Direct algorithm for computation of derivatives of the Daubechies basis functions

We extend the direct algorithm for computing the derivatives of the compactly supported Daubechies N-vanishing-moment basis functions. The method yields exact values at dyadic rationals for the nth derivative (0 ⩽ n ⩽ N − 1) of the basis functions, when it exists. Example results are shown for the f...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 170; no. 2; pp. 1006 - 1013
Main Authors: Lin, Wenbin, Kovvali, Narayan, Carin, Lawrence
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 15.11.2005
Elsevier
Subjects:
Cascade algorithm
Daubechies basis functions
Derivatives
Direct algorithm
Exact sciences and technology
Fourier analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
Wavelets
Cascade algorithm
Wavelets
Derivatives
Direct algorithm
Daubechies basis functions
Numerical approximation
Numerical analysis
Wavelet transformation
Applied mathematics
Function derivative
Computing
Spline approximation
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:We extend the direct algorithm for computing the derivatives of the compactly supported Daubechies N-vanishing-moment basis functions. The method yields exact values at dyadic rationals for the nth derivative (0 ⩽ n ⩽ N − 1) of the basis functions, when it exists. Example results are shown for the first derivatives of the basis functions from the Daubechies N-vanishing-moment extremal phase orthonormal family (for N = 3, 4, and 5), and the CDF(2, N) spline-based biorthogonal family (for N = 6, 8, and 10).
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2004.12.038