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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 7, Pages 1059–1077
DOI: https://doi.org/10.7868/S0044466914070047 (Mi zvmmf10059) 		 
This article is cited in 6 scientific papers (total in 6 papers)

General algorithm for the numerical integration of functions of several variables

E. A. Bailova, M. B. Sikhovb, N. Temirgalieva

a Institute of Theoretical Mathematics and Scientific Computations, Eurasian National University, ul. Mirzoyana 2, Astana, 010008, Kazakhstan
b Kazakh National University, pr. Al-Farabi 71, Almaty, Kazakhstan
Full-text PDF (330 kB) Citations (6)
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DOI: https://doi.org/10.7868/S0044466914070047
Abstract: An algorithm is proposed for the numerical integration of an arbitrary function representable as a sum of an absolutely converging multiple trigonometric Fourier series. The resulting quadrature formulas have identical weights, and the nodes form a Korobov grid that is completely defined by two positive integers, of which one is the number of nodes. In the case of classes of functions with dominant mixed smoothness, it is shown that the algorithm is almost optimal in the sense that the construction of a grid of $N$ nodes requires far fewer elementary arithmetic operations than $N\ln\ln N$. Solutions of related problems are also given.
Key words: discrepancy, uniformly distributed grids, Korobov grids, optimal coefficients, quadrature formulas, divisor theory, lattice, ideal.
Received: 04.02.2011
Revised: 21.01.2014
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 7, Pages 1061–1078
DOI: https://doi.org/10.1134/S0965542514070045
Bibliographic databases:
Document Type: Article
UDC: 519.644.7
MSC: 65D15
Language: Russian
Citation: E. A. Bailov, M. B. Sikhov, N. Temirgaliev, “General algorithm for the numerical integration of functions of several variables”, Zh. Vychisl. Mat. Mat. Fiz., 54:7 (2014), 1059–1077; Comput. Math. Math. Phys., 54:7 (2014), 1061–1078
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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