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Cubic spline prewavelets on the four-directional mesh

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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    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.

    Item type: Article
    ID code: 36561
    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
    Related URLs:
      Depositing user: Pure Administrator
      Date Deposited: 22 Dec 2011 16:05
      Last modified: 06 Sep 2014 06:04
      URI: http://strathprints.strath.ac.uk/id/eprint/36561

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