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MULTIDIMENSIONAL CUBATURES WITH SUPER-POWER CONVERGENCE
- Authors: Belov A.A.1,2, Tintul M.A.1
-
Affiliations:
- M.V. Lomonosov Moscow State University, Faculty of Physics
- Peoples’ Friendship University of Russia (RUDN University)
- Issue: Vol 514 (2023)
- Pages: 107-111
- Section: MATHEMATICS
- URL: https://cardiosomatics.ru/2686-9543/article/view/647948
- DOI: https://doi.org/10.31857/S2686954323600118
- EDN: https://elibrary.ru/DAUIMM
- ID: 647948
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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.
About the authors
A. A. Belov
M.V. Lomonosov Moscow State University, Faculty of Physics; Peoples’ Friendship University of Russia (RUDN University)
Author for correspondence.
Email: aa.belov@physics.msu.ru
Russian Federation, Moscow; Russian Federation, Moscow
M. A. Tintul
M.V. Lomonosov Moscow State University, Faculty of Physics
Author for correspondence.
Email: maksim.tintul@mail.ru
Russian Federation, Moscow
References
- Калиткин Н.Н., Альшина Е.А. Численные методы. Т. 1. Численный анализ. М.: Академия, 2013.
- Соболь И.М. Численные методы Монте-Карло. М.: Наука, 1975.
- Коробов Н.М. Теоретико-числовые методы в приближенном анализе. М.: Физматгиз, 1963.
- Калиткин Н.Н., Альшин А.Б., Альшина Е.А., Рогов Б.В. Вычисления на квазиравномерных сетках. М.: Физматлит, 2005.
- Демидов С.С. и др. // Чеб. сборник. 2017. Т. 18. № 4. С. 6.
- Коробов Н.М. // ДАН. 1982. Т. 267. № 2. С. 289.
- Гельфанд И.М. и др. // Изв. ВУЗов. Матем. 1958. Т. 6. № 5. С. 32.
- Iri M., Moriguti S., Takasawa Y. // J. Comp. Appl. Math. 1987. V. 17. P. 3.
