Approximate Interpolation with Applications to Selecting Smoothing Parameters
Approximate Interpolation with Applications to Selecting Smoothing Parameters
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DOI：
10.1007/s00211-005-0637-y
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发表时间：
2005-10
影响因子：
2.1
通讯作者：
H. Wendland;C. Rieger
中科院分区：
文献类型：
--
作者：
H. Wendland;C. Rieger
在本文中，我们研究了已知在给定离散数据集上较小的函数的全局行为。这样的函数可以被解释为未知函数和给定近似值之间的误差函数。我们将证明，在温和的假设下，离散数据集上的小错误会自动导致较大区域上的小错误。我们将这些结果应用于样条平滑，并表明平滑参数的特定先验选择是可能的，并且导致与经典插值相同的近似阶数。这在通过样条和正定核稳定插值过程方面也有令人惊讶的应用。
In this paper, we study the global behavior of a function that is known to be small at a given discrete data set. Such a function might be interpreted as the error function between an unknown function and a given approximant. We will show that a small error on the discrete data set leads under mild assumptions automatically to a small error on a larger region. We will apply these results to spline smoothing and show that a specific, a priori choice of the smoothing parameter is possible and leads to the same approximation order as the classical interpolant. This has also a surprising application in stabilizing the interpolation process by splines and positive definite kernels.