Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems

Beyn W-J, Effenberger C, Kressner D (2011)
Numerische Mathematik 119(3): 489-516.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Beyn, Wolf-JürgenUniBi; Effenberger, Cedric; Kressner, Daniel
Abstract / Bemerkung
Invariant pairs have been proposed as a numerically robust means to represent and compute several eigenvalues along with the corresponding (generalized) eigenvectors for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In this work, we consider nonlinear eigenvalue problems that depend on an additional parameter and our interest is to track several eigenvalues as this parameter varies. Based on the concept of invariant pairs, a theoretically sound and reliable numerical continuation procedure is developed. Particular attention is paid to the situation-when the procedure approaches a singularity, that is, when eigenvalues included in the invariant pair collide with other eigenvalues. For the real generic case, it is proven that such a singularity only occurs when two eigenvalues collide on the real axis. It is shown how this situation can be handled numerically by an appropriate expansion of the invariant pair. The viability of our continuation procedure is illustrated by a numerical example.
Erscheinungsjahr
2011
Zeitschriftentitel
Numerische Mathematik
Band
119
Ausgabe
3
Seite(n)
489-516
ISSN
0029-599X
Page URI
https://pub.uni-bielefeld.de/record/2454800

Zitieren

Beyn W-J, Effenberger C, Kressner D. Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems. Numerische Mathematik. 2011;119(3):489-516.
Beyn, W. - J., Effenberger, C., & Kressner, D. (2011). Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems. Numerische Mathematik, 119(3), 489-516. doi:10.1007/s00211-011-0392-1
Beyn, W. - J., Effenberger, C., and Kressner, D. (2011). Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems. Numerische Mathematik 119, 489-516.
Beyn, W.-J., Effenberger, C., & Kressner, D., 2011. Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems. Numerische Mathematik, 119(3), p 489-516.
W.-J. Beyn, C. Effenberger, and D. Kressner, “Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems”, Numerische Mathematik, vol. 119, 2011, pp. 489-516.
Beyn, W.-J., Effenberger, C., Kressner, D.: Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems. Numerische Mathematik. 119, 489-516 (2011).
Beyn, Wolf-Jürgen, Effenberger, Cedric, and Kressner, Daniel. “Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems”. Numerische Mathematik 119.3 (2011): 489-516.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Suchen in

Google Scholar