Generalized block Lanczos methods for large unsymmetric eigenproblems are presented, which contain the block Arnoldi method, and the block Arnoldi algorithms are developed. The convergence of this class of methods is analyzed when the matrix A is diagonalizable. Upper bounds for the distances between normalized eigenvectors and a block Krylov subspace are derived, and a priori theoretical error...

Lyapunov exponents and direction elds are used to characterize the time-scales and geometry of general linear time-varying (LTV) systems of di erential equations. Lyapunov exponents are already known to correctly characterize the time-scales present in a general LTV system; they reduce to real parts of eigenvalues when computed for linear time-invariant(LTI) systems and real parts of Floquet ex...

In physics, it is sometimes desirable to compute the so-called Density Of States (DOS), also known as the spectral density, of a Hermitian (or symmetric) matrix A. The spectral density can be viewed as a probability density distribution that measures the likelihood of finding eigenvalues near some point on the real line. The most straightforward way to obtain this density is to compute all eige...

In this paper we compare various preconditioners for the numerical solution of partial differential equations. We compare the well-known balancing preconditioner used in domain decomposition methods with a so-called deflation preconditioner. We prove that the effective condition number of the deflated preconditioned system is always, i.e., for all deflation vectors and all restrictions and prol...

Let $G$ be a graph with eigenvalues $lambda_1(G)geqcdotsgeqlambda_n(G)$. In this paper we find all simple graphs $G$ such that $G$ has at most twelve vertices and $G$ has exactly two non-negative eigenvalues. In other words we find all graphs $G$ on $n$ vertices such that $nleq12$ and $lambda_1(G)geq0$, $lambda_2(G)geq0$ and $lambda_3(G)0$, $lambda_2(G)>0$ and $lambda_3(G)

For the free vibrations of multi-degree mechanical structures appeared in structural dynamics, we solve quadratic eigenvalue problem either by linearizing it to a generalized or directly treating developing iterative detection methods for real and complex eigenvalues. To problem, impose nonzero exciting vector into eigen-equation, nonhomogeneous linear system obtain response curve, which consis...

Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruen...

The eigenvalues of a graph is the root of its characteristic polynomial. A fullerene F is a 3- connected graphs with entirely 12 pentagonal faces and n/2 -10 hexagonal faces, where n is the number of vertices of F. In this paper we investigate the eigenvalues of a class of fullerene graphs.

In this paper, a new algorithm using 2DPCA and Gram-Schmidt Orthogonalization Procedure for recognition of face images is proposed. The algorithm consists of two parts. In the first part, a common feature matrix is obtained; and in the second part, the dimension of the common feature matrix is reduced. Resulting common feature matrix with reduced dimension is used for face recognition. Column a...

‎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 ...