We consider the quadratic eigenvalues problem (QEP) of gyroscopic systems ðlMþ lGþ KÞx 1⁄4 0, where M 1⁄4 M>;G 1⁄4 G> and K 1⁄4 K> 2 R n with M being positive definite. Guo [Numerical solution of a quadratic eigenvalue problem, Linear Algebra and its Applications 385 (2004) 391–406] showed that all eigenvalues of the QEP can be found by solving the maximal solution of a nonlinear matrix equatio...

We provide Completely Positive and Copositive Optimization formulations for the Constrained Fractional Quadratic Problem (CFQP) and Standard Fractional Quadratic Problem (StFQP). Based on these formulations, Semidefinite Programming (SDP) relaxations are derived for finding good lower bounds to these fractional programs, which can be used in a global optimization branch-and-bound approach. Appl...

We present two methods for calculating resonant frequencies and mode shapes for fluid-structure vibration problems. We model the fluid-structure interaction problem using the #-V-P, finite element technique. This eigenproblem is more complicated than for ordinary structural analyses, as the formulation produces a quadratic eigenproblem (similar to those for gyroscopic systems). We derive proper...

Updating a model framed as a real symmetric quadratic eigenvalue problem to match observed spectral information has been a powerful tool for practitioners in different discipline areas. It is often desirable in updating to match only the part of newly measured data without tampering with the other part of unmeasured and often unknown eigenstructure inhering in the original model. Such an updati...

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 subspac...

1 This paper extends the theory of trust region subproblems in two ways: (i) it allows indeenite inner products in the quadratic constraint and (ii) it uses a two sided (upper and lower bound) quadratic constraint. Characterizations of optimality are presented, which have no gap between necessity and suuciency. Conditions for the existence of solutions are given in terms of the deeniteness of a...