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Polynomial reproduction for univariate subdivision schemes of any arity

Conti, Costanza ; Hormann, Kai

In: Journal of approximation theory, 2011, vol. 163, no. 4, p. 413-437

In this paper, we study the ability of convergent subdivision schemes to reproduce polynomials in the sense that for initial data, which is sampled from some polynomial function, the scheme yields the same polynomial in the limit. This property is desirable because the reproduction of polynomials up to some degree d implies that a scheme has approximation order d+1. We first show that any...