Adaptive frame methods with cubic spline-wavelet bases. (English) Zbl 1203.65293

Černá, Dana; Finěk, Václav

Chleboun, J. (ed.) et al., Programs and algorithms of numerical mathematics 14. Proceedings of the seminar, Dolní Maxov, Czech Republic, June 1–6, 2008. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-55-4). 59-64 (2008).

From the introduction: We propose a construction of cubic spline-wavelet bases on the interval adapted for complementary boundary conditions of the first order. We show that these bases are well-conditioned and that the corresponding stiffness matrices have small condition numbers. Furthermore, we show that the adaptive wavelet frame method of S. Dahlke, M. Fornasier, and T. Raasch [Adv. Comput. Math. 27, No. 1, 27–63 (2007; Zbl 1122.65103)] with bases constructed in our paper realizes the optimal convergence rate.
For the entire collection see [Zbl 1194.65013].

MSC:

65T60

Numerical methods for wavelets

Keywords:

numerical examples; cubic spline-wavelet bases; condition numbers; convergence

Citations:

Zbl 1122.65103