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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; in revised form: 21 March 2013 / Accepted: 26 March 2013 / Published: 17 April 2013
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
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MDPI and ACS Style
Altürk, A.; Keinert, F. Construction of Multiwavelets on an Interval. Axioms 2013, 2, 122-141.
Altürk A, Keinert F. Construction of Multiwavelets on an Interval. Axioms. 2013; 2(2):122-141.
Altürk, Ahmet; Keinert, Fritz. 2013. "Construction of Multiwavelets on an Interval." Axioms 2, no. 2: 122-141.