@article{d76c7d90bbb24aa3a4f7068c52c228f1,
title = "Approximation order of interpolatory nonlinear subdivision schemes",
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.",
keywords = "Approximation order, Interpolatory subdivision, Nonlinear subdivision, Proximity inequalities",
author = "Nira Dyn and Philipp Grohs and Johannes Wallner",
note = "Funding Information: The second author gratefully acknowledges the support of the Austrian Science Fund (FWF, Grant No. 19780). ",
year = "2010",
month = feb,
day = "1",
doi = "10.1016/j.cam.2009.02.017",
language = "אנגלית",
volume = "233",
pages = "1697--1703",
journal = "Journal of Computational and Applied Mathematics",
issn = "0377-0427",
publisher = "Elsevier B.V.",
number = "7",
}