نتایج جستجو برای: largest eigenvalue

تعداد نتایج: 109243  

Journal: :Linear Algebra and its Applications 2021

Let $G$ be a connected graph and let $T$ spanning tree of $G$. A partial orientation $\sigma$ respect to is an the edges except those $T$, resulting associated with which denoted by $G_T^\sigma$. In this paper we prove that there exists such largest eigenvalue Hermitian adjacency matrix $G_T^\sigma$ at most absolute value roots matching polynomial

Journal: :IET Communications 2012
Jacobus D. Vlok Jan C. Olivier

Eigenvalue distributions of Wishart matrices are given in the literature as functions or distributions defined in terms of matrix arguments requiring numerical evaluation. As a result the relationship between parameter values and statistics is not available analytically and the complexity of the numerical evaluation involved may limit the implementation, evaluation and use of eigenvalue techniq...

Let $D$ be a diameter and $d_G(v_i, v_j)$ be the distance between the vertices $v_i$ and $v_j$ of a connected graph $G$. The complementary distance signless Laplacian matrix of a graph $G$ is $CDL^+(G)=[c_{ij}]$ in which $c_{ij}=1+D-d_G(v_i, v_j)$ if $ineq j$ and $c_{ii}=sum_{j=1}^{n}(1+D-d_G(v_i, v_j))$. The complementary transmission $CT_G(v)$ of a vertex $v$ is defined as $CT_G(v)=sum_{u in ...

1998
Ivan Tomov Dimov Vassil N. Alexandrov Aneta Karaivanova

The problem of evaluating the dominant eigenvalue of real matrices using Monte Carlo numerical methods is considered. Three almost optimal Monte Carlo algorithms are presented: – Direct Monte Carlo algorithm (DMC) for calculating the largest eigenvalue of a matrix A. The algorithm uses iterations with the given matrix. – Resolvent Monte Carlo algorithm (RMC) for calculating the smallest or the ...

Journal: :CoRR 2012
Victor M. Preciado Moez Draief Ali Jadbabaie

We study how the behavior of viral spreading processes is influenced by local structural properties of the network over which they propagate. For a wide variety of spreading processes, the largest eigenvalue of the adjacency matrix of the network plays a key role on their global dynamical behavior. For many real-world large-scale networks, it is unfeasible to exactly retrieve the complete netwo...

2012
László Erdős Antti Knowles Horng-Tzer Yau Jun Yin

We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs, i.e. graphs on N vertices where every edge is chosen independently and with probability p ≡ p(N). We rescale the matrix so that its bulk eigenvalues are of order one. Under the assumption pN N, we prove the universality of eigenvalue distributions both in the bulk and at the edge of the spectrum. More precisely, we pro...

2008
A. B. Dieker J. Warren

Using a change-of-measure argument, we prove an equality in law between the process of largest eigenvalues in a generalized Wishart random-matrix process and a last-passage percolation process. This equality in law was conjectured by Borodin and Péché (2008).

2016
Charles Carlson Karthekeyan Chandrasekaran Hsien-Chih Chang Alexandra Kolla

The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of identifying symmetric signings of matrices with natural spectral properties. Our results are twofold: 1. We show NP-completeness for the following three problems: verifying whether a given matrix has a symmetric signing th...

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