Open Access
2006 Construction of orthogonal multiscaling functions and multiwavelets with higher approximation order based on the matrix extension algorithm
Shouzhi Yang, Zengjian Lou
J. Math. Kyoto Univ. 46(2): 275-290 (2006). DOI: 10.1215/kjm/1250281777

Abstract

An algorithm is presented for constructing orthogonal multiscaling functions and multiwavelets with higher approximation order in terms of any given orthogonal multiscaling functions. That is, let $\Phi (x) = [\phi _{1}(x), \phi _{2}(x),\ldots , \phi _{r}(x)]^{T} \in (L^{2}(R))^{r}$ be an orthogonal multiscaling function with multiplicity $r$ and approximation order $m$. We can construct a new orthogonal multiscaling function $\Phi ^{new}(x) = [\Phi ^{T} (x), \phi _{r+1}(x), \phi _{r+2}(x),\ldots ,\phi _{r+s}(x)]^{T}$ with approximation order $n(n > m)$. Namely, we raise approximation order of a given multiscaling function by increasing its multiplicity. Corresponding to the new orthogonal multiscaling function $\Phi ^{new}(x)$, orthogonal multiwavelet $\Psi ^{new}(x)$ is constructed. In particular, the spacial case that $r = s$ is discussed. Finally, we give an example illustrating how to use our method to construct an orthogonal multiscaling function with higher approximation order and its corresponding multiwavelet.

Citation

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Shouzhi Yang. Zengjian Lou. "Construction of orthogonal multiscaling functions and multiwavelets with higher approximation order based on the matrix extension algorithm." J. Math. Kyoto Univ. 46 (2) 275 - 290, 2006. https://doi.org/10.1215/kjm/1250281777

Information

Published: 2006
First available in Project Euclid: 14 August 2009

zbMATH: 1118.42013
MathSciNet: MR2284344
Digital Object Identifier: 10.1215/kjm/1250281777

Subjects:
Primary: ‎42C40
Secondary: 65T60

Rights: Copyright © 2006 Kyoto University

Vol.46 • No. 2 • 2006
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