in this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. furthermore, we obtain the zeros of eigenfunctions.

for a simple digraph $g$ of order $n$ with vertex set${v_1,v_2,ldots, v_n}$, let $d_i^+$ and $d_i^-$ denote theout-degree and in-degree of a vertex $v_i$ in $g$, respectively. let$d^+(g)=diag(d_1^+,d_2^+,ldots,d_n^+)$ and$d^-(g)=diag(d_1^-,d_2^-,ldots,d_n^-)$. in this paper we introduce$widetilde{sl}(g)=widetilde{d}(g)-s(g)$ to be a new kind of skewlaplacian matrix of $g$, where $widetilde{d}(g...

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...

In this paper, we investigate connected nonregular graphs with four distinct Laplacian eigenvalues. We characterize all such graphs which are bipartite or have exactly one multiple Laplacian eigenvalue. Other examples of interest are also presented.

Quantum–mechanical multiple–well oscillators exhibit curious complex eigenvalues that resemble resonances in models with continuum spectra. We discuss a method for the accurate calculation of their real and imaginary parts.

Motivated by applications in matrix constructions used the inverse eigenvalue problem for graphs, we study a concept of genericity eigenvectors associated with given spectrum and connected graph. This generalizes established notion nowhere-zero eigenbasis. Given any simple graph G on n vertices no multiple eigenvalues, show that family eigenbases symmetric matrices this is generic, strengthenin...

This paper presents a parallel algorithm to solve the eigenvalue problem for non-symmetric matrices. The idea of homotopy is used to generate initial approximations, then the Aberth method and our modiied Aberth method are used to nd simultaneously all the eigenvalues. The advantage of this approach is that multiple eigenvalues can be handled. In addition, the multiplicities of the eigenvalues ...