In this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. Some examples are provided to show the accuracy and reliability of the proposed method. It is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to th...

We study the problem of localization in a disordered one-dimensional nonlinear medium modeled by the nonlinear Schr6dinger equation. Devillard and SouiUard have shown that almost every time-harmonic solution of this random PDE exhibits localization. We consider the temporal stability of such timeharmonic solutions and derive bounds on the location of any unstable eigenvalues. By direct numerica...

This note aims to give prominence some new results on the absence and localization of eigenvalues for Dirac Klein-Gordon operators, starting from known resolvent estimates already established in literature combined with renowned Birman-Schwinger principle.

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

the analysis of cross-correlations is extensively applied for understanding of interconnections in stock markets. variety of methods are used in order to search stock cross-correlations including the random matrix theory (rmt), the principal component analysis (pca) and the hierachical ‎structures.‎ in ‎this work‎, we analyze cross-crrelations between price fluctuations of 20 ‎company ‎stocks‎‎...

An extra-stabilized Morley finite element method (FEM) directly computes guaranteed lower eigenvalue bounds with optimal a priori convergence rates for the bi-Laplacian Dirichlet eigenvalues. The smallness assumption in 2D (resp., 3D) on maximal mesh-size makes computed th discrete bound . This holds multiple and clusters of eigenvalues serves localization eigenvalues, particular coarse meshes....

In this paper we study the eigenvalues of laplacian matrices cyclic graphs with one edge weight α and others 1. We denote by n order graph suppose that tends to infinity. notice characteristic polynomial depend only on Re(α). After that, through rest 0<α<1. It is easy see belong [0,4] are asymptotically distributed as function g(x)=4sin2⁡(x/2) [0,π]. obtain a series results about individual beh...

We consider the Anderson model at large disorder on $${\mathbb {Z}}^2$$ where potential has a symmetric Bernoulli distribution. prove that localization happens outside small neighborhood of finitely many energies. These energies are Dirichlet eigenvalues minus Laplacian restricted some finite subsets {Z}}^{2}$$ .

We present a method for calculating some select eigenvalues and corresponding eigenvectors of a given Hamiltonian. We show that it is possible to target the eigenvalues and eigenvectors of interest without diagonalizing the full Hamiltonian, by using any arbitrary physical property of the eigenvectors. This allows us to target, for example, the eigenvectors based on their localization propertie...

We give a simple, transparent, and intuitive proof that all eigenvalues of the Anderson model in the region of localization are simple. The Anderson tight binding model is given by the random Hamiltonian Hω = −∆ + Vω on 2(Z), where ∆(x, y) = 1 if |x − y| = 1 and zero otherwise, and the random potential Vω = {Vω(x), x ∈ Zd} consists of independent identically distributed random variables whose c...