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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

Received:
Aug 27, 2002
Published:
Aug 27, 2002
MSC Codes:
45B05, 65N45
Keywords:
panel clustering, interpolation, admissibility

Related publications

inJournal
2004 Repository Open Access
Steffen Börm and Lars Grasedyck

Low-rank approximation of integral operators by interpolation

In: Computing, 72 (2004) 3/4, pp. 325-332