Volume 3, Number 3 (2018)
Year Launched: 2016
Journal Menu
Archive
Previous Issues
Why Us
-  Open Access
-  Peer-reviewed
-  Rapid publication
-  Lifetime hosting
-  Free indexing service
-  Free promotion service
-  More citations
-  Search engine friendly
Contact Us
Email:   service@scirea.org
Home > Journals > SCIREA Journal of Mathematics > Archive > Paper Information

Calculation of extended gcd by normalization

Volume 3, Issue 3, June 2018    |    PP. 118-131    |PDF (269 K)|    Pub. Date: August 2, 2018
229 Downloads     1897 Views  

Author(s)
WOLF Marc, Independent researchers.
WOLF François, Independent researchers.
LE COZ Corentin, Independent researchers.

Abstract
We propose a new algorithm solving the extended gcd problem, which provides a solution minimizing one of the two coordinates. The algorithm relies on elementary arithmetic properties.

Keywords
extended gcd; normalizer; co-normalizer; minimizing one of the two coordinates; normal solution; linear diophantine equation; mixed Euclid algorithm

Cite this paper
WOLF Marc, WOLF François, LE COZ Corentin, Calculation of extended gcd by normalization, SCIREA Journal of Mathematics. Vol. 3 , No. 3 , 2018 , pp. 118 - 131 .

References

[ 1 ] R. P. Brent, H. T. Kung, Systolic VLSI arrays for polynomial GCD computations. IEEE Trans. Comput. C-33, 731-736 (1984)
[ 2 ] R. P. Brent. An improved Monte Carlo factorization algorithm. BIT 20, 176-184 (1980).
[ 3 ] Denis Serre. Matrices, theory and Applications. Springer 2010.
[ 4 ] Doran, Lu, Smith. New algorithms for modular inversion and representation by binary quadrtic forms arising from structure in the Euclidean algorithm, 2015. arXiv:1408.4638v2
[ 5 ] H. Leung, A Note on Extended Euclid’s Algorithm, arXiv:1607.00106, 2016
[ 6 ] R. P. Brent. Further analysis of the Binary Euclidean algorithm. PRG TR-7-99. 1999

Submit A Manuscript
Review Manuscripts
Join As An Editorial Member
Most Views
Article
by Sergey M. Afonin
2935 Downloads 40130 Views
Article
by Syed Adil Hussain, Taha Hasan Associate Professor
2295 Downloads 19058 Views
Article
by Omprakash Sikhwal, Yashwant Vyas
2366 Downloads 15996 Views
Article
by Munmun Nath, Bijan Nath, Santanu Roy
2263 Downloads 15916 Views
Upcoming Conferences