On classical number-theoretic nets
https://doi.org/10.22405/2226-8383-2018-19-4-118-176
Abstract
The paper considers the hyperbolic Zeta function of nets with weights and the distribution of error values of approximate integration with modifications of nets. Considered: parallelepipedal nets M(~a,p), consisting of points
Mk =({a1k/p },...,{ask/p }) (k = 1,2,...,p);
non-uniform nets M(P), the coordinates of which are expressed via power functions modulo P:
Mk =({k/P},{k2/P}...,{ks/P}) (k = 1,2,...,P),
where P = p or P = p2 and p — odd prime number;
generalized uniform nets M(~n) of N = n1 ·...·ns points of the form
M k =({k1/n1},{k2/n2}...,{ks/ns}) (kj = 1,2,...,nj (j = 1,...,s));
algebraic nets introduced by K. K. Frolov in 1976 and generalized parallelepipedal nets, the study of which began in 1984.
In addition, the review of p-nets is considered: Hammersley, Halton, Faure, Sobol, and Smolyak nets.
In conclusion, the current problems of applying the number-theoretic method in geophysics are considered, which require further study.
About the Authors
I. Yu. Rebrova
Tula State L.N. Tolstoy Pedagogical University
Russian Federation
Russian Federation
Rebrova Irina Yuryevna — candidate of physical and mathematical Sciences, associate professor, dean of the faculty of mathematics, physics and computer science
V. N. Chubarikov
M.V. Lomonosov Moscow State University
Russian Federation
Russian Federation
Chubarikov Vladimir Nikolaevich — doctor of physical and mathematical sciences, professor, head of the department of mathematical and computer methods of analysis, dean of the mechanics and mathematics faculty
N. N. Dobrovolsky
Tula State University
Russian Federation
Russian Federation
Dobrovolsky Nikolai Nikolaevich — candidate of physical and mathematical sciences, assistant of the department of applied mathematics and computer science
М. Добровольский
M. N. Dobrovolsky
Geophysical centre of RAS
Russian Federation
Russian Federation
Dobrovolsky Mikhail Nikolaevich — candidate of candidate of physical and mathematical sciences, senior researcher
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For citations:
Rebrova I.Yu., Chubarikov V.N., Dobrovolsky N.N., , Dobrovolsky M.N. On classical number-theoretic nets. Chebyshevskii Sbornik. 2018;19(4):118-176. (In Russ.) https://doi.org/10.22405/2226-8383-2018-19-4-118-176
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