Low-rank approximation of integral operators by interpolation

Authors:
Steffen Börm;Lars Grasedyck
Affiliations:
Max-Planck-Instituie for Mathematics in the Sciences, Leipzig Germany;Max-Planck-Instituie for Mathematics in the Sciences, Leipzig Germany
Venue:
Computing
Year:
2004

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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.