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On the Construction of Stable B-Spline Wavelet Bases

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • D. Černá

    (Technical University in Liberec)

  • V. Finěk

    (Technical University in Liberec)

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.

Suggested Citation

  • D. Černá & V. Finěk, 2008. "On the Construction of Stable B-Spline Wavelet Bases," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 167-174, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_19
    DOI: 10.1007/978-3-540-69777-0_19
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