alexa On the Exact Values of Daubechies Wavelets
ISSN: 2090-0902

Journal of Physical Mathematics
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Research Article

On the Exact Values of Daubechies Wavelets

Hajji MA*

Department of Mathematical Sciences, United Arab Emirates University, United Arab Emirates

*Corresponding Author:
Hajji MA
Department of Mathematical Sciences
United Arab Emirates University
United Arab Emirates
Tel: 971 3 7136385
E-mail: [email protected]

Received Date: January 12, 2016; Accepted Date: February 01, 2016; Published Date: February 05, 2016

Citation: Hajji MA (2016) On the Exact Values of Daubechies Wavelets. J Phys Math 7:157. doi:10.4172/2090-0902.1000157

Copyright: © 2016 Hajji MA. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

 

Abstract

In this paper we propose an algorithm for the calculation of the exact values of compactly-supported Daubechies wavelet functions. The algorithm is iterative, performing a single convolution operation at each step. It requires solving, at the first step only, a linear system of a relatively small size. The novelty of the algorithm is that once the values at dyadic points at a certain level j are calculated they do not need to be updated at the next step. We find that this algorithm is superior to the well-known cascade algorithm proposed by Ingrid Daubechies. This algorithm can serve well in wavelet based methods for the numerical solutions of differential equations. The algorithm is tested on Daubechies scaling functions as well as Daubechies coiflets. Comparison with the values obtained using the cascade algorithm is made. We found that the cascade algorithm results converge to ours

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