TY - JOUR
T1 - Approximation order of interpolatory nonlinear subdivision schemes
AU - Dyn, Nira
AU - Grohs, Philipp
AU - Wallner, Johannes
N1 - Funding Information:
The second author gratefully acknowledges the support of the Austrian Science Fund (FWF, Grant No. 19780).
PY - 2010/2/1
Y1 - 2010/2/1
N2 - 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.
AB - 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.
KW - Approximation order
KW - Interpolatory subdivision
KW - Nonlinear subdivision
KW - Proximity inequalities
UR - http://www.scopus.com/inward/record.url?scp=70449633402&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2009.02.017
DO - 10.1016/j.cam.2009.02.017
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AN - SCOPUS:70449633402
SN - 0377-0427
VL - 233
SP - 1697
EP - 1703
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 7
ER -