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 functions 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.

翻译：内核函数离散产生的矩阵,例如,在整体方程式或取样概率分布的情况下,往往可以通过内插相近,为了提高效率,可以采用多层次的办法,把内核函数及其近似多次相互混合,这一条提出了一种新的办法,分析这些迭代内插程序引起的错误,这种程序比以前的程序要优于以前的程序,使我们不仅能够处理内核功能本身,而且能够处理其衍生物。