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Interpolatory subdivision schemes with the optimal approximation order

Author

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

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.

Suggested Citation

  • Zhang, Baoxing & Zheng, Hongchan & Song, Weijie & Lin, Zengyao & Zhou, Jie, 2019. "Interpolatory subdivision schemes with the optimal approximation order," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 1-14.
    • Handle: RePEc:eee:apmaco:v:347:y:2019:i:c:p:1-14
    DOI: 10.1016/j.amc.2018.10.078
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    References listed on IDEAS

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    1. Novara, Paola & Romani, Lucia & Yoon, Jungho, 2016. "Improving smoothness and accuracy of Modified Butterfly subdivision scheme," Applied Mathematics and Computation, Elsevier, vol. 272(P1), pages 64-79.
    2. Zheng, Hongchan & Zhang, Baoxing, 2017. "A non-stationary combined subdivision scheme generating exponential polynomials," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 209-221.
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    Cited by:

    1. Romani, Lucia, 2019. "Interpolating m-refinable functions with compact support: The second generation class," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 735-746.

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