in this paper, we represent an inexact inverse subspace iteration method for com- puting a few eigenpairs of the generalized eigenvalue problem ax = bx[q. ye and p. zhang, inexact inverse subspace iteration for generalized eigenvalue problems, linear algebra and its application, 434 (2011) 1697-1715 ]. in particular, the linear convergence property of the inverse subspace iteration is preserved.

For the eigenvalue function on symmetric matrices, we have gathered a number of it’s properties.We show that this map has the properties of continuity, strict continuity, directional differentiability, Frechet differentiability, continuous  differentiability. Eigenvalue function will be extended to a larger set of matrices and then the listed properties will prove again.

The undirected power graph of a finite group $G$, $P(G)$, is a graph with the group elements of $G$ as vertices and two vertices are adjacent if and only if one of them is a power of the other. Let $A$ be an adjacency matrix of $P(G)$. An eigenvalue $lambda$ of $A$ is a main eigenvalue if the eigenspace $epsilon(lambda)$ has an eigenvector $X$ such that $X^{t}jjneq 0$, where $jj$ is the all-one...

rapid urban growth is resulting into increase in travel demand and private vehicle ownership in urban areas. in the present scenario the existing infrastructure has failed to match the demand that leads to traffic congestion, vehicular pollution and accidents. with traffic congestion augmentation on the road, delay of commuters has increased and reliability of road network has decreased. four s...

We consider three known bounds for the quadratic assignment problem (QAP): an eigenvalue, a convex programming (CQP), and semidefinite (SDP) bound. Since last two were not compared directly before, we prove that SDP bound is stronger than CQP then apply these to improve on discrete energy minimization problem, reformulated as QAP, which aims minimize potential between repulsive particles toric ...

given four complex matrices a, b, c and d where a 2 cnn and d 2 cmm andlet the matrix(a bc d)be a normal matrix and assume that  is a given complex number that is not eigenvalue of matrix a. we present a method to calculate the distance norm (with respect to 2-norm) from d to the set of matrices x 2 cmm such that,  be a multiple eigenvalue of matrix(a bc x). we also nd the nearest matrix ...

Finite element model correction of quadratic eigenvalue problems (QEPs) using a symmetric eigenstructure assignment technique was proposed by Zimmerman and Widengren (Zimmerman, D., and Widengren, M., “Correcting Finite Element Models Using a Symmetric Eigenstructure Assignment Technique,” AIAA Journal, Vol. 28, No. 9, 1990, pp. 1670–1676) and incorporates the measured model data into the finit...

in this paper, a new approach was presented for bus network design which took the effects of three out of four stages of the bus planning process into account. the presented model consisted of three majors steps 1- network design procedure (ndp), 2- frequency determination and assignment procedure (fdap), and 3- network evaluation procedure (nep). genetic algorithm (ga) was utilized to solve th...