In fast direct solvers for integral equations with the Laplace kernel, a hierarchical compression process needs to compute interpolative decompositions of off-diagonal block rows of the discretized integral operators. This computation can be dramatically accelerated by a technique called the proxy surface method, which is motivated by potential theory. We present a long overdue, rigorous error analysis of this acceleration technique. The analysis provides theoretical guidance for the discretization of the proxy surface used in the technique.

中文翻译：

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3D Laplace问题的加速插值分解的误差分析

在带有Laplace核的积分方程的快速直接求解器中，层次压缩过程需要计算离散积分算子的非对角块行的插值分解。这种计算可以通过一种称为“代理曲面法”的技术来大大加速，该技术是由势能理论激发的。我们对这种加速技术提出了一个迟来的，严格的错误分析。该分析为该技术中使用的代理曲面的离散化提供了理论指导。