Zobrazeno 1 - 10 of 130 pro vyhledávání: '"Lehmer's GCD algorithm"'
1
A fast parallel sparse polynomial GCD algorithm
Autor: Michael Monagan, Jiaxiong Hu
Publikováno v: ISSAC
We present a parallel GCD algorithm for sparse multivariate polynomials with integer coefficients. The algorithm combines a Kronecker substitution with a Ben-Or/Tiwari sparse interpolation modulo a smooth prime to determine the support of the GCD. We
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1c4d363d1b0a36f05ac5f62f31ae0db3
https://doi.org/10.1016/j.jsc.2020.06.001
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2
Calculation of Bezout’s coefficients for the k-ary algorithm of finding GCD
Autor: B. G. Mubarakov, Kamal Al-Anni Maad, Sh. T. Ishmukhametov
Publikováno v: Russian Mathematics. 61:26-33
Bezout’s equation is a representation of the greatest common divisor d of integers A and B as a linear combination Ax + By = d, where x and y are integers called Bezout’s coefficients. The task of finding Bezout’s coefficients has numerous appl
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f203ae624e36e3fdf7a48df9285d7e3f
https://doi.org/10.3103/s1066369x17110044
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3
An approximating k-ary GCD algorithm
Autor: Sh. T. Ishmukhametov
Publikováno v: Lobachevskii Journal of Mathematics. 37:723-729
In our paper we elaborate a new version of the k-ary GCD algorithm. Our algorithm is based on the Farey Series and surpasses all existing realizations of the k-ary algorithm. It can have practical applications inMathematics and Cryptography.
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::8caaf52aee9698f9f17392009f3004a4
https://doi.org/10.1134/s1995080216060147
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4
New Modified Euclidean and Binary Greatest Common Divisor Algorithm
Autor: Shailesh R. Sathe, Jitendra V. Tembhurne
Publikováno v: IETE Journal of Research. 62:852-858
The greatest common divisor (GCD) computation of non-negative integers are the open problem in arithmetic calculations such as cryptography, and factorization attacks. The integer GCD algorithm applies one or more different transformations to reduce
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::bda6579485bb1ef724fe3ec7d650be4b
https://doi.org/10.1080/03772063.2016.1216809
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6
GENERALIZED CULLEN NUMBERS WITH THE LEHMER PROPERTY
Autor: Dae-June Kim, Byeong-Kweon Oh
Publikováno v: Bulletin of the Korean Mathematical Society. 50:1981-1988
We say a positive integer n satisfies the Lehmer property if �(n) divides n 1, where �(n) is the Euler's totient function. Clearly, every prime satisfies the Lehmer property. No composite integer satisfy- ing the Lehmer property is known. In this
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::4298cfea7aea80d9a9e96e5336148027
https://doi.org/10.4134/bkms.2013.50.6.1981
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7
Divisibility of power LCM matrices by power GCD matrices on gcd-closed sets
Autor: Jianrong Zhao
Publikováno v: Linear and Multilinear Algebra. 62:735-748
Let and be positive integers and a set of distinct positive integers. The matrix whose -entry is th power of the greatest common divisor (GCD) of and is called the th power GCD matrix on , denoted by . Similarly, we can define th power least common m
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::c0b2636f964ef4618423bac3a0e09e9f
https://doi.org/10.1080/03081087.2013.786717
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9
Analysis of the Brun gcd algorithm
Autor: Valérie Berthé, Brigitte Vallée, Loïck Lhote
Publikováno v: ISSAC '16: Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation
ISSAC '16: 41st International Symposium on Symbolic and Algebraic Computation
ISSAC '16: 41st International Symposium on Symbolic and Algebraic Computation, Jun 2016, Waterloo, Canada. pp.87-94, ⟨10.1145/2930889.2930899⟩
ISSAC
ISSAC 2016: The 41st International Symposium on Symbolic and Algebraic Computation
ISSAC 2016: The 41st International Symposium on Symbolic and Algebraic Computation, Jun 2016, Waterloo, Canada
We introduce and study a multiple gcd algorithm that is a natural extension of the usual Euclid algorithm, and coincides with it for two entries; it performs Euclidean divisions, between the largest entry and the second largest entry, and then re-ord
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::96449bb88caa41d5e5b3cdad313e131c
https://hal.archives-ouvertes.fr/hal-01578425
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10
Numerical matrix methods in the computation of the greatest common divisor (GCD) of polynomials
Autor: Siti Nor Asiah Isa, Nor’aini Aris, Shazirawati Mohd Puzi
Publikováno v: AIP Conference Proceedings.
In this research, the method for computing the GCD of two polynomials in the orthogonal basis, using the comrade matrix approach is further investigated. Generally, polynomials in the orthogonal basis may be better conditioned than that of the power
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::3a9fce3aae286cbf00836336542c0caa
https://doi.org/10.1063/1.4965184
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