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Computing interior eigenvalues of nonlinear Hermitean eigenvalue problems

Betcke, MM; Lochmann, V; Voss, H; (2007) Computing interior eigenvalues of nonlinear Hermitean eigenvalue problems. (Technical Report Institut fuer Numerische Simulation, Hamburg University of Technology, Ham- burg, Germany 113 , pp. ? - ? ). : Institut fuer Numerische Simulation, Hamburg University of Technology, Ham- burg, Germany.

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Abstract

A nonlinear eigenvalue problem T (λ)x = 0, the eigenvalues of which satisfy a minmax characterization shares many valuable properties of linear Hermitean eigenvalue problems. For instance, its eigenvalues can be computed safely one after another by means of iterative projection methods, where the projected problems are solved by the safeguarded iteration. Though, such methods hit their limitations if a large number of eigenvalues possibly in the interior of the spectrum is required. In this paper we propose a localized version of safeguarded iteration which overcomes the problem of growing search subspace dimension by means of a local numbering of the eigenvalues. The efficiency of the new method is demonstrated on a real-life gyroscopic eigenvalue problem modeling free vibrations of a rolling tire.

Type:Report
Title:Computing interior eigenvalues of nonlinear Hermitean eigenvalue problems
Keywords:nonlinear eigenvalue problem, iterative projection method, Arnoldi method, minmax characterization, local restart
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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