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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:To infinity and beyond! Numerical linear algebra i
n infinite dimensions - Sheehan Olver (Imperial Co
llege London)
DTSTART;TZID=Europe/London:20240704T140000
DTEND;TZID=Europe/London:20240704T143000
UID:TALK214948AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/214948
DESCRIPTION:A classic application of Wiener&ndash\;Hopf is the
computation of the UL factorisation of Toeplitz o
perators. I'll review numerical approaches to comp
uting this factorisation\, both based on the Wiene
r&ndash\;Hopf representation and based on a simple
numerical linear algebra interpretation\, leading
to numerical techniques that also work for finite
-dimensional perturbations of Toeplitz operators.
Going beyond this classical setting are the (infin
ite) QR and QL factorisations\, the latter having
the same feature as the UL factorisation that one
needs to kick off the factorisation from the botto
m-right of the matrix\, which in this case is at i
nfinity! Extensions to block Toeplitz operators an
d their perturbation will further be discussed.\nA
pplications include exploring the continuous spect
rum of Toeplitz operators\, computing orthogonal p
olynomials\, and topological insulators with defec
ts.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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