  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.
