10.18453/rosdok_id00003125 Zhou, Ming Ming Zhou http://d-nb.info/gnd/1024105881 https://orcid.org/0000-0001-7096-1649 Universität Rostock 2020 510 Mathematics 2020 en http://purl.uni-rostock.de/rosdok/id00003125 urn:nbn:de:gbv:28-rosdok_id00003125-0 This thesis contributes to the convergence theory of Krylov subspace eigensolvers for discretized self-adjoint elliptic differential operators. A central topic refers to a priori convergence estimates with weak assumptions and concise bounds, which can reasonably predict the convergence rate, in particular for clustered eigenvalues. By avoiding the dependence on current approximate eigenvalues, such estimates significantly improve certain state-of-the-art estimates with regard to their sharpness and applicability.