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

Construction of Multiwavelets on an Interval

Department of Mathematics, Amasya University, Amasya, Turkey
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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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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