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Nonlinear Eigenvalue Problems: A Challenge for Modern Eigenvalue Methods
Citation Link: https://doi.org/10.15480/882.61
Publikationstyp
Technical Report
Date Issued
2004-01
Sprache
English
Author(s)
Voß, Heinrich
Institut
TORE-DOI
First published in
Number in series
83
Citation
Preprints des Institutes für Mathematik 83: (2004)
Publisher DOI
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.
Subjects
matrix polynomial
projection method
Krylov-subspace method
Arnoldi method
rational-Krylov method
linearization
structure preservation
DDC Class
510: Mathematik
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