Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization

Details Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization

2007-08-03

arxiv.org/abs/0708.0517v2

Mathematics

Numerical Analysis

submitted to Adv. Comp. Math

Scientific paper

In this paper we discuss an abstract iteration scheme for the calculation of the smallest eigenvalue of an elliptic operator eigenvalue problem. A short and geometric proof based on the preconditioned inverse iteration (PINVIT) for matrices [Knyazev and Neymeyr, (2009)] is extended to the case of operators. We show that convergence is retained up to any tolerance if one only uses approximate applications of operators which leads to the perturbed preconditioned inverse iteration (PPINVIT). We then analyze the Besov regularity of the eigenfunctions of the Poisson eigenvalue problem on a polygonal domain, showing the advantage of an adaptive solver to uniform refinement when using a stable wavelet base. A numerical example for PPINVIT, applied to the model problem on the L-shaped domain, is shown to reproduce the predicted behaviour.

Affiliated with

Also associated with

No associations

Rating

Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-602132