Abstract
Generalized eigenvalue problems involving a singular pencil are very challenging to solve, with respect to both accuracy and efficiency. The existing package Guptri is very elegant but may 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.
Original language | English |
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Pages (from-to) | 1022-1046 |
Number of pages | 25 |
Journal | SIAM Journal on Matrix Analysis and Applications |
Volume | 40 |
Issue number | 3 |
DOIs | |
Publication status | Published - 5 Sep 2019 |
Keywords
- Differential algebraic equations
- Double eigenvalues
- Guptri
- Model updating
- Quadratic two-parameter eigenvalue problem
- Rank-completing perturbation
- Singular generalized eigenvalue problem
- Singular pencil
- Two-parameter eigenvalue problem