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A non-stationary combined subdivision scheme generating exponential polynomials

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  • Zheng, Hongchan
  • Zhang, Baoxing

Abstract

In this paper, a non-stationary combined subdivision scheme is presented, which can unify several existing non-stationary approximating and interpolatory subdivision schemes. This scheme is obtained by generalizing the connection between the approximating and interpolatory schemes in the stationary case, first formalized by Maillot & Stam using a push-back operator, to the non-stationary case. For such a combined scheme, we investigate its Cl convergence and exponential polynomial generation/reproduction property and get that it can reach C4 degree of smoothness and generate/reproduce certain exponential polynomials with suitable choices of the parameters. Besides, we give a more generalized combined scheme for the purpose of generating and reproducing more general exponential polynomials. The performance of our new schemes is illustrated by several numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:313:y:2017:i:c:p:209-221
    DOI: 10.1016/j.amc.2017.05.066
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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.
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    Cited by:

    1. 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.
    2. Baoxing Zhang & Hongchan Zheng, 2021. "A Variant Cubic Exponential B-Spline Scheme with Shape Control," Mathematics, MDPI, vol. 9(23), pages 1-11, December.

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    1. 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.
    2. Baoxing Zhang & Hongchan Zheng, 2021. "A Variant Cubic Exponential B-Spline Scheme with Shape Control," Mathematics, MDPI, vol. 9(23), pages 1-11, December.

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