A quadratic spline-wavelet basis on the interval

Černá, Dana, Finěk, Václav, and Šimůnková, Martina. "A quadratic spline-wavelet basis on the interval." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics AS CR, 2013. 29-34. <http://eudml.org/doc/271295>.

@inProceedings{Černá2013,
abstract = {In signal and image processing as well as in numerical solution of differential equations, wavelets with short support and with vanishing moments are important because they have good approximation properties and enable fast algorithms. A B-spline of order $m$ is a spline function that has minimal support among all compactly supported refinable functions with respect to a given smoothness. And recently, B. Han and Z. Shen constructed Riesz wavelet bases of $L_2(\mathbb \{R\})$ with $m$ vanishing moments based on B-spline of order $m$. In our contribution, we present an adaptation of their quadratic spline-wavelets to the interval $[0,1]$ which preserves vanishing moments.},
author = {Černá, Dana, Finěk, Václav, Šimůnková, Martina},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {B-spline; biorthogonal wavelets; quadratic spline-wavelets; condition number; stiffness matrix},
location = {Prague},
pages = {29-34},
publisher = {Institute of Mathematics AS CR},
title = {A quadratic spline-wavelet basis on the interval},
url = {http://eudml.org/doc/271295},
year = {2013},
}

TY - CLSWK
AU - Černá, Dana
AU - Finěk, Václav
AU - Šimůnková, Martina
TI - A quadratic spline-wavelet basis on the interval
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2013
CY - Prague
PB - Institute of Mathematics AS CR
SP - 29
EP - 34
AB - In signal and image processing as well as in numerical solution of differential equations, wavelets with short support and with vanishing moments are important because they have good approximation properties and enable fast algorithms. A B-spline of order $m$ is a spline function that has minimal support among all compactly supported refinable functions with respect to a given smoothness. And recently, B. Han and Z. Shen constructed Riesz wavelet bases of $L_2(\mathbb {R})$ with $m$ vanishing moments based on B-spline of order $m$. In our contribution, we present an adaptation of their quadratic spline-wavelets to the interval $[0,1]$ which preserves vanishing moments.
KW - B-spline; biorthogonal wavelets; quadratic spline-wavelets; condition number; stiffness matrix
UR - http://eudml.org/doc/271295
ER -