Buhmann, M.D. and Davydov, Oleg and Goodman, T.N.T. (2003) Cubic spline prewavelets on the four-directional mesh. Foundations of Computational Mathematics, 3 (2). pp. 113-133.
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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.
|Keywords:||prewavelets , cubic polynomials , spline constructions, Mathematics, Computational Theory and Mathematics, Computational Mathematics, Theoretical Computer Science, Applied Mathematics, Mathematics(all)|
|Subjects:||Science > Mathematics|
|Department:||Faculty of Science > Mathematics and Statistics|
|Depositing user:||Pure Administrator|
|Date Deposited:||22 Dec 2011 16:05|
|Last modified:||17 Jun 2015 17:02|
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