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.
@article{bwmeta1.element.bwnjournal-article-amcv17i4p463bwm,
author = {Tzekis, Panagiotis and Karampetakis, Nicholas and Terzidis, Haralambos},
title = {On the computation of the GCD of 2-D polynomials},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {17},
year = {2007},
pages = {463-470},
zbl = {1229.68086},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv17i4p463bwm}
}
Tzekis, Panagiotis; Karampetakis, Nicholas; Terzidis, Haralambos. On the computation of the GCD of 2-D polynomials. International Journal of Applied Mathematics and Computer Science, Tome 17 (2007) pp. 463-470. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv17i4p463bwm/
[000] 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. | Zbl 1169.15300
[001] 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. | Zbl 1049.65011
[002] 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. | Zbl 0984.65016
[003] 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. | Zbl 0807.93021
[004] 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. | Zbl 0777.93053
[005] 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. | Zbl 0747.65034
[006] 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. | Zbl 0253.93014
[007] 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.
[008] Schuster, A.and Hippe, P., (1992): Inversion of polynomial matrices by interpolation. IEEE Transactions on Automatic Control, Vol.37, No.3, pp.363-365.