Algebraic conditions on non-stationary subdivision symbols for exponential polynomial reproduction
نویسندگان
چکیده
منابع مشابه
On polynomial symbols for subdivision schemes
Given a dilation matrix A : Z d → Z d , and G a complete set of coset representatives of 2π(A −− Z d /Z d), we consider polynomial solutions M to the equation g∈G M (ξ + g) = 1 with the constraints that M ≥ 0 and M (0) = 1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbol...
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One of the important capabilities for a subdivision scheme is the reproducing property of circular shapes or parts of conics that are important analytical shapes in geometrical modelling. In this regards, the first goal of this study is to provide necessary and sufficient conditions for a non-stationary subdivision to have the reproducing property of exponential polynomials. The result in fact ...
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We study the necessary and sufficient conditions for the generation of polynomials by stationary subdivision schemes, and we show how to derive appropriate quasiinterpolation rules that have the optimal approximation order. We show that these conditions hold in the context of non-uniform subdivision as well, and we demonstrate how they can be used for the construction of stationary non-uniform ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2011
ISSN: 0377-0427
DOI: 10.1016/j.cam.2011.03.031