## On the Computation of the GCD of 2-D Polynomials

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.

4 Issues per year

IMPACT FACTOR increased in 2013: 1.390

Rank 29 out of 59 in category Automation & Control Systems, 52 out of 121 in category Computer Science, Artificial Intelligence and 45 out of 250 in category Mathematics, Applied in the 2013 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR): 0.661

Source Normalized Impact per Paper (SNIP): 1.563

Mathematical Citation Quotient 2013: 0.09

Open Access

- Noise effects in the quantum search algorithm from the viewpoint of computational complexity by Gawron, Piotr/ Klamka, Jerzy and Winiarczyk, Ryszard
- Scalable PP-1 block cipher by Bucholc, Krzysztof/ Chmiel, Krzysztof/ Grocholewska-Czuryło, Anna/ Idzikowska, Ewa/ Janicka-Lipska, Izabela and Stokłosa, Janusz
- Application of agent-based simulated annealing and tabu search procedures to solving the data reduction problem by Czarnowski, Ireneusz and Jędrzejowicz, Piotr
- Parallel implementation of local thresholding in Mitrion-C by Kryjak, Tomasz and Gorgoń, Marek
- Localization in wireless sensor networks: Classification and evaluation of techniques by Niewiadomska-Szynkiewicz, Ewa

Panagiotis Tzekis^{1} / Nicholas Karampetakis^{1} / Haralambos Terzidis^{1}

Department of Mathematics, School of Sciences, Technological Educational Institution of Thessaloniki, P.O. Box 14561, GR-541 01 Thessaloniki, Greece^{1}

Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54006, Greece^{2}

Citation Information: International Journal of Applied Mathematics and Computer Science. Volume 17, Issue 4, Pages 463–470, ISSN (Print) 1641-876X, DOI: 10.2478/v10006-007-0038-8, January 2008

- Published Online:
- 2008-01-07

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

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.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.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.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.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.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.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.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.Schuster, A. and Hippe, P., (1992):

*Inversion of polynomial matrices by interpolation.**IEEE Transactions on Automatic Control*, Vol. 37, No. 3, pp. 363-365.

## Comments (0)