Approximation order of interpolatory nonlinear subdivision schemes

作者：Dyn Nira; Grohs Philipp; Wallner Johannes^*

来源：Journal of Computational and Applied Mathematics, 2010, 233(7): 1697-1703.

DOI：10.1016/j.cam.2009.02.017

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

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.

• 出版日期2010-2-1