IDEAS home Printed from https://ideas.repec.org/a/bpj/mcmeap/v14y2008i2p129-149n2.html
   My bibliography  Save this article

Component-by-component construction of low-discrepancy point sets of small size

Author

Listed:
  • Doerr Benjamin

    (Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany.)

  • Gnewuch Michael

    (Department of Computer Science, Christian-Albrechts-Universität Kiel, Christian-Albrechts-Platz 4, 24098 Kiel, Germany. Email: mig@informatik.uni-kiel.de)

  • Kritzer Peter

    (Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34, 5020 Salzburg, Austria, and School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, Australia. Email: p.kritzer@unsw.edu.au)

  • Pillichshammer Friedrich

    (Institut für Finanzmathematik, Universität Linz, Altenbergerstr. 69, 4040 Linz, Austria. Email: friedrich.pillichshammer@jku.at)

Abstract

We investigate the problem of constructing small point sets with low star discrepancy in the s-dimensional unit cube. The size of the point set shall always be polynomial in the dimension s. Our particular focus is on extending the dimension of a given low-discrepancy point set.This results in a deterministic algorithm that constructs N-point sets with small discrepancy in a component-by-component fashion. The algorithm also provides the exact star discrepancy of the output set. Its run-time considerably improves on the run-times of the currently known deterministic algorithms that generate low-discrepancy point sets of comparable quality.We also study infinite sequences of points with infinitely many components such that all initial subsegments projected down to all finite dimensions have low discrepancy. To this end, we introduce the inverse of the star discrepancy of such a sequence, and derive upper bounds for it as well as for the star discrepancy of the projections of finite subsequences with explicitly given constants. In particular, we establish the existence of sequences whose inverse of the star discrepancy depends linearly on the dimension.

Suggested Citation

  • Doerr Benjamin & Gnewuch Michael & Kritzer Peter & Pillichshammer Friedrich, 2008. "Component-by-component construction of low-discrepancy point sets of small size," Monte Carlo Methods and Applications, De Gruyter, vol. 14(2), pages 129-149, January.
    • Handle: RePEc:bpj:mcmeap:v:14:y:2008:i:2:p:129-149:n:2
    DOI: 10.1515/MCMA.2008.007
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/MCMA.2008.007
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/MCMA.2008.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:mcmeap:v:14:y:2008:i:2:p:129-149:n:2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.