MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

A framework for robust eigenvalue and eigenvector error estimation and Ritz value convergence enhancement

Luka Grubišić, Jeffrey Ovall and Randolph Bank


We present a general framework for the a posteriori estimation and enhancement of error in eigenvalue/eigenvector computations for symmetric and elliptic eigenvalue problems, and provide detailed analysis of a specific and important example within this framework---finite element methods with continuous, affine elements. A distinguishing feature of the proposed approach is that it provides provably efficient and reliable error estimation under very realistic assumptions, not only for single, simple eigenvalues, but also for clusters which may contain degenerate eigenvalues. We reduce the study of the eigenvalue/eigenvector error estimators to the study of associated boundary value problems, and make use of the wealth of knowledge available for such problems. Our choice of a posteriori error estimator, computed using hierarchical bases, very naturally offers a means not only for estimating error in eigenvalue/eigenvector computations, but also cheaply accelerating the convergence of these computations---sometimes with convergence rates which are nearly twice that of the unaccelerated approximations.

Aug 5, 2010
Aug 5, 2010
MSC Codes:
65N30, 65N25, 65N15

Related publications

2013 Repository Open Access
Luka Grubisic, Jeffrey S. Ovall and Randolph E. Bank

A framework for robust eigenvalue and eigenvector error estimation and Ritz value convergence enhancement

In: Applied numerical mathematics, 66 (2013), pp. 1-29