Approximation order of interpolatory nonlinear subdivision schemes

Nira Dyn, Philipp Grohs, Johannes Wallner*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish
Pages (from-to)1697-1703
Number of pages7
JournalJournal of Computational and Applied Mathematics
Issue number7
StatePublished - 1 Feb 2010


FundersFunder number
Austrian Science Fund19780


    • Approximation order
    • Interpolatory subdivision
    • Nonlinear subdivision
    • Proximity inequalities


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