  Matrices resulting from the discretization of a kernel function, e.g., in the
context of integral equations or sampling probability distributions, can
frequently be approximated by interpolation. In order to improve the
efficiency, a multi-level approach can be employed that involves interpolating
the kernel function and its approximations multiple times.
  This article presents a new approach to analyze the error incurred by these
iterated interpolation procedures that is considerably more elegant than its
predecessors and allows us to treat not only the kernel function itself, but
also its derivatives.
