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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:TALK214975AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/214975
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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