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Axioms 2013, 2(2), 122-141; doi:10.3390/axioms2020122
Article

Construction of Multiwavelets on an Interval

1
 and
2,*
1 Department of Mathematics, Amasya University, Amasya, Turkey 2 Department of Mathematics, Iowa State University, Ames, IA 50011, USA
* Author to whom correspondence should be addressed.
Received: 5 February 2013 / Revised: 21 March 2013 / Accepted: 26 March 2013 / Published: 17 April 2013
(This article belongs to the Special Issue Wavelets and Applications)
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Abstract

Boundary functions for wavelets on a finite interval are often constructed as linear combinations of boundary-crossing scaling functions. An alternative approach is based on linear algebra techniques for truncating the infinite matrix of the DiscreteWavelet Transform to a finite one. In this article we show how an algorithm of Madych for scalar wavelets can be generalized to multiwavelets, given an extra assumption. We then develop a new algorithm that does not require this additional condition. Finally, we apply results from a previous paper to resolve the non-uniqueness of the algorithm by imposing regularity conditions (including approximation orders) on the boundary functions.
Keywords: wavelets on an interval; multiwavelets; discrete wavelet transform; boundary handling wavelets on an interval; multiwavelets; discrete wavelet transform; boundary handling
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Altürk, A.; Keinert, F. Construction of Multiwavelets on an Interval. Axioms 2013, 2, 122-141.

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