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SUMMARY:Computing the Spectrum in One\, Two and Three Limits - Ben Jenning
 s (CCA)
DTSTART:20150211T160000Z
DTEND:20150211T170000Z
UID:TALK57701@talks.cam.ac.uk
CONTACT:Davide Piazzoli
DESCRIPTION:Computing the eigenvalues of a matrix is a classic computation
 al problem with obvious practical relevance. While calculating the eigenva
 lues of matrices has long had a solution\, it is not without its complexit
 ies. We take these complexities as our starting point. Generalizing\, we c
 onsider the Finite Section (Ritz) method for calculating the spectrum of a
 n operator defined on Hilbert space. While this can provide a practical me
 thod for bounded self-adjoint operators\, the computation introduces spect
 ral pollution for some operators of physical significance. After introduci
 ng the notions of the Solvability Complexity Index (SCI) and Towers of Alg
 orithms\, we construct an algorithm that recovers the spectrum for any bou
 nded operator on $l^2(\\mathbb{N})$.
LOCATION:MR14\, Centre for Mathematical Sciences
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