Next Article in Journal / Special Issue
A Sequential, Implicit, Wavelet-Based Solver for Multi-Scale Time-Dependent Partial Differential Equations
Previous Article in Journal / Special Issue
Divergence-Free Multiwavelets on the Half Plane
Open AccessArticle

Construction of Multiwavelets on an Interval

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.
Axioms 2013, 2(2), 122-141; https://doi.org/10.3390/axioms2020122
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)
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. View Full-Text
Keywords: wavelets on an interval; multiwavelets; discrete wavelet transform; boundary handling wavelets on an interval; multiwavelets; discrete wavelet transform; boundary handling
Show Figures

Figure 1

MDPI and ACS Style

Altürk, A.; Keinert, F. Construction of Multiwavelets on an Interval. Axioms 2013, 2, 122-141.

Show more citation formats Show less citations formats

Article Access Map

1
Only visits after 24 November 2015 are recorded.
Back to TopTop