Construction of Multiwavelets on an Interval
AbstractBoundary 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.
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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.Chicago/Turabian Style
Altürk, Ahmet; Keinert, Fritz. 2013. "Construction of Multiwavelets on an Interval." Axioms 2, no. 2: 122-141.