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Optimized dual interpolating subdivision schemes

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  • Viscardi, Alberto

Abstract

This work investigates the non-stepwise interpolation property of the recently introduced class of dual interpolating subdivision schemes, and the “loss of memory” phenomenon that comes with it. New differences between schemes having an odd and an even dilation factors are highlighted. In particular, dual interpolating schemes having an odd dilation factor are proven to satisfy a 2-step interpolation property, while an even dilation factor corresponds to a completely non-stepwise interpolation process. These facts are exploited to define an optimized non-uniform level dependent implementation of dual interpolating schemes in order to overcome the computational drawback due to the “loss of memory”.

Suggested Citation

  • Viscardi, Alberto, 2023. "Optimized dual interpolating subdivision schemes," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    • Handle: RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323003843
    DOI: 10.1016/j.amc.2023.128215
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    References listed on IDEAS

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    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.
    2. Charina, Maria & Conti, Costanza & Guglielmi, Nicola & Protasov, Vladimir, 2016. "Limits of level and parameter dependent subdivision schemes: A matrix approach," Applied Mathematics and Computation, Elsevier, vol. 272(P1), pages 20-27.
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