On the norms of the Dubuc-Deslauriers subdivision schemes

Abstract

Conti et al. (2012, Remark 3.4) conjecture that the norm of the interpolatory 2n-point Dubuc–Deslauriers subdivision scheme is bounded from above by 4 for any n ∈ N. We disprove their conjecture by showing that the norm grows logarithmically in n and therefore diverges as n increases. 
DOI: 10.1016/j.cagd.2013.05.001

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