‎let $g$ be a graph without an isolated vertex‎, ‎the normalized laplacian matrix $tilde{mathcal{l}}(g)$‎‎is defined as $tilde{mathcal{l}}(g)=mathcal{d}^{-frac{1}{2}}mathcal{l}(g) mathcal{d}^{-frac{1}{2}}$‎, where ‎$‎mathcal{‎d}‎$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎g‎$‎‎. ‎the eigenvalues of‎‎$tilde{mathcal{l}}(g)$ are ‎called ‎ ‎ as ‎the ‎normalized laplacian ...

This article presents an analysis of free vibration of elastically supported Timoshenko beams by using the spectral element method. The governing partial differential equation is elaborated to formulate the spectral stiffness matrix. Effectively, the non classical end boundary conditions of the beam are the primordial task to calibrate the phenomenon of the Timoshenko beam-soil foundation inter...

This paper gives max characterizations for the sum of the largest eigen-values of a symmetric matrix. The elements which achieve the maximum provide a concise characterization of the generalized gradient of the eigenvalue sum in terms of a dual matrix. The dual matrix provides the information required to either verify rst-order optimality conditions at a point or to generate a descent direction...

Iterative eigenvalue solvers for large, sparse matrices may miss some of the required eigenvalues that are of high algebraic multiplicity or tightly clustered. Block methods, locking, a-posteriori validation, or simply increasing the required accuracy are often used to avoid missing or to detect a missed eigenvalue, but each has its own shortcomings in robustness or performance. To resolve thes...

In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

In this paper, the effect of spatial smoothing on performance of widely used stochastic narrowband multiple-input multiple-output (MIMO) radio channel model, namely the Kronecker model, is investigated based on data measured in urban microcellular environment at 5.3 GHz carrier frequency. Results from non-line of sight (NLOS) and line of sight (LOS) traveling routes are analyzed. It is noticed ...

In coupled learning rules for principal component analysis, eigenvectors and eigenvalues are simultaneously estimated in a coupled system of equations. Coupled single-neuron rules have favorable convergence properties. For the estimation of multiple eigenvectors, orthonormalization methods have to be applied, either full Gram-Schmidt orthonormalization, its first-order approximation as used in ...

We show that the average characteristic polynomial P n (z) = E[det(zI−M)] of the random Hermitian matrix ensemble Z −1 n exp(−Tr(V (M) − AM))dM is characterized by multiple orthogonality conditions that depend on the eigenvalues of the external source A. For each eigenvalue a j of A, there is a weight and P n has n j orthogonality conditions with respect to this weight, if n j is the multiplici...

The eigenvalues and eigenvectors of a symmetric matrix are needed in a myriad of applications in computational engineering and computational science. One of the fastest and most accurate eigensolvers is the Algorithm of Multiple Relatively Robust Representations (MRRR). This is the first stable algorithm that computes k eigenvalues and eigenvectors of a tridiagonal symmetric matrix in O(nk) tim...

The eigenvalue shift technique is the most well-known and fundamental tool for matrix computations. Applications include the search of eigeninformation, the acceleration of numerical algorithms, the study of Google’s PageRank. The shift strategy arises from the concept investigated by Brauer [1] for changing the value of an eigenvalue of a matrix to the desired one, while keeping the remaining ...