电邮这篇文章 MULTIDIMENSIONAL CUBATURES WITH SUPER-POWER CONVERGENCE
- 作者: Belov A.1,2, Tintul M.1
-
隶属关系:
- M.V. Lomonosov Moscow State University, Faculty of Physics
- Peoples’ Friendship University of Russia (RUDN University)
- 期: 卷 514, 编号 1 (2023)
- 页面: 107-111
- 栏目: МАТЕМАТИКА
- URL: https://journals.rcsi.science/2686-9543/article/view/247101
- DOI: https://doi.org/10.31857/S2686954323600118
- EDN: https://elibrary.ru/DAUIMM
- ID: 247101
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详细
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.
作者简介
A. Belov
M.V. Lomonosov Moscow State University, Faculty of Physics; Peoples’ Friendship University of Russia (RUDN University)
编辑信件的主要联系方式.
Email: aa.belov@physics.msu.ru
Russian Federation, Moscow; Russian Federation, Moscow
M. Tintul
M.V. Lomonosov Moscow State University, Faculty of Physics
编辑信件的主要联系方式.
Email: maksim.tintul@mail.ru
Russian Federation, Moscow
参考
- Калиткин Н.Н., Альшина Е.А. Численные методы. Т. 1. Численный анализ. М.: Академия, 2013.
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- 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.
