Voß, HeinrichHeinrichVoßMehrmann, VolkerVolkerMehrmann2005-12-142005-12-142004-01Preprint. Published in: GAMM Mitteilungen ; 27.2004, S.121-152http://tubdok.tub.tuhh.de/handle/11420/63We discuss the state of the art in numerical solution methods for large scale polynomial or rational eigenvalue problems. We present the currently available solution methods such as the Jacobi-Davidson, Arnoldi or the rational Krylov method and analyze their properties. We briefly introduce a new linearization technique and demonstrate how it can be used to improve structure preservation and with this the accuracy and efficiency of linearization based methods. We present several recent applications where structured and unstructured nonlinear eigenvalue problems arise and some numerical results.enhttp://rightsstatements.org/vocab/InC/1.0/matrix polynomialprojection methodKrylov-subspace methodArnoldi methodrational-Krylov methodlinearizationstructure preservationMathematikTechnical Report2005-12-19urn:nbn:de:gbv:830-opus-116710.15480/882.61Nichtlineares EigenwertproblemMatrizenpolynomProjektionsverfahrenKrylov-VerfahrenEigenvalues, singular values, and eigenvectorsEigenvalues, eigenvectors11420/6310.1002/gamm.20149000710.15480/882.61930768125Other