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Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods
Author(s) -
Mehrmann Volker,
Voss Heinrich
Publication year - 2005
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201490007
Subject(s) - eigenvalues and eigenvectors , linearization , nonlinear system , arnoldi iteration , mathematics , divide and conquer eigenvalue algorithm , polynomial , scale (ratio) , computer science , mathematical optimization , preconditioner , iterative method , mathematical analysis , physics , quantum mechanics
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. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)