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Publisher DOI: 10.1007/s00211-016-0804-3
Title: Restarting iterative projection methods for Hermitian nonlinear eigenvalue problems with minmax property
Language: English
Authors: Betcke, Marta 
Voß, Heinrich 
Keywords: Iterative projection method; Jacobi-Davidson method; minmax characterization; nonlinear Arnoldi method; nonlinear eigenvalue problem; restart; purge and lock
Issue Date: 14-May-2016
Publisher: Springer
Source: Numerische Mathematik 2 (135): 397-430 (2017)
Abstract (english): 
In this work we present a new restart technique for iterative projection methods for nonlinear eigenvalue problems admitting minmax characterization of their eigenvalues. Our technique makes use of the minmax induced local enumeration of the eigenvalues in the inner iteration. In contrast to global numbering which requires including all the previously computed eigenvectors in the search subspace, the proposed local numbering only requires a presence of one eigenvector in the search subspace. This effectively eliminates the search subspace growth and therewith the super-linear increase of the computational costs if a large number of eigenvalues or eigenvalues in the interior of the spectrum are to be computed. The new restart technique is integrated into nonlinear iterative projection methods like the Nonlinear Arnoldi and Jacobi-Davidson methods. The efficiency of our new restart framework is demonstrated on a range of nonlinear eigenvalue problems: quadratic, rational and exponential including an industrial real-life conservative gyroscopic eigenvalue problem modeling free vibrations of a rolling tire. We also present an extension of the method to problems without minmax property but with eigenvalues which have a dominant either real or imaginary part and test it on two quadratic eigenvalue problems.
DOI: 10.15480/882.1800
ISSN: 0945-3245
Journal: Numerische Mathematik 
Institute: Mathematik E-10 
Document Type: Article
More Funding information: EPSRC Postdoctoral Fellowship (Grant Number EP/H02865X/1)
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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