On the computation of the GCD of 2-D polynomials

• Autorzy: Tzekis P. , Karampetakis N. P. , Terzidis H. K.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

greatest common divisor; discrete Fourier transform; two-variable polynomial

PL

największy wspólny dzielnik; dyskretne przekształcenie Fouriera; wielomian dwuzmienny

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2007
• Tom: Vol. 17, no 4
• Strony: 463--470
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Tzekis P.

• Department of Mathematics, School of Sciences, Technological Educational Institution of Thessaloniki, P.O. Box 14561, GR-541 01 Thessaloniki, Greece

autor

Karampetakis N. P.

• Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54006, Greece

autor

Terzidis H. K.

• Department of Mathematics, School of Sciences, Technological Educational Institution of Thessaloniki, P.O. Box 14561, GR-541 01 Thessaloniki, Greece

Bibliografia

• [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.