Article
On Estimators for Eigenvalue/Eigenvector Approximations
Mathematics of Computation
(2009)
Abstract
We consider a large class of residuum based a posteriori eigenvalue/eigenvector estimates and present an abstract framework for proving their asymptotic exactness. Equivalence of the estimator and the error is also established. To demonstrate the strength of our abstract approach we present a detailed study of hierarchical error estimators for Laplace eigenvalue problems in planar polygonal regions. To this end we develop new error analysis for the Galerkin approximation which avoids the use of the strengthened Cauchy- Schwarz inequality and the saturation assumption, and gives reasonable and explicitly computable upper bounds on the discretization error. A brief discussion is also given concerning the design of estimators which are in the same spirit, but are based on different a posteriori techniques—notably, those of gradient recovery type.
Disciplines
Publication Date
2009
DOI
10.1090/S0025-5718-08-02181-9
Citation Information
Jeffrey S. Ovall. "On Estimators for Eigenvalue/Eigenvector Approximations" Mathematics of Computation (2009) Available at: http://works.bepress.com/jeffrey_ovall/40/