Error estimates and condition numbers for radial basis function interpolation
Error estimates and condition numbers for radial basis function interpolation
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DOI：
10.1007/bf02432002
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发表时间：
1995-04
影响因子：
1.7
通讯作者：
R. Schaback
中科院分区：
文献类型：
--
作者：
R. Schaback
对于用径向基函数插值离散多变量数据，证明了可得误差与插值矩阵条件之间的“不确定关系”。它指出误差和条件数不能同时保持小。勒贝格常数的边界是作为副产物得到的。提出了关于插值矩阵逆范数上界的Narcowich-Ward理论的一种变体，以便处理目前使用的整个径向基函数集。
For interpolation of scattered multivariate data by radial basis functions, an “uncertainty relation” between the attainable error and the condition of the interpolation matrices is proven. It states that the error and the condition number cannot both be kept small. Bounds on the Lebesgue constants are obtained as a byproduct. A variation of the Narcowich-Ward theory of upper bounds on the norm of the inverse of the interpolation matrix is presented in order to handle the whole set of radial basis functions that are currently in use.