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
C. Conti, K. Jetter: A new subdivision method for bivariate splines on the four-directional mesh, J. Comput. Appl. Math. 119 (2000), 936–952.
C. Conti, G. Zimmermann: Interpolatory vector subdivision schemes, submitted.
S. Dekel, N. Dyn: Poly-scale refinability and subdivision, Appl. Comput. Harmon. Anal. 13 (2002), 35–62.
S. Dubuc: Interpolation through an iterative scheme, J. Math. Anal. Appl. 114 (1986), 185–204.
N. Dyn, J. A. Gregory, D. Levin: A four-point interpolatory subdivision scheme for curve design, Comput. Aided Geom. Design 4 (1987), 257–268.
T. Goodman: Pairs of refinable bivariate splines, In: Advanced Topics in Multivariate Approximation, Approximations and Decompositions Vol. 8, 125–138, World Scientific, Singapore 1996.
K. Jetter, G. Zimmermann: Polynomial reproduction in subdivision, Adv. Comp. Math., to appear (2002).
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Zimmermann, G. (2003). Three Scale Versus Matrix Refinement Equations. In: Haussmann, W., Jetter, K., Reimer, M., Stöckler, J. (eds) Modern Developments in Multivariate Approximation. International Series of Numerical Mathematics, vol 145. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8067-1_18
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DOI: https://doi.org/10.1007/978-3-0348-8067-1_18
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9427-2
Online ISBN: 978-3-0348-8067-1
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