A Jacobi–Davidson like method for nonlinear eigenvalue problems based on singularity theory
Kathrin Schreiber, Hubert Schwetlick · PAMM · 2007
Abstract We present a Jacobi–Davidson like correction formula for left and right eigenvector approximations for non‐Hermitian nonlinear eigenvalue problems. It exploits techniques from singularity theory for characterizing singular points of nonlinear equations. Unlike standard nonlinear Jacobi‐Davidson, the correction formula does not contain derivative information and works with orthogonal projectors only. Moreover, the basic method is modified in that the new eigenvalue approximation is taken as a nonlinear Rayleigh functional obtained as root of a certain scalar nonlinear equation the existence of which – as well as a first order perturbation expansion – is shown. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)