… In this paper, the term linearization means that the nonlinear QEP is transformed into a …
eigenvalue problem with the same eigenvalues. Our treatment of the large existing body of theory …

… for the computation of all the eigenvalues and optionally the right and left eigenvectors of
dense quadratic … It incorporates scaling of the problem parameters prior to the computation of …

… aid of a “pseudo-inner product,” attempted the construction of a nonlinear variational … say,
to the RayleighRitz method. The phenomenon of a quadratic eigenvalue problem having a …

… We consider the quadratic eigenvalue problem (QEP) (λ2M + … The eigenvalues of the QEP
occur in quadruplets (λ, λ, −λ, −λ… eigenvalues of the QEP can be found efficiently and with the …

… By applying the standard Rayleigh– Ritz orthogonal projection technique, we derive an …
a large-scale quadratic eigenvalue problem (QEP). This method is applied to the QEP directly. …

… the closest analog (among all kinds of quadratic eigenvalue problem) to the standard Hermitian
eigenvalue problem (among all kinds of standard eigenvalue problem). In this paper, we …

… which transforms the Lagrange equations into a quadratic eigenvalue problem. The two …
Subsequently we will compare the solutions of the quadratic eigenvalue problem (32) with …

… of the mode shapes (ie, the eigenvectors). Krylov methods for the solution of quadratic
eigenvalue problems … The quadratic eigenvalue problem and solution methods are reviewed by …

… the theory. Indeed we prove in Appendix A.1 that for the discretized beam problem half of the
eigenvalues … they coincide with half of the eigenvalues of the undamped quadratic 2M + K. …

… In this section, we consider the quadratic eigenvalue problem (QEP) of the form … numbers
for the quadratic eigenvalue problem, and more generally, the polynomial eigenvalue problem, …