Using the Spectral Projector for Eigenvalue/vector Approximation and Error Estimation
The spectral projector of a second-order differential operator, formally given as A =-∇ • A∇u + b•∇u + cu, is defined in terms of the (operator-valued) Dunford-Cauchy integral,
S= ∫Γ (z-A)-1dz,
where Γ ⊂ C is a contour enclosing some portion of its spectrum. We discuss how this projector can be used to approximate eigenvalues enclosed by Γ, as well as their corresponding invariant subspaces, via a "filtered" subspace iteration procedure. We also show how computable error estimates may be derived for eigenvalue and eigenvector approximations, regardless of how they are obtained.
(Tea served in First Floor Commons Room at 3:30pm.)