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.
@article{702661,
title = {Quantitative properties of quadratic spline wavelet bases in higher dimensions},
booktitle = {Programs and Algorithms of Numerical Mathematics},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2015},
pages = {41-46},
url = {http://dml.mathdoc.fr/item/702661}
}
Černá, Dana; Finěk, Václav; Šimůnková, Martina. Quantitative properties of quadratic spline wavelet bases in higher dimensions, dans Programs and Algorithms of Numerical Mathematics, GDML_Books, (2015), pp. 41-46. http://gdmltest.u-ga.fr/item/702661/