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SUMMARY:To infinity and beyond! Numerical linear algebra in infinite dimen
 sions - Sheehan Olver (Imperial College London)
DTSTART:20240704T130000Z
DTEND:20240704T133000Z
UID:TALK214948@talks.cam.ac.uk
DESCRIPTION:A classic application of Wiener&ndash\;Hopf is the computation
  of the UL factorisation of Toeplitz operators. I'll review numerical appr
 oaches to computing this factorisation\, both based on the Wiener&ndash\;H
 opf representation and based on a simple numerical linear algebra interpre
 tation\, leading to numerical techniques that also work for finite-dimensi
 onal perturbations of Toeplitz operators. Going beyond this classical sett
 ing are the (infinite) QR and QL factorisations\, the latter having the sa
 me feature as the UL factorisation that one needs to kick off the factoris
 ation from the bottom-right of the matrix\, which in this case is at infin
 ity! Extensions to block Toeplitz operators and their perturbation will fu
 rther be discussed.\nApplications include exploring the continuous spectru
 m of Toeplitz operators\, computing orthogonal polynomials\, and topologic
 al insulators with defects.
LOCATION:Seminar Room 1\, Newton Institute
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