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SUMMARY:Computing spectral measures of differential and integral operators
  - Andrew Horning (Cornell University)
DTSTART:20191210T140000Z
DTEND:20191210T143000Z
UID:TALK135520@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Unlike its matrix counterpart\, the spectral measure of a self
 -adjoint operator may have an absolutely continuous component and an assoc
 iated density function\, e.g.\, in applications posed on unbounded domains
 . The state-of-the-art computational methods for these problems typically 
 approximate the density function using a smoothed sum of Dirac measures\, 
 corresponding to the spectral measure of a matrix discretization of the op
 erator. However\, it is often difficult to determine the smoothing and dis
 cretization parameters that are necessary to accurately and efficiently re
 solve the density function. In this talk\, we present an adaptive framewor
 k for computing the spectral measure of a self-adjoint operator that provi
 des insight into the selection of smoothing and discretization parameters.
  We show how to construct local approximations to the density that converg
 e rapidly when the density function is smooth and discuss possible connect
 ions with Pade approximation that could alleviate deteriorating convergenc
 e rates near non-smooth points.
LOCATION:Seminar Room 1\, Newton Institute
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