Hochstenbach, MichielMehl, ChristianPlestenjak, Bor2021-12-172021-12-172018-05-222197-8085https://depositonce.tu-berlin.de/handle/11303/15909http://dx.doi.org/10.14279/depositonce-14682Generalized eigenvalue problems involving a singular pencil are very challenging to solve, both with respect to accuracy and efficiency. The existing package Guptri is very elegant but may sometimes be time-demanding, even for small and medium-sized matrices. We propose a simple method to compute the eigenvalues of singular pencils, based on one perturbation of the original problem of a certain specific rank. For many problems, the method is both fast and robust. This approach may be seen as a welcome alternative to staircase methods.en510 Mathematiksingular pencilsingular generalized eigenvalue problemrank-completing perturbationGuptrimodel updatingdouble eigenvaluestwo-parameter eigenvalue problemdifferential algebraic equationsquadratic two-parameter eigenvalue problemResearch Paper