Analysis of Hermite subdivision using piecewise polynomials
Analysis of Hermite subdivision using piecewise polynomials
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使用分段多项式分析 Hermite 细分
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
B. Siwek
中科院分区：
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作者：
M. Floater;B. Siwek
在本文中，我们开始探索一种分析由局部多项式插值定义的 Hermite 细分方案规律性的新方法。该方法的思想是将方案的极限视为由这些局部插值形成的样条曲线的极限，而不是多边形的极限。我们通过获得简单但不平凡的方案的精确霍尔德正则性来证明该方法的成功，其中数据均匀分布，并且细化规则由四个值和两个导数的五次插值定义。
In this paper we begin to explore a new method of analyzing the regularity of Hermite subdivision schemes that are defined from local polynomial interpolants. The idea of the method is to view the limit of the scheme as the limit of splines formed by these local interpolants rather than as the limit of polygons. We demonstrate the success of the method by obtaining the precise Hölder regularity of the simple, but non-trivial scheme in which the data are uniformly spaced and the refinement rule is defined by quintic interpolation of four values and two derivatives.