On global convergence of subspace projection methods for Hermitian eigenvalue problems

Abstract

We provide a concise overview of some iterative approaches, by which large and sparse eigenvalue problems are successfully dealt with. Our main goal in this paper is to prove the global convergence of a few state-of-the art iteration methods, such as the Jacobi–Davidson, the rational Krylov sequence and the Lanczos methods. We also derive some conditions to ensure global convergence of the corresponding inexact variants of the above-mentioned methods. These global convergence analyses result either in a depth understanding or in an efficient improvement to the original methods.