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.

中文翻译：

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关于迭代插值

由核函数离散化产生的矩阵，例如，在积分方程或采样概率分布的上下文中，经常可以通过插值来近似。为了提高效率，可以采用涉及多次内插核函数及其近似值的多级方法。本文提出了一种分析由这些迭代插值过程引起的误差的新方法，该方法比其前辈更加优雅，使我们不仅可以处理核函数本身，还可以处理其导数。