Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization (Q618775)

The paper is concerned with the study of an abstract iteration scheme for calculation of the smallest eigenvalue of an elliptic operator eigenvalue problem. The main goal of the authors is to prove the convergence of a perturbed preconditioned inverse iteration for solving operator eigenvalue problems and to apply the abstract iteration to wavelet discretization for to analyze the Besov regularity of the eigenfunctions of the Poisson eigenvalue problem on a polygonal domain. A numerical example is applied to the case of a planar Poisson eigenvalue problem, calculating the eigenfunctions and providing numerical results for the L-shaped domain.