Approximation order of interpolatory nonlinear subdivision schemes

Authors:
Nira Dyn;Philipp Grohs;Johannes Wallner
Affiliations:
School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel;Institut für Geometrie, Technische Universität Graz, A8010 Graz, Austria;Institut für Geometrie, Technische Universität Graz, A8010 Graz, Austria
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

Linear interpolatory subdivision schemes of C^r 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.