IDEAS home Printed from https://ideas.repec.org/a/bpj/mcmeap/v16y2010i3-4p379-398n7.html
   My bibliography  Save this article

A genetic algorithm approach to estimate lower bounds of the star discrepancy

Author

Listed:
  • Shah Manan

    (Gaming Laboratories International, 600 Airport Drive, Lakewood, NJ 08701, USA. E-mail:)

Abstract

We consider a new method using genetic algorithms to obtain lower bounds for the star discrepancy for any number of points in [0, 1]s. We compute lower bounds for the star discrepancy of samples of a number of sequences in several dimensions and successfully compare with existing results from the literature. Despite statements in the quasi-Monte Carlo literature stating that computing the star discrepancy is either intractable or requires a lot of computational work for s ≥ 3, we show that it is possible to compute the star discrepancy exactly or at the very least obtain reasonable lower bounds without a huge computational burden. Our method is fast and consistent and can be easily extended to estimate lower bounds of other discrepancy measures. Our method can be used by researchers to measure the uniformity quality of point sets as given by the star discrepancy rather than having to rely on the L 2 discrepancy, which is easy to compute, but is flawed (and it is well known that the L 2 discrepancy is flawed).

Suggested Citation

  • Shah Manan, 2010. "A genetic algorithm approach to estimate lower bounds of the star discrepancy," Monte Carlo Methods and Applications, De Gruyter, vol. 16(3-4), pages 379-398, January.
    • Handle: RePEc:bpj:mcmeap:v:16:y:2010:i:3-4:p:379-398:n:7
    DOI: 10.1515/mcma.2010.014
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/mcma.2010.014
    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.2010.014?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.

    More about this item

    Statistics

    Access and download statistics

    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:16:y:2010:i:3-4:p:379-398:n:7. 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.