We consider the interpolation problem for a class of radial basis functions (RBFs) that includes the classical polyharmonic splines (PHS). We show that the inverse of the system matrix for this interpolation problem can be approximated at an exponential rate in the block rank in the \(\mathcal {H}\)-matrix format, if the block structure of the \(\mathcal {H}\)-matrix arises from a standard clustering algorithm.

中文翻译：

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$$\mathcal {H}$$ - RBF 插值的逆

我们考虑一类径向基函数 (RBF) 的插值问题，其中包括经典的多调和样条 (PHS)。我们证明，该插值问题的系统矩阵的逆可以以\(\mathcal {H}\)矩阵格式的块秩中的指数率近似，如果\(\mathcal { H}\) -矩阵源自标准聚类算法。