Results 81 to 90 of about 196,426 (238)
Rank one perturbation with a generalized eigenvector [PDF]
arXiv, 2020 The relationship between the Jordan structures of two matrices sufficiently close has been largely studied in the literature, among which a square matrix $A$ and its rank one updated matrix of the form $A+xb^*$ are of special interest. The eigenvalues of $A+xb^*$, where $x$ is an eigenvector of $A$ and $b$ is an arbitrary vector, were first expressed ...
arxiv
Civil and Environmental Engineering, 2014 The paper presents the perturbation method which was used for computation of eigenvalues and eigenvectors for the assumed homogeneous state of strain in the hyperelastic Murnaghan material.
Major Izabela, Major Maciej
doaj +1 more source
A random matrix definition of the boson peak
, 2015 The density of vibrational states for glasses and jammed solids exhibits universal features, including an excess of modes above the Debye prediction known as the boson peak located at a frequency $\omega^*$ .
Liu, Andrea J., Manning, M. Lisa
core +1 more source
Reliable a-posteriori error estimators for $hp$-adaptive finite element approximations of eigenvalue/eigenvector problems [PDF]
, 2011 We present reliable a-posteriori error estimates for $hp$-adaptive finite element approximations of eigenvalue/eigenvector problems. Starting from our earlier work on $h$ adaptive finite element approximations we show a way to obtain reliable and ...
Giani, Stefano +2 more
core +2 more sources
, 2005 As a continuum work of Bhaumik et al who derived the common eigenvector of the number-difference operator Q and pair-annihilation operator ab (J. Phys.
Erdèlyi A. +3 more
core +1 more source
Eigenvectors of the discrete Laplacian on regular graphs - a statistical approach [PDF]
, 2008 In an attempt to characterize the structure of eigenvectors of random regular graphs, we investigate the correlations between the components of the eigenvectors associated to different vertices. In addition, we provide numerical observations, suggesting that the eigenvectors follow a Gaussian distribution. Following this assumption, we reconstruct some
arxiv +1 more source
, 1997 The decomposition of a matrix A into a product of two or three matrices can (depending on the characteristics of those matrices) be a very useful first step in computing such things as the rank, the determinant, or an (ordinary or generalized) inverse (of A) as well as a solution to a linear system having A as its coefficient matrix.
openaire +3 more sources
Eigenvectors of random matrices: A survey [PDF]
arXiv, 2016 Eigenvectors of large matrices (and graphs) play an essential role in combinatorics and theoretical computer science. The goal of this survey is to provide an up-to-date account on properties of eigenvectors when the matrix (or graph) is random.
arxiv
Faster Eigenvector Computation via Shift-and-Invert Preconditioning
, 2016 We give faster algorithms and improved sample complexities for estimating the top eigenvector of a matrix $\Sigma$ -- i.e. computing a unit vector $x$ such that $x^T \Sigma x \ge (1-\epsilon)\lambda_1(\Sigma)$: Offline Eigenvector Estimation: Given an ...
Garber, Dan +6 more
core
Eigenvectors and Reconstruction [PDF]
arXiv, 2006 In this paper, I study the simple eigenvectors of two hypomorphic matrices using linear algebra. I give new proofs of results of Godsil and MaKay.
arxiv