Interpolatory subdivision schemes with the optimal approximation order

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摘要

In this paper, we show that the univariate interpolatory subdivision schemes with the optimal approximation order, which are the D-D interpolatory ones, can be obtained from the cubic B-spline scheme. Such schemes are derived in this paper by suitably using the push-back operation, a connection between the approximating and interpolatory subdivision. Then, the process to obtain the D-D schemes is generalized to the bivariate case and bivariate interpolatory schemes with the optimal approximation order are generated based on the triangular meshes. Compared with the existing bivariate interpolatory schemes with the optimal approximation order, the newly constructed ones own some advantages, such as a better performance in terms of the number of nonzero coefficients in the mask. Several examples are given and explicitly computed.

论文关键词:D-D interpolatory schemes,Butterfly subdivision,Approximation order,Push-back,Sobolev regularity

论文评审过程:Received 27 March 2018, Revised 18 October 2018, Accepted 23 October 2018, Available online 12 November 2018, Version of Record 12 November 2018.

论文官网地址:https://doi.org/10.1016/j.amc.2018.10.078

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