Interpolatory subdivision schemes with the optimal approximation order

Zhang, Baoxing; Zheng, Haibin; Song, Weijie; Lin, Zehao; Zhou, Jie

doi:10.1016/j.amc.2018.10.078

Cited by 4 publications

(1 citation statement)

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“…a j z j , z ∈ C \ {0} (1.5) as τ a = A (1) m (see, e.g., [5]) where A (z) denotes the first derivative of A(z). In particular, in [5] it is proven that, in case of a subdivision scheme with odd-symmetry (see Definition 2.2), τ a ∈ Z; conversely, in case of even-symmetry (see Definition 2.3), τ a ∈ Z 2 \ Z. Symmetric, compactly supported interpolating m-refinable functions that we can find in the literature always fulfill equation (1.4) in the case τ a ∈ Z, i.e., are associated with an odd-symmetric subdivision mask a satisfying (1.3) for an even integer M (see, e.g., [1,2,8,11,15,16,18,23,24]). In addition, for all of them the odd-symmetric subdivision mask a is such that…”

Section: Introduction and Purpose Of The Workmentioning

confidence: 99%

Interpolating m-refinable functions with compact support: The second generation class

Romani

2019

Applied Mathematics and Computation

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We present an algorithm for the construction of a new class of compactly supported interpolating refinable functions that we call the second generation class since, contrary to the existing class, is associated to subdivision schemes with an even-symmetric mask that does not contain the submask {0..., 0, 1, 0, ...0}.As application examples of the proposed algorithm we present interpolating 4-refinable functions that are generated by parameter-dependent, even-symmetric quaternary schemes never considered in the literature so far.

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