Polynomial reproduction of multivariate scalar subdivision schemes
نویسندگان
چکیده
منابع مشابه
Scalar multivariate subdivision schemes and box splines
We study convergent scalar d-variate subdivision schemes satisfying sum rules of order k ∈ N, with dilation matrix 2I . Using the results of Möller and Sauer in [18], stated for general expanding dilation matrices, we characterize the structure of the mask symbols of such schemes by showing that they must be linear combinations of shifted box spline generators of a quotient polynomial ideal J ....
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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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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2013
ISSN: 0377-0427
DOI: 10.1016/j.cam.2012.06.013