Error analysis of an accelerated interpolative decomposition for 3D Laplace problems
Provides theoretical grounding for a computational acceleration technique in numerical linear algebra for 3D Laplace problems.
The paper provides an error bound for the proxy surface method, which accelerates interpolative decomposition for 3D Laplace problems, offering theoretical guidance for discretization.
In constructing the $\mathcal{H}^2$ representation of dense matrices defined by the Laplace kernel, the interpolative decomposition of certain off-diagonal submatrices that dominates the computation can be dramatically accelerated using the concept of a proxy surface. We refer to the computation of such interpolative decompositions as the proxy surface method. We present an error bound for the proxy surface method in the 3D case and thus provide theoretical guidance for the discretization of the proxy surface in the method.