title: On the Halton quasi-random sequences randomization
metadata.name: dc.contributor.author
metadata.value: Ermakov, Sergey M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-12-27T14:03:41Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-12-27T14:03:41Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ermakov S.M. On the Halton quasi-random sequences randomization. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2017, vol. 4 (62), issue 4, pp. 570–576.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2017.404
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/8802
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The problem of estimating the error of quasi-Monte Carlo methods with the use of randomization is
  considered. The well-known Koksma Hlawka inequality allows us to estimate the asymptotics for the
  error, but it is not suitable for practical use in the process of computation, since calculation of the quantities occurring in it is a variation of the function and discrepancy of the sequence, is an extremely
  time-consuming and impractical process. For this reason, there were numerous attempts to solve the
  aforementioned problem with the probability theory methods. One common approach is to randomly
  shift the points of the pseudo-random sequence. Cases of practical use of this approach are known, but
  theoretically it has been scantily studied.
  In this paper it is shown that estimates obtained this way are the upper estimates. A connection with
  the theory of cubature formulas with one random node is established. The case of the Halton sequences
  is considered in details. The Van der Corput transformation for sequence of natural numbers is analyzed,
  with its help the Halton points are constructed. It is shown that the cubature formula with one free node
  corresponding to the Halton sequence is exact for some class of step functions. The class is explicitly
  described. The obtained results allow us to use the mentioned sequences more effectively for integral
  calculation and extremum finding, and can also serve as a starting point for further theoretical studies in
  the field of the quasi-random methods. Refs 6. Fig. 1. Table 1.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РФФИ (грант №17-01-00267-а).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 4(62); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: quasi-random sequences
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Monte Carlo methods
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Halton sequences
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: random quadrature formulas
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the Halton quasi-random sequences randomization
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 05-Ermakov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/8802/1/05-Ermakov.pdf
resources.format: Adobe PDF
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