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Limits of level and parameter dependent subdivision schemes: A matrix approach

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  • Charina, Maria
  • Conti, Costanza
  • Guglielmi, Nicola
  • Protasov, Vladimir

Abstract

In this paper, we present a new matrix approach for the analysis of subdivision schemes whose non-stationarity is due to linear dependency on parameters whose values vary in a compact set. Indeed, we show how to check the convergence in Cℓ(Rs) and determine the Hölder regularity of such level and parameter dependent schemes efficiently via the joint spectral radius approach. The efficiency of this method and the important role of the parameter dependency are demonstrated on several examples of subdivision schemes whose properties improve the properties of the corresponding stationary schemes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:272:y:2016:i:p1:p:20-27
    DOI: 10.1016/j.amc.2015.08.120
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    References listed on IDEAS

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    1. Conti, Costanza, 2010. "Stationary and nonstationary affine combination of subdivision masks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 623-635.
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    Cited by:

    1. Viscardi, Alberto, 2023. "Optimized dual interpolating subdivision schemes," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    2. Samsul Ariffin Abdul Karim & Faheem Khan & Ghulam Mustafa & Aamir Shahzad & Muhammad Asghar, 2023. "An Efficient Computational Approach for Computing Subdivision Depth of Non-Stationary Binary Subdivision Schemes," Mathematics, MDPI, vol. 11(11), pages 1-12, May.

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