On the Construction of Stable B-Spline Wavelet Bases

D. Černá () and V. Finěk ()
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D. Černá: Technical University in Liberec
V. Finěk: Technical University in Liberec

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 167-174 from Springer

Abstract: Abstract The paper is concerned with the construction of wavelet bases on the interval derived from B-splines. The resulting bases generate multiresolution analyses on the unit interval with the desired number of vanishing wavelet moments for primal and dual wavelets. Inner wavelets are translated and dilated versions of well-known wavelets designed by Cohen, Daubechies, Feauveau [4] while boundary wavelets are constructed by combination of methods from [3], [8] and [11]. By this approach, we obtain bases with small Riesz condition numbers. The other important feature of wavelet bases, the sparseness of refinement matrices, is preserved. Finally, Riesz condition numbers of scaling and wavelet bases are computed for some of the constructed bases.

Keywords: Wavelet Base; Riesz Basis; Riesz Basis Property; Elliptic Control Problem; Multiscale Base (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69777-0_19

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DOI: 10.1007/978-3-540-69777-0_19

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