Optimal Interpolatory Subdivision Schemes in Multidimensional Spaces X1. Introduction
نویسنده
چکیده
We analyse the approximation and smoothness properties of fundamental and reenable functions that arise from interpolatory subdivision schemes in mul-tidimensional spaces. In particular, we provide a general way for the construction of bivariate interpolatory reenement masks such that the corresponding fundamental and reenable functions attain the optimal approximation order and smoothness order. In addition, these interpolatory reenement masks are minimally supported and enjoy full symmetry. Several examples are explicitly computed. In this paper we are interested in fundamental and reenable functions with compact support. A function is said to be fundamental if is continuous, (0) = 1, and () = 0 for all 2 Z s nf0g. A function is said to be reenable if it satisses the following reenement equation (1.1) = X 2Z s a()(2 ?); where a is a nitely supported sequence on Z s , called the reenement mask. If a satisses (1.2) X 2Z s a() = 2 s ; then it is known (see 1]) that there exists a unique compactly supported distribution satisfying the reenement equation (1.1) subject to the condition b (0) = 1. This distribution is said to be the normalized solution of the reenement equation (1.1). Throughout this paper, we will assume that the condition (1.2) is satissed. The Fourier transform of a function f 2 L 1 (R s) is deened to be b f() :=
منابع مشابه
Optimal Interpolatory Subdivision Schemes in Multidimensional Spaces * Bin Han † and Rong-qing Jia ‡
We analyse the approximation and smoothness properties of fundamental and refinable functions that arise from interpolatory subdivision schemes in multidimensional spaces. In particular, we provide a general way for the construction of bivariate interpolatory refinement masks such that the corresponding fundamental and refinable functions attain the optimal approximation order and smoothness or...
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