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Three Scale Versus Matrix Refinement Equations

  • Georg Zimmermann
Conference paper
Part of the International Series of Numerical Mathematics book series (ISNM, volume 145)

Abstract

We show under what conditions three scale refinement equations are equivalent to matrix refinement equations of a certain structure, and how this equivalence can be used in the modification of refinement masks.

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References

  1. 1.
    C. Conti, K. Jetter: A new subdivision method for bivariate splines on the four-directional mesh, J. Comput. Appl. Math. 119 (2000), 936–952.CrossRefMathSciNetGoogle Scholar
  2. 2.
    C. Conti, G. Zimmermann: Interpolatory vector subdivision schemes, submitted.Google Scholar
  3. 3.
    S. Dekel, N. Dyn: Poly-scale refinability and subdivision, Appl. Comput. Harmon. Anal. 13 (2002), 35–62.CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    S. Dubuc: Interpolation through an iterative scheme, J. Math. Anal. Appl. 114 (1986), 185–204.CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    N. Dyn, J. A. Gregory, D. Levin: A four-point interpolatory subdivision scheme for curve design, Comput. Aided Geom. Design 4 (1987), 257–268.zbMATHMathSciNetGoogle Scholar
  6. 6.
    T. Goodman: Pairs of refinable bivariate splines, In: Advanced Topics in Multivariate Approximation, Approximations and Decompositions Vol. 8, 125–138, World Scientific, Singapore 1996.Google Scholar
  7. 7.
    K. Jetter, G. Zimmermann: Polynomial reproduction in subdivision, Adv. Comp. Math., to appear (2002).Google Scholar

Copyright information

© Springer Basel AG 2003

Authors and Affiliations

  • Georg Zimmermann
    • 1
  1. 1.Institut für Angewandte Mathematik und StatistikUniversität HohenheimStuttgartGermany

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