In this paper we investigate the least eigenvalue of a graph whose complement is connected, and present a lower bound for the least eigenvalue of such graph. We also characterize the unique graph whose least eigenvalue attains the second minimum among all graphs of fixed order.

We study local bifurcation from an eigenvalue with multiplicity greater than one for a class of semilinear elliptic equations. In particular, we obtain the exact number of bifurcation branches of non trivial solutions at every eigenvalue of a square and at the second eigenvalue of a cube. We also compute the Morse index of the solutions in those branches.

This paper concerns with the sensitivity analysis for the multivariate eigenvalue problem (MEP). The concept of a simple multivariate eigenvalue of a matrix is generalized to the MEP and the first-order perturbation expansions of a simple multivariate eigenvalue and the corresponding multivariate eigenvector are presented. The explicit expressions of condition numbers, perturbation upper bounds...

consider an n × n matrix polynomial p(λ). a spectral norm distance from p(λ) to the set of n × n matrix polynomials that havea given scalar µ ∈ c as a multiple eigenvalue was introducedand obtained by papathanasiou and psarrakos. they computedlower and upper bounds for this distance, constructing an associated perturbation of p(λ). in this paper, we extend this resultto the case of two given di...

BACKGROUND AND PURPOSE Diffusion tensor imaging may reflect pathology of the optic nerve; however, the ability of DTI to evaluate alterations of the optic nerve in retinitis pigmentosa has not yet been assessed, to our knowledge. The aim of this study was to investigate the diagnostic potential of reduced FOV-DTI in optic neuropathy of retinitis pigmentosa at 3T. MATERIALS AND METHODS Thirty-...

For the nonlinear eigenvalue problem T (λ)x = 0 we consider a Jacobi–Davidson type iterative projection method. The resulting projected nonlinear eigenvalue problems are solved by inverse iteration. The method is applied to a rational eigenvalue problem governing damped vibrations of a structure.

Let G be a connected simple graph. The relationship between the third smallest eigenvalue of the Laplacian matrix and the graph structure is explored. For a tree the complete description of the eigenvector corresponding to this eigenvalue is given and some results about the multiplicity of this eigenvalue are given.

We develop a model of regular, infinite hypertrees, to mimic for hypergraphs what infinite trees do for graphs. We then examine two notions of spectra or “first eigenvalue” for the infinite tree, obtaining a precise value for the first notion and obtaining some estimates for the second. The results indicate agreement of the first eigenvalue of the infinite hypertree with the “second eigenvalue”...

In this paper, we propose a palindromic quadratization approach, transforming a palindromic matrix polynomial of even degree to a palindromic quadratic pencil. Based on the (S + S−1)-transform and Patel’s algorithm, the structurepreserving algorithm can then be applied to solve the corresponding palindromic quadratic eigenvalue problem. Numerical experiments show that the relative residuals for...

In this paper, a parametric algorithm is introduced for computing all eigenvalues for two Eigenvalue Complementarity Problems discussed in the literature. The algorithm searches a finite number of nested intervals [ ?̄?, ?̄?] in such a way that, in each iteration, either an eigenvalue is computed in [?̄?, ?̄?] or a certificate of nonexistence of an eigenvalue in [ ?̄?, ?̄?] is provided. A hybrid meth...