Quantitative properties of quadratic spline wavelet bases in higher dimensions

Černá, Dana; Finěk, Václav; Šimůnková, Martina

  • Programs and Algorithms of Numerical Mathematics, Publisher: Institute of Mathematics AS CR(Prague), page 41-46

Abstract

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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.

How to cite

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Černá, Dana, Finěk, Václav, and Šimůnková, Martina. "Quantitative properties of quadratic spline wavelet bases in higher dimensions." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics AS CR, 2015. 41-46. <http://eudml.org/doc/269900>.

@inProceedings{Černá2015,
abstract = {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.},
author = {Černá, Dana, Finěk, Václav, Šimůnková, Martina},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {wavelet bases; higher dimension; condition number},
location = {Prague},
pages = {41-46},
publisher = {Institute of Mathematics AS CR},
title = {Quantitative properties of quadratic spline wavelet bases in higher dimensions},
url = {http://eudml.org/doc/269900},
year = {2015},
}

TY - CLSWK
AU - Černá, Dana
AU - Finěk, Václav
AU - Šimůnková, Martina
TI - Quantitative properties of quadratic spline wavelet bases in higher dimensions
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2015
CY - Prague
PB - Institute of Mathematics AS CR
SP - 41
EP - 46
AB - 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.
KW - wavelet bases; higher dimension; condition number
UR - http://eudml.org/doc/269900
ER -

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