On the convergence of an inverse iteration method for nonlinear elliptic eigenvalue problems

Abstract

In recent years, a group of inverse iteration type algorithms have been developed for solving nonlinear elliptic eigenvalue problems in plasma physics [4]. Although these algorithms have been very successful in practice, no satisfactory theoretical justification of convergence has been available. The present paper fills this gap and proves for a large class of such problems and a simple version of such algorithms that linear convergence to a local maximum of a certain potential is obtained.