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An algorithm for constructing biorthogonal multiwavelets with higher approximation orders

Published online by Cambridge University Press:  17 February 2009

Yang Shouzhi
Yang Shouzhi
Affiliation:
Department of Mathematics, Shantou University, Shantou 515063, P. R. China; e-mail: szyang@stu.edu.cn.
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Given a pair of biorthogonal multiscaling functions, we present an algorithm for raising their approximation orders to any desired level. Precisely, let Φ(x) and (x) be a pair of biorthogonal multiscaling functions of multiplicity r, with approximation orders m and , respectively. Then for some integer s, we can construct a pair of new biorthogonal multiscaling functions Φnew(x) = [ΦT (x), φr+1 (x), φr+2(x),… φr+s(x)]T and new(x) = [ (x) T, r+1(x), r+2(x),… r+s(x)]T with approximation orders n (n > m) and ñ (ñ > ), respectively. In addition, corresponding to Φnew(x) and new(x) a biorthogonal multiwavelet pair ψnew(x) and new(x) is constructed explicitly. Finally, an example is given.

Keywords

biorthogonalmultiscaling functionsmultiwaveletsapproximation order.
Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 4 , April 2006 , pp. 513 - 526
Copyright
Copyright © Australian Mathematical Society 2006

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