by: Professor Michael Levitin (University of Cardiff).
Approximating (or finding numerically) eigenvalues of a self-adjoint operator in the gaps of the essential spectrum is a non-trivial task, as there are no ready-made variational methods.
Standard projection techniques may often lead to appearance of spurious eigenvalues - such an effect is known as spectral pollution. I will present a new abstract scheme which does not pollute, illustrate its effectiveness by considering some simple (and less simple) examples, and will discuss some unexpected related phenomena in the theory of Toeplitz matrices.
1.15 p.m. 21st January 2008
Venue: BICS seminar room. (1W 3.6, University of Bath).