A number of authors have recently suggested solving quasi birth-and-death (QBD) processes through the use of eigenvalue-based methods. These methods take on a special form when there are multiple eigenvalues present. We investigate this problem in a general setting as well as in the context of a specific preemptive priority queueing model.

The eigenvalues of the monodromy matrix, known as Floquet characteristic multipliers, are used to study the local stability of periodic motions of a nonlinear system of differential-algebraic equations (DAE). When the size of the underlying system is large, the cost of computing the monodromy matrix and its eigenvalues may be too high. In addition, for non-minimal set equations, such as those o...

We study the sensitivity of algebraic eigenvalue problems associated with matrices arising from linearization and discretization of the steady-state Navier-Stokes equations. In particular, for several choices of preconditioners applied to the system of discrete equations, we derive upper bounds on perturbations of eigenvalues as functions of the viscosity and discretization mesh size. The bound...

Determination of the eigenvalues and eigenvectors of a matrix is important in many areas of science, for example in web ranking [8, 15], computer graphics and visualization [24], quantum mechanics [5], statistics [12, 20], medicine, communications, construction vibration analysis [3, 23]. One of the most important numerical methods designed to calculate the eigenvalues and eigenvectors of matri...

We consider the existence of localized modes corresponding to eigenvalues of the periodic Schrödinger operator −∂ x + V (x) with an interface. The interface is modeled by a jump either in the value or the derivative of V (x) and, in general, does not correspond to a localized perturbation of the perfectly periodic operator. The periodic potentials on each side of the interface can, moreover, be...