Eigenvalues of the Lamé operator are studied as complex-analytic functions in period τ of an elliptic function. We investigate the branching of eigenvalues numerically and clarify the relationship between the branching of eigenvalues and the convergent radius of a perturbation series.

Inequalities which bound the closed-loop eigenvalues in an LQ-optimal system are presented. It is shown that the eigenvalues are bounded by two half circles with radii r1 and r2 and center at 0, where = 0 is the imaginary axis, and that the imaginary parts of these eigenvalues are bounded from up and below by two lines parallel to the real axis.

The classical perturbation theory for Hermitian matrix eigenvalue and singular value problems provides bounds on the absolute differences between approximate eigenvalues (singular values) and the true eigenvalues (singular values) of a matrix. These bounds may be bad news for small eigenvalues (singular values), which thereby suffer worse relative uncertainty than large ones. However, there are...

Left-definite regular self-adjoint Sturm-Liouville problems with separated and coupled boundary conditions are studied. A characterization is given in terms of right-definite problems, a concrete and “natural” indexing scheme for the eigenvalues is proposed. Pruefer transformation techniques can be used to establish the existence of and to give a characterization for the eigenvalues in the case...

The eigenvalues of the kernel matrix play an important role in a number of kernel methods, in particular, in kernel principal component analysis. It is well known that the eigenvalues of the kernel matrix converge as the number of samples tends to infinity. We derive probabilistic finite sample size bounds on the approximation error of individual eigenvalues which have the important property th...

We consider three dimensional lossless periodic dielectric (photonic crystals) and acoustic media having a gap in the spectrum. If such a periodic medium is perturbed by a strong enough defect, defect eigenmodes arise, localized exponentially around the defect, with the corresponding eigenvalues in the gap. We use a modified Birman-Schwinger method to derive equations for these eigenmodes and c...

The stability study of a multi-phase (six-phase) induction machine has been performed by applying the eigenvalues stability criterion to the small displacement equations obtained by linearization about an operating point. The eigenvalues provide a simple means of predicting the behavior of an induction machine at any balanced operating condition. The eigenvalues are dependent upon the parameter...

A truncation of a Haar distributed orthogonal random matrix gives rise to a matrix whose eigenvalues are either real or complex conjugate pairs, and are supported within the closed unit disk. This is also true for a product Pm of m independent truncated orthogonal random matrices. One of most basic questions for such asymmetric matrices is to ask for the number of real eigenvalues. In this pape...

In this paper, we present a theory for bounding the minimum eigenvalues, maximum eigenvalues, and condition numbers of stiffness matrices arising from the p-version of finite element analysis. Bounds are derived for the eigenvalues and the condition numbers, which are valid for stiffness matrices based on a set of general basis functions that can be used in the p-version. For a set of hierarchi...

A procedure is described for computing range and orientation invariant spectral signatures of buried unexploded ordnance (UXO) from electromagnetic induction (EMI) data. The normalized eigenvalues of the magnetic polarizability tensor that characterizes the target response are used as the orientation-invariant spectral signatures. It is shown that the eigenvalues can be normalized with respect ...