Preprint 3-2018

Solving singular generalized eigenvalue problems by a rank-completing perturbation

Author(s) : Michiel Hochstenbach, Christian Mehl , Bor Plestenjak

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 3-2018

MSC 2000

15A18 Eigenvalues, singular values, and eigenvectors

65F15 Eigenvalues, eigenvectors

Abstract :
Generalized eigenvalue problems involving a singular pencil are very challenging to solve, both with respect to accuracy and eciency. 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 specic rank. For many problems, the method is both fast and robust. This approach may be seen as a welcome alternative to staircase methods.

Keywords : Singular pencil, singular generalized eigenvalue problem, rank-completing perturbation, Guptri, model updating, double eigenvalues, two-parameter eigenvalue problem, dierential algebraic equations, quadratic two-parameter eigenvalue problem