The Rayleigh quotient iteration for quadratic eigenvalue problems
Urs Miller, Lothar Gaul · PAMM · 2011
Abstract For the direct solution of quadratic eigenvalue problems of the form(λ2M+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 matrixP. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)