, M., (2000): Numerical computation of the least common multiple of a set of polynomials, Reliable Computing, Vol. 6, No. 4, pp. 439-457.

[4] Karcanias N. and Mitrouli M., (1994): A matrix pencil based numerical method for the computation of the GCD of polynomials. IEEE Transactions on Automatic Control, Vol. 39, No. 5, pp. 977-981.

[5] Mitrouli M. and Karcanias N., (1993): Computation of the GCD of polynomials using Gaussian transformation and shifting. International Journal of Control, Vol. 58, No. 1, pp. 211-228.

[6] Noda M. and Sasaki T., (1991): Approximate GCD and its applications to ill-conditioned algebraic equations. Journal of Computer and Applied Mathematics Vol. 38, No. 1-3, pp. 335-351.

[7] Pace I. S. and Barnett S., (1973): Comparison of algorithms for calculation of GCD of polynomials. International Journal of Systems Science Vol. 4, No. 2, pp. 211-226.

[8] Paccagnella, L. E. and Pierobon, G. L., (1976): FFT calculation of a determinantal polynomial. IEEE Transactions on Automatic Control, Vol. 21, No. 3, pp. 401-402.

[9] Schuster, A. and Hippe, P., (1992): Inversion of polynomial matrices by interpolation. IEEE Transactions on Automatic Control, Vol. 37, No. 3, pp. 363-365.