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：

---

RBF 插值的 $\mathcal{H}$-inverses

我们考虑一类径向基函数 (RBF) 的插值问题，其中包括经典的多谐样条 (PHS)。我们表明，如果 $\mathcal{H}$-matrix 格式的块结构，该插值问题的系统矩阵的逆可以在块等级中以指数速率近似为 $\mathcal{H}$-矩阵来自标准的聚类算法。