Cubic Spline Prewavelets on the Four-Directional Mesh |
| |
Authors: | Buhmann Davydov and Goodman |
| |
Affiliation: | (1) Mathematical Institute Justus Liebig University D-35392 Giessen, Germany martin.buhmann@math.uni-giessen.de, DE;(2) Mathematical Institute Justus Liebig University D-35392 Giessen, Germany oleg.davydov@math.uni-giessen.de, DE;(3) Department of Mathematics The University of Dundee Dundee DD1 4HN, UK tgoodman@mcs.dundee.ac.uk, GB |
| |
Abstract: | Dedicated to Professor M. J. D. Powell on the occasion
of his sixty-fifth birthday and his retirement.
In this paper, we design differentiable, two-dimensional, piecewise polynomial cubic prewavelets of particularly small compact
support. They are given in closed form, and provide stable, orthogonal decompositions of L
2
(R
2
) . In particular, the splines we use in our prewavelet constructions give rise to stable bases of spline spaces that contain
all cubic polynomials, whereas the more familiar box spline constructions cannot reproduce all cubic polynomials, unless resorting
to a box spline of higher polynomial degree. |
| |
Keywords: | AMS Classification 41A15 41A63 65D07 65D15 65T60 |
本文献已被 SpringerLink 等数据库收录! |
|