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  4. Rational Krylov for nonlinear eigenproblems, an iterative projection method
 
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Rational Krylov for nonlinear eigenproblems, an iterative projection method

Citation Link: https://doi.org/10.15480/882.136
Publikationstyp
Working Paper
Date Issued
2003-11
Sprache
English
Author(s)
Jarlebring, Elias  
Voß, Heinrich 
Institut
Mathematik E-10  
TORE-DOI
10.15480/882.136
TORE-URI
http://tubdok.tub.tuhh.de/handle/11420/138
First published in
Preprints des Institutes für Mathematik  
Number in series
69
In recent papers Ruhe [10], [12] suggested a rational Krylov method for nonlinear eigenproblems knitting together a secant method for linearizing the nonlinear problem and the Krylov method for the linearized problem. In this note we point out that the method can be understood as an iterative projection method. Similar to the Arnoldi method presented in [13], [14] the search space is expanded by the direction from residual inverse iteration. Numerical methods demonstrate that the rational Krylov method can be accelerated considerably by replacing an inner iteration by an explicit solver of projected problems.
Subjects
nonlinear eigenvalue problem
rational Krylov
Arnoldi
projection method
DDC Class
510: Mathematik
Lizenz
http://rightsstatements.org/vocab/InC/1.0/
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