Remarks on randomization of quasi-random numbers

Ermakov Sergej M. () and Leora Svetlana N. ()
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Ermakov Sergej M.: The Faculty of Mathematics and Mechanics, St. Petersburg State University, Bibliotechnay Sq. 2 Petrodvorets 198904, St. Petersburg, Russia
Leora Svetlana N.: The Faculty of Mathematics and Mechanics, St. Petersburg State University, Bibliotechnay Sq. 2 Petrodvorets 198904, St. Petersburg, Russia

Monte Carlo Methods and Applications, 2018, vol. 24, issue 2, 139-145

Abstract: In this paper we discuss estimation of the quasi-Monte Carlo methods error in the case of calculation of high-order integrals. Quasi-random Halton sequences are considered as a special case. Randomization of these sequences by the random shift method turns out to lead to well-known random quadrature formulas with one free node. Some new properties of such formulas are pointed out. The subject is illustrated by a number of numerical examples.

Keywords: Quasi-Monte Carlo methods; high-dimensional integration; random cubature formulas; Halton sequences (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:mcmeap:v:24:y:2018:i:2:p:139-145:n:6

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DOI: 10.1515/mcma-2018-0012

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