The University of Arizona

Using the Spectral Projector for Eigenvalue/vector Approximation and Error Estimation

Using the Spectral Projector for Eigenvalue/vector Approximation and Error Estimation

Series: Mathematics Colloquium
Location: Math 501
Presenter: Jeffrey Ovall, Portland State University

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.)

Department of Mathematics, The University of Arizona 617 N. Santa Rita Ave. P.O. Box 210089 Tucson, AZ 85721-0089 USA Voice: (520) 621-6892 Fax: (520) 621-8322 Contact Us © Copyright 2017 Arizona Board of Regents All rights reserved