In this paper, we derive new relative perturbation bounds for eigenvectors and eigenvalues regular quadratic eigenvalue problems of the form $\lambda^2 M x + \lambda C K = 0$, where $M$ $K$ are nonsingular Hermitian matrices $C$ is a general matrix. We base our findings on results an equivalent matrix pair $A-\lambda B$. The can be applied to many interesting appearing in applications, such as ...

The detailed spectral structure of symmetric, algebraic, quadratic eigenvalue problems has been developed recently. In this paper we take advantage of these canonical forms to provide a detailed analysis of inverse problems of the form: construct the coefficient matrices from the spectral data including the classical eigenvalue/eigenvector data and sign characteristics for the real eigenvalues....

Bounds on the optimal value of a convex 0-1 quadratic programming problem with linear constraints can be improved by a preprocessing step that adds to the quadratic objective function terms which are equal to 0 for all 0-1 feasible solutions yet increase its continuous minimum. The continuous and the CHR bounds are improved if one first uses Plateau’s QCR method (2005), or one of its predecesso...

Given a graph and a vector defined on the graph, a quadratic form is defined on the graph depending on its edges. In order to minimize the quadratic form on trees or unicyclic graphs associated with signless Laplacian, the notion of basic edge set of a graph is introduced, and the behavior of the least eigenvalue and the corresponding eigenvectors is investigated. Using these results a characte...