Comparison of wavelet approximation order in different smoothness spaces

M. R. Islam, S. F. Ahemmed and S. M. A. Rahman

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-7

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.

Date: 2006
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2006/063670.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2006/063670.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:063670

DOI: 10.1155/IJMMS/2006/63670

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().