Low-Rank Approximation of Integral Operators by Interpolation

Abstract

A central component of the analysis of panel clustering techniques for the approximation of integral operators is the so-called η -admissibility condition “ min {diam(τ),diam(σ)} ≤ 2ηdist(τ,σ)” that ensures that the kernel function is approximated only on those parts of the domain that are far from the singularity. Typical techniques based on a Taylor expansion of the kernel function require a subdomain to be “far enough” from the singularity such that the parameter η has to be smaller than a given constant depending on properties of the kernel function. In this paper, we demonstrate that any η is sufficient if interpolation instead of Taylor expansion␣is␣used for the kernel approximation, which paves the way for grey-box panel clustering algorithms.