IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-18743-8_3.html
   My bibliography  Save this book chapter

On Tractability of Weighted Integration for Certain Banach Spaces of Functions

In: Monte Carlo and Quasi-Monte Carlo Methods 2002

Author

Listed:
  • Fred J. Hickernell

    (Hong Kong Baptist University, Department of Mathematics)

  • Ian H. Sloan

    (School of Mathematics)

  • Grzegorz W. Wasilkowski

    (University of Kentucky, Department of Computer Science)

Abstract

Summary There are a number of results on tractability and strong tractability for the integration problem over bounded domains. However, the majority of them assume functions with dominating mixed partial derivatives bounded in the L 2 norm. Much less is known when the derivatives are bounded in the L 1 norm, and almost nothing when a finite L p norm is assumed for an arbitrary p. The focus of this paper is to extend known tractability results to weighted spaces of functions with the derivatives bounded in L p norms and the norms of the derivatives then combined via weighted L q norms. Moreover, we consider weighted integration with the domain of integration being not necessarily bounded. It turns out that tractability and strong tractability depend only on q for bounded D, whereas they depend on both parameters p and q for unbounded D.

Suggested Citation

  • Fred J. Hickernell & Ian H. Sloan & Grzegorz W. Wasilkowski, 2004. "On Tractability of Weighted Integration for Certain Banach Spaces of Functions," Springer Books, in: Harald Niederreiter (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2002, pages 51-71, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18743-8_3
    DOI: 10.1007/978-3-642-18743-8_3
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    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:spr:sprchp:978-3-642-18743-8_3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.