- AutorIn
- Peter Benner
- Cedric Effenberger
- Titel
- A rational SHIRA method for the Hamiltonian eigenvalue problem
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:ch1-200900026
- Schriftenreihe
- Chemnitz Scientific Computing Preprints
- Bandnummer
- 08-08
- ISSN
- 1864-0087
- Abstract (EN)
- The SHIRA method of Mehrmann and Watkins belongs among the structure preserving Krylov subspace methods for solving skew-Hamiltonian eigenvalue problems. It can also be applied to Hamiltonian eigenproblems by considering a suitable transformation. Structure induced shift-and-invert techniques are employed to steer the algorithm towards the interesting region of the spectrum. However, the shift cannot be altered in the middle of the computation without discarding the information that has been accumulated so far. This paper shows how SHIRA can be combined with ideas from Ruhe's Rational Krylov algorithm to yield a method that permits an adjustment of shift after every step of the computation, adding greatly to the flexibility of the algorithm. We call this new method rational SHIRA. A numerical example is presented to demonstrate its efficiency.
- Andere Ausgabe
- Link: http://www.tu-chemnitz.de/mathematik/csc/preprints.php
- Freie Schlagwörter
- Hamiltonian matrix
- eigenvalue problem
- rational Krylov subspace method
- shift-and-invert Arnoldi
- skew-Hamiltonian matrix
- Klassifikation (DDC)
- 510
- Normschlagwörter (GND)
- Eigenwertproblem
- Publizierende Institution
- Technische Universität Chemnitz, Chemnitz
- URN Qucosa
- urn:nbn:de:bsz:ch1-200900026
- Veröffentlichungsdatum Qucosa
- 07.01.2009
- Dokumenttyp
- Preprint
- Sprache des Dokumentes
- Englisch