Low-rank approximation of integral operators by interpolation
Steffen Börm and Lars Grasedyck
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Submission date: 27. Aug. 2002
published in: Computing, 72 (2004) 3/4, p. 325-332
DOI number (of the published article): 10.1007/s00607-003-0036-0
MSC-Numbers: 45B05, 65N45
Keywords and phrases: panel clustering, interpolation, admissibility
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A central component of the analysis of panel clustering techniques for
the approximation of integral operators is the so-called
min( diam(<b><i>tau</i></b>), diam(<b><i>sigma</i></b>) )
< 2 <b><i>eta</i></b> dist(<b><i>tau</i></b>, <b><i>sigma</i></b>)
that ensures that the kernel function
is approximated only on those parts of the domain that are far from
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
if interpolation instead of Taylor expansion is used for the kernel
approximation, which paves the way for grey-box panel clustering algorithms.