MULTIDIMENSIONAL CUBATURES WITH SUPER-POWER CONVERGENCE-Reference-Cited by-同舟云学术

MULTIDIMENSIONAL CUBATURES WITH SUPER-POWER CONVERGENCE

Published:2023-11-01 Issue:1 Volume:514 Page:107-111
ISSN:2686-9543
Container-title:Доклады Российской академии наук. Математика, информатика, процессы управления
language:
Short-container-title:Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ

Author:

Belov A. A.¹²,Tintul M. A.¹

Affiliation:

1. M.V. Lomonosov Moscow State University, Faculty of Physics

2. Peoples’ Friendship University of Russia (RUDN University)

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.

Publisher

The Russian Academy of Sciences

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