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MiS Preprint
72/2002
Low-rank approximation of integral operators by interpolation
Steffen Börm and Lars Grasedyck
Abstract
A central component of the analysis of panel clustering techniques forthe approximation of integral operators is the so-called $\eta$-admissibility condition $$min\{diam(\tau), diam(\sigma)\} \leq 2\eta dist(\tau,\sigma)$$ 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 the distance of such a subdomain to be "far enough" from the singularity such that the parameter $\eta$ has to be smaller than a given constant depending on properties of the kernel function.
In this paper, we demonstrate that any $\eta$ is sufficient if interpolation instead of Taylor expansion is used for the kernel approximation, which paves the way for grey-box panel clustering algorithms.
