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SUMMARY:Infinite-dimensional linear algebra and spectral problems - Imperi
 al College
DTSTART:20180502T130000Z
DTEND:20180502T140000Z
UID:TALK105628@talks.cam.ac.uk
CONTACT:Dr Hansen
DESCRIPTION:We give an overview of numerical linear algebra applied direct
 ly to infinite-dimensional operators – as opposed to finite-dimensional 
 linear algebra applied to discretizations – which is made possible by ex
 ploiting structure in the operators\, e.g.\, operators that are perturbati
 ons of Toeplitz operators. Algorithms discussed include the adaptive QR de
 composition\, infinite QR algorithm and infinite QL algorithm. These metho
 ds allow for the systematic solution of equations\, calculation of continu
 ous and discrete spectrum\, and spectral measures. The benefit over the tr
 aditional discretize-and-solve approach is that the algorithm is rigorous 
 (in applications\, this translates to reliability)\, fast and extremely ac
 curate. Having a hands-on representation of the spectral transformation al
 lows for a robust implementation of functional calculus\, used for example
  to solve the time-dependent Schrodinger equation.
LOCATION:MR 5
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