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In constructing the $\mathcal{H}^2$ representation of dense matrices definedby the Laplace kernel, the interpolative decomposition of certain off-diagonalsubmatrices that dominates the computation can be dramatically acceleratedusing the concept of a proxy surface. We refer to the computation of suchinterpolative decompositions as the proxy surface method. We present an errorbound for the proxy surface method in the 3D case and thus provide theoreticalguidance for the discretization of the proxy surface in the method.

Error analysis of an accelerated interpolative decomposition for 3D Laplace problems