Efficient evaluation of subdivision schemes with polynomial reproduction property
نویسندگان
چکیده
منابع مشابه
Polynomial reproduction by symmetric subdivision schemes
We first present necessary and sufficient conditions for a linear, binary, uniform, and stationary subdivision scheme to have polynomial reproduction of degree d and thus approximation order d + 1. Our conditions are partly algebraic and easy to check by considering the symbol of a subdivision scheme, but also relate to the parameterization of the scheme. After discussing some special propertie...
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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 conve...
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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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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2016
ISSN: 0377-0427
DOI: 10.1016/j.cam.2015.09.008