IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v101y2001i1p143-14710.1023-a1010916406274.html
   My bibliography  Save this article

Continuity of Approximation by Neural Networks in Lp Spaces

Author

Listed:
  • Paul Kainen
  • Věra Kůrková
  • Andrew Vogt

Abstract

Devices such as neural networks typically approximate the elements of some function space X by elements of a nontrivial finite union M of finite-dimensional spaces. It is shown that if X=L p (Ω) (1>p>∞ and Ω⊂R d ), then for any positive constant Γ and any continuous function φ from X to M, ‖f−φ(f)‖>‖f−M‖+Γ for some f in X. Thus, no continuous finite neural network approximation can be within any positive constant of a best approximation in the L p -norm. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • Paul Kainen & Věra Kůrková & Andrew Vogt, 2001. "Continuity of Approximation by Neural Networks in Lp Spaces," Annals of Operations Research, Springer, vol. 101(1), pages 143-147, January.
    • Handle: RePEc:spr:annopr:v:101:y:2001:i:1:p:143-147:10.1023/a:1010916406274
    DOI: 10.1023/A:1010916406274
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/A:1010916406274
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/A:1010916406274?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Manuel Castejón-Limas & Joaquín Ordieres-Meré & Ana González-Marcos & Víctor González-Castro, 2011. "Effort estimates through project complexity," Annals of Operations Research, Springer, vol. 186(1), pages 395-406, June.

    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:annopr:v:101:y:2001:i:1:p:143-147:10.1023/a:1010916406274. 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.