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The Rayleigh quotient iteration for quadratic eigenvalue problems
Author(s) -
Miller Urs,
Gaul Lothar
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110157
Subject(s) - rayleigh quotient iteration , rayleigh quotient , eigenvalues and eigenvectors , mathematics , quotient , quadratic equation , perturbation (astronomy) , convergence (economics) , inverse iteration , mathematical analysis , generalization , pure mathematics , physics , geometry , quantum mechanics , economics , economic growth
For the direct solution of quadratic eigenvalue problems of the form (λ 2 M + P + Q ) x = 0 , a generalization of the Rayleigh quotient iteration is presented. Numerical simulations show good convergence for problems where the eigenvalues have nonzero imaginary part. The method is used to calculate eigenvalue paths of parameter dependent problems in structural dynamics. Bifurcations with double eigenvalues, which can occur in the path, are passed by using a perturbation of the velocity dependent matrix P . (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)