Nonlinear Eigenvalue Problems: A Challenge for Modern Eigenvalue Methods

Publikationstyp
Technical Report
Publikationsdatum
2004-01
Sprache
English
Author
Voß, Heinrich 
Mehrmann, Volker 
Institut
Mathematik E-10 
DOI
10.15480/882.61
TORE-URI
http://tubdok.tub.tuhh.de/handle/11420/63
Lizenz
http://rightsstatements.org/vocab/InC/1.0/
First published in
Preprints des Institutes für Mathematik 
Preprints des Institutes für Mathematik;Bericht 83
Number in series
83
Citation
Preprint. Published in: GAMM Mitteilungen ; 27.2004, S.121-152
Publisher DOI
10.1002/gamm.201490007
We discuss the state of the art in numerical solution methods for large scale polynomial or rational eigenvalue problems. We present the currently available solution methods such as the Jacobi-Davidson, Arnoldi or the rational Krylov method and analyze their properties. We briefly introduce a new linearization technique and demonstrate how it can be used to improve structure preservation and with this the accuracy and efficiency of linearization based methods. We present several recent applications where structured and unstructured nonlinear eigenvalue problems arise and some numerical results.
Schlagworte
matrix polynomial
projection method
Krylov-subspace method
Arnoldi method
rational-Krylov method
linearization
structure preservation
DDC Class
510: Mathematik