尺度Shepard逼近的最优阶Jackson型不等式
Optimal order Jackson type inequality for scaled Shepard approximation
摘要：
我们研究了Shepard近似方案的一个变化，通过引入一个膨胀因子到基函数中，它与数据集和域之间的Hausdorff距离相关。新的方法使我们能够建立一个最优阶Jackson \cite{jackson}型误差估计（具有显式常数）的有界连续函数在任何给定的凸区域。我们还改进了Narcowich和Ward对薄环中分离良好的点的数量的上界估计，这是独立感兴趣的。
英文摘要：
We study a variation of the Shepard approximation scheme by introducing a dilation factor into the base function, which synchronizes with the Hausdorff distance between the data set and the domain. The novelty enables us to establish an optimal order Jackson \cite{jackson} type error estimate (with an explicit constant) for bounded continuous functions on any given convex domain. We also improve en route an upper bound estimate due to Narcowich and Ward for the numbers of well-separated points in thin annuli, which is of independent interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
