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DTSTART:19700329T010000
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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Computing spectral measures of differential and in
tegral operators - Andrew Horning (Cornell Univers
ity)
DTSTART;TZID=Europe/London:20191210T140000
DTEND;TZID=Europe/London:20191210T143000
UID:TALK135520AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/135520
DESCRIPTION:Unlike its matrix counterpart\, the spectral measu
re of a self-adjoint operator may have an absolute
ly continuous component and an associated density
function\, e.g.\, in applications posed on unbound
ed domains. The state-of-the-art computational met
hods for these problems typically approximate the
density function using a smoothed sum of Dirac mea
sures\, corresponding to the spectral measure of a
matrix discretization of the operator. However\,
it is often difficult to determine the smoothing a
nd discretization parameters that are necessary to
accurately and efficiently resolve the density fu
nction. In this talk\, we present an adaptive fram
ework for computing the spectral measure of a self
-adjoint operator that provides insight into the s
election of smoothing and discretization parameter
s. We show how to construct local approximations t
o the density that converge rapidly when the densi
ty function is smooth and discuss possible connect
ions with Pade approximation that could alleviate
deteriorating convergence rates near non-smooth po
ints.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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