Abstract
Results from the analysis of binary subdivision schemes are reviewed with a focus on properties which are special to interpolatory schemes. Some new results are presented, in particular the known sufficient conditions for the convergence of binary subdivision schemes to Cv limit functions are proved to be necessary in the case of interpolatory schemes. Specific examples of interpolatory schemes are reviewed, and their properties are concluded from the general theory.
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Dyn, N., Levin, D. (1990). Interpolating Subdivision Schemes for the Generation of Curves and Surfaces. In: Haußmann, W., Jetter, K. (eds) Multivariate Approximation and Interpolation. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 94. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5685-0_6
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DOI: https://doi.org/10.1007/978-3-0348-5685-0_6
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