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:: International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies

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ISSN 2228-9860
eISSN 1906-9642


FEATURE PEER-REVIEWED ARTICLES

Vol.10(1) (2019)

  • A STUDY OF THE CONVERGENCE OF THE BEZOUT COEFFICIENTS SEARCH ALGORITHM
  • Alisher R. Zhumaniezov (Department of Computer Science, Faculty of Electrical Engineering, Kazan Federal University, Kazan 420008, RUSSIAN FEDERATION, and Department of Computer Science and Engineering, Faculty of Electrical Engineering, Czech Technical University in Prague, CZECH REPUBLIC )

    (Backup file)

    doi: 10.14456/ITJEMAST.2019.1

    Keywords: Euclidean algorithm; extended Euclidean algorithm; k-ary algorithm for computing GCD; calculation of inverse elements modulo; parallel GCD computation

    Abstract
    Time is very valuable in modern technology era. An important indicator of the program’s work is its computational speed. This article describes the optimization of Bezout coefficients search algorithm by introduction different optimization schemes. Among all schemes, the following are chosen: K-ary, approximating and parallel approximating optimization schemes. Bezout’s equation is a representation of the greatest common divisor d of two integers A and B as a linear combination Ax+By = d, where x, and y are integers called Bezout’s coefficients. Bezout’s coefficients are counted using the extended version of the classical Euclidian Algorithm..


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