Cubic spline prewavelets on the four-directional mesh

Buhmann, M. D. and Davydov, O. and Goodman, T .N. T. (2003) Cubic spline prewavelets on the four-directional mesh. Foundations of Computational Mathematics, 3 (2). pp. 113-133. (https://doi.org/10.1007/s10208-002-0054-x)

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Abstract

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 $L^2(\RR^2)$. 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.

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• Item metadata

  Item type:	Article
  ID code:	36561
  Dates:	Date Event 31 May 2003 Published 17 January 2003 Published Online 19 November 2002 Accepted
  Subjects:	Science > Mathematics
  Department:	Faculty of Science > Mathematics and Statistics
  Depositing user:	Pure Administrator
  Date deposited:	22 Dec 2011 16:05
  Last modified:	14 Nov 2024 01:06
  URI:	https://strathprints.strath.ac.uk/id/eprint/36561