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Article

Černá, Dana ; Finěk, Václav ; Šimůnková, Martina
Quantitative properties of quadratic spline wavelet bases in higher dimensions. (English). In: Chleboun, J., Přikryl, P., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 8-13, 2014. Institute of Mathematics AS CR, Prague, 2015. pp. 41-46
MSC: 65T60
Keywords:
wavelet bases; higher dimension; condition number
Summary:
To use wavelets efficiently to solve numerically partial differential equations in higher dimensions, it is necessary to have at one’s disposal suitable wavelet bases. Ideal wavelets should have short supports and vanishing moments, be smooth and known in closed form, and a corresponding wavelet basis should be well-conditioned. In our contribution, we compare condition numbers of different quadratic spline wavelet bases in dimensions d = 1, 2 and 3 on tensor product domains (0,1)^d.
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