From density-functional calculations, we show that localized states stemming from defects or topological disorder exhibit an anomalously large electron–phonon coupling. We provide a simple analysis to explain the observation and perform a detailed study on an interesting system: amorphous silicon. We compute firstprinciples deformation potentials (by computing the sensitivity of specific electr...

Based on Lyapunov-exponent generation and the Gram-Schimdt orthogonalization, analysis and design of some anti-controlled higher-dimensional hyperchaotic systems are investigated in this paper. First, some theoretical results for Lyapunov-exponent generating algorithms are proposed. Then, the relationship between the number of Lyapunov exponents and the number of positive real parts of the eige...

in this paper we consider the solutions of linear systems of saddle point problems‎. ‎by using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the hermitian and skew hermitian splitting method‎.

Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors i...

The spectrum of a square matrix A, denoted by σ(A) is the set of all eigenvalues of A. The spectral radius of A, denoted by ρ(A) is defined as: ρ(A) = max{|λ| : λ ∈ σ(A)} An eigenvalue of A that is larger in absolute value than any other eigenvalue is called the dominant eigenvalue; a corresponding eigenvector is called a dominant eigenvector. The most commonly encountered vector norm (often si...

Let V be a real valued potential that is smooth everywhere on R3, except at a periodic, discrete set of points, where it has singularities of the Coulomb form Z/r. We assume that the potential V is periodic with period lattice L. We study the spectrum of the Schrödinger operator H = −∆ + V acting on the space of Bloch waves with arbitrary, but fixed, wavevector k. Let T := R3/L. Let u be an eig...

In the vibration analysis of high speed trains arises such a palindromic quadratic eigenvalue problem (PQEP) (λ2AT + λQ + A)z = 0, where A, Q ∈ Cn×n have special structures: both Q and A are m ×m block matrices with each block being k × k (thus n = m × k), and Q is complex symmetric and tridiagonal block-Toeplitz, and A has only one nonzero block in the (1,m)th block position which is the same ...

The efficient estimation of an approximate model order is very important for real applications with multi-dimensional data if the observed low-rank corrupted by additive noise. In this paper, we present a novel robust method noise-corrupted based on LineAr Regression Global Eigenvalues (LaRGE). LaRGE uses multi-linear singular values obtained from HOSVD measurement tensor to construct global ei...

We present a direct method for reordering eigenvalues in the generalized periodic real Schur form of a regular K-cyclic matrix pair sequence (Ak, Ek). Following and generalizing existing approaches, reordering consists of consecutively computing the solution to an associated Sylvester-like equation and constructingK pairs of orthogonal matrices. These pairs define an orthogonal K-cyclic equival...

Abstract. The Automated Multi-Level Substructuring (AMLS) method has been developed to reduce the computational demands of frequency response analysis and has recently been proposed as an alternative to iterative projection methods like Lanczos or Jacobi–Davidson for computing a large number of eigenvalues for matrices of very large dimension. Based on Schur complements and modal approximations...