IDEAS home Printed from https://ideas.repec.org/a/hin/jijmms/063670.html
   My bibliography  Save this article

Comparison of wavelet approximation order in different smoothness spaces

Author

Listed:
  • M. R. Islam
  • S. F. Ahemmed
  • S. M. A. Rahman

Abstract

In linear approximation by wavelet, we approximate a givenfunction by a finite term from the wavelet series. Theapproximation order is improved if the order of smoothness of thegiven function is improved, discussed by Cohen(2003), DeVore (1998), and Siddiqi (2004). But in the case ofnonlinear approximation, the approximation order is improvedquicker than that in linear case. In thisstudy we proved this assumption only for the Haar wavelet. Haarfunction is an example of wavelet and this fundamental examplegives major feature of the general wavelet. A nonlinear spacecomes from arbitrary selection of wavelet coefficients, whichrepresent the target function almost equally. In this case ourcomputational work will be reduced tremendously in the sense thatapproximation error decays more quickly than that inlinear case.

Suggested Citation

  • M. R. Islam & S. F. Ahemmed & S. M. A. Rahman, 2006. "Comparison of wavelet approximation order in different smoothness spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-7, July.
    • Handle: RePEc:hin:jijmms:063670
    DOI: 10.1155/IJMMS/2006/63670
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/IJMMS/2006/063670.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/IJMMS/2006/063670.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/IJMMS/2006/63670?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
    ---><---

    Citations

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


    Cited by:

    1. Shyam Lal & Susheel Kumar, 2016. "Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-7, October.

    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:hin:jijmms:063670. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.