Low-rank approximation of integral operators by interpolation

Steffen Börm, and Lars Grasedyck
(Please use for correspondence this email).

Submission date: 27. Aug. 2002
Pages: 9
published in: Computing, 72 (2004) 3-4, p. 325-332 
MSC-Numbers: 45B05, 65N45
Keywords and phrases: panel clustering, interpolation, admissibility
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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 eta-admissibility condition

min( diam(tau), diam(sigma) ) < 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.