Approximation order of interpolatory nonlinear subdivision schemes |
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Authors: | Nira Dyn Philipp Grohs Johannes Wallner |
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Affiliation: | a School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel b Institut für Geometrie, Technische Universität Graz, A 8010 Graz, Austria |
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Abstract: | Linear interpolatory subdivision schemes of Cr smoothness have approximation order at least r+1. The present paper extends this result to nonlinear univariate schemes which are in proximity with linear schemes in a certain specific sense. The results apply to nonlinear subdivision schemes in Lie groups and in surfaces which are obtained from linear subdivision schemes. We indicate how to extend the results to the multivariate case. |
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Keywords: | 65D17 41A25 |
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