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.

翻译：我们考虑的是包括古典多声调样条(PHS)在内的一类辐射基函数(RBFs)的内插问题。 我们发现,如果$\mathcal{H}$-matrix 格式的区块结构由标准组合算法产生,那么用于这一内插问题的系统矩阵的反向矩阵可以以指数速率接近于 $\mathcal{H}$-matrix 格式的区块级 。