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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2023, Volume 514, Number 1, Pages 107–111
DOI: https://doi.org/10.31857/S2686954323600118 (Mi danma440) 		 
MATHEMATICS

Multidimensional cubatures with super-power convergence

A. A. Belovab, M. A. Tintula

a Faculty of Physics, Lomonosov Moscow State University, Moscow, Russian Federation
b Peoples Friendship University of Russia, Faculty of Physical, Mathematical and Natural Sciences, Moscow, Russian Federation
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DOI: https://doi.org/10.31857/S2686954323600118
Abstract: In many applications, multidimensional integrals over the unit hypercube arise, which are calculated using Monte Carlo methods. The convergence of the best of them turns out to be quite slow. In this paper, fundamentally new cubatures with super-power convergence based on the improved Korobov grids and special variable substitution are proposed. A posteriori error estimates are constructed, which are practically indistinguishable from the actual accuracy. Examples of calculations illustrating the advantages of the proposed methods are given.
Keywords: multidimensional integrals, Monte Carlo method, super-power convergence, Korobov grids.
Funding agency Grant number
Russian Science Foundation 22-71-00028
This work was supported by the Russian Science Foundation, project no. 22-71-00028.
Presented: E. E. Tyrtyshnikov
Received: 06.03.2023
Revised: 18.09.2023
Accepted: 15.11.2023
English version:
Doklady Mathematics, 2023, Volume 108, Issue 3, Pages 514–518
DOI: https://doi.org/10.1134/S1064562423701478
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: A. A. Belov, M. A. Tintul, “Multidimensional cubatures with super-power convergence”, Dokl. RAN. Math. Inf. Proc. Upr., 514:1 (2023), 107–111; Dokl. Math., 108:3 (2023), 514–518
Citation in format AMSBIB
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\by A.~A.~Belov, M.~A.~Tintul
\paper Multidimensional cubatures with super-power convergence
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2023
\vol 514
\issue 1
\pages 107--111
\mathnet{http://mi.mathnet.ru/danma440}
\crossref{https://doi.org/10.31857/S2686954323600118}
\elib{https://elibrary.ru/item.asp?id=56718085}
\transl
\jour Dokl. Math.
\yr 2023
\vol 108
\issue 3
\pages 514--518
\crossref{https://doi.org/10.1134/S1064562423701478}
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