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...

Large-scale eigenvalue problems arise in a number of DOE applications. This paper provides an ovcrvicw of thc recent dcvclopriicrit of cigciivaluc computation in the coritcxt of two SciDAC applications. We emphasize the importance of Krylov suhspace methods, and point out its limitations. M7e discuss the value of alternative approaches that are more amenable to the use of prcconditioncrs, arid ...

In this paper, a type of multi-level correction scheme is proposed to solve eigenvalue problems by the nonconforming finite element method. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which only needs to solve a source problem on finer finite element space and an eigenvalue problem on the coarsest finite element space. This correctio...

This is a survey paper on the recent development of the spectral theory of nonnegative tensors and its applications. After a brief review of the basic definitions on tensors, the H eigenvalue problem and the Z eigenvalue problem for tensors are studied separately. To the H eigenvalue problem for nonnegative tensors, the whole Perron-Frobenius theory for nonnegative matrices is completely extend...