IDEAS home Printed from https://ideas.repec.org/a/bpj/mcmeap/v25y2019i2p163-176n2.html
   My bibliography  Save this article

On the sample-mean method for computing hyper-volumes

Author

Listed:
  • Rabiei Nima

    (Department of Mathematics, The American University of Iraq, Sulaimani, Iraq)

  • Saleeby Elias G.

    (Mount Lebanon, Beirut, Lebanon)

Abstract

Estimating hyper-volumes of convex and non-convex sets are of interest in a number of areas. In this article we develop further a simple geometric Monte Carlo method, known also as the sample-mean method, which transforms the domain to an equivalent hyper-sphere with the same volume. We first examine the performance of the method to compute the volumes of star-convex unit balls and show that it gives accurate estimates of their volumes. We then examine the use of this method for computing the volumes of nonstar-shaped domains. In particular, we develop two algorithms, which couple the sample-mean method with algebraic and geometric techniques, to generate and compute the volumes of low-dimensional stability domains in parameter space.

Suggested Citation

  • Rabiei Nima & Saleeby Elias G., 2019. "On the sample-mean method for computing hyper-volumes," Monte Carlo Methods and Applications, De Gruyter, vol. 25(2), pages 163-176, June.
    • Handle: RePEc:bpj:mcmeap:v:25:y:2019:i:2:p:163-176:n:2
    DOI: 10.1515/mcma-2019-2034
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/mcma-2019-2034
    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-2019-2034?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:25:y:2019:i:2:p:163-176: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.