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Interpolatory subdivision schemes with the optimal approximation order

Baoxing Zhang, Hongchan Zheng, Weijie Song, Zengyao Lin and Jie Zhou

Applied Mathematics and Computation, 2019, vol. 347, issue C, 1-14

Abstract: 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.

Keywords: D-D interpolatory schemes; Butterfly subdivision; Approximation order; Push-back; Sobolev regularity (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:347:y:2019:i:c:p:1-14

DOI: 10.1016/j.amc.2018.10.078

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