# On the computation of the GCD of 2-D polynomials

Panagiotis Tzekis; Nicholas Karampetakis; Haralambos Terzidis

International Journal of Applied Mathematics and Computer Science (2007)

- Volume: 17, Issue: 4, page 463-470
- ISSN: 1641-876X

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topTzekis, Panagiotis, Karampetakis, Nicholas, and Terzidis, Haralambos. "On the computation of the GCD of 2-D polynomials." International Journal of Applied Mathematics and Computer Science 17.4 (2007): 463-470. <http://eudml.org/doc/207851>.

@article{Tzekis2007,

abstract = {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.},

author = {Tzekis, Panagiotis, Karampetakis, Nicholas, Terzidis, Haralambos},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {greatest common divisor; discrete Fourier transform; two-variable polynomial},

language = {eng},

number = {4},

pages = {463-470},

title = {On the computation of the GCD of 2-D polynomials},

url = {http://eudml.org/doc/207851},

volume = {17},

year = {2007},

}

TY - JOUR

AU - Tzekis, Panagiotis

AU - Karampetakis, Nicholas

AU - Terzidis, Haralambos

TI - On the computation of the GCD of 2-D polynomials

JO - International Journal of Applied Mathematics and Computer Science

PY - 2007

VL - 17

IS - 4

SP - 463

EP - 470

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/207851

ER -

## References

top- 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. Zbl1169.15300
- 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. Zbl1049.65011
- 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. Zbl0984.65016
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- 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. Zbl0777.93053
- 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. Zbl0747.65034
- 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. Zbl0253.93014
- 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.

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