Related papers: New Approach to Identify Common Eigenvalues of rea…
In matrix theory and numerical analysis there are two very famous and important results. One is Gersgorin circle theorem, the other is strictly diagonally dominant theorem. They have important application and research value, and have been…
The sparse generalized eigenvalue problem arises in a number of standard and modern statistical learning models, including sparse principal component analysis, sparse Fisher discriminant analysis, and sparse canonical correlation analysis.…
We introduce an eigenvalue-preserving transformation algorithm from the generalized eigenvalue problem by matrix pencil of the upper and the lower bidiagonal matrices into a standard eigenvalue problem while preserving sparsity, using the…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
We present two approximation methods for computing eigenfrequencies and eigenmodes of large-scale nonlinear eigenvalue problems resulting from boundary element method (BEM) solutions of some types of acoustic eigenvalue problems in…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
This paper presents techniques for digital image watermarking based on eigenvalue decomposition of normal matrices. The introduced methods are convenient and self-explanatory, achieve satisfactory results, as well as require less and easy…
Motivated by canonical problems in medical diagnostics, we propose and study properties of an objective function that uniformly bounds uncertainties in quantities of interest extracted from classifiers and related data analysis tools. We…
The non-linear transformations incurred by the rays in an optical system can be suitably described by matrices to any desired order of approximation. In systems composed of uniform refractive index elements, each individual ray refraction…
A generalization of the Bernstein matrix concentration inequality to random tensors of general order is proposed. This generalization is based on the use of Einstein products between tensors, from which a strong link can be established…
A real square matrix is Perron-like if it has a real eigenvalue $s$, called the principal eigenvalue of the matrix, and $\mbox{Re}\,\mu<s$ for any other eigenvalue $\mu$. Nonnegative matrices and symmetric ones are typical examples of this…
Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Iterative random sparsification methods allow for the estimation of a single dominant eigenvalue at reduced cost by…
In this paper a generalization of the Gram-Schmidt Algorithm is presented. Actually we provide an algorithm to construct a set of equiangular vectors with a given angle $\theta\in(0,\arccos(\frac{-1}{n-1}))$ using a set of input independent…
The Bayesian Conjugate Gradient method (BayesCG) is a probabilistic generalization of the Conjugate Gradient method (CG) for solving linear systems with real symmetric positive definite coefficient matrices. Our CG-based implementation of…
The aim of this paper is the study of the bisection method in $\mathbb{R}^n$. In this work we propose a multivariate bisection method supported by the Poincar\'e-Miranda theorem in order to solve non-linear system of equations. Given an…
The homography matrix is a key component in various vision-based robotic tasks. Traditionally, homography estimation algorithms are classified into feature- or intensity-based. The main advantages of the latter are their versatility,…
In this paper we present an efficient algorithm to compute the eigen decomposition of a matrix that is a weighted sum of the self outer products of vectors such as a covariance matrix of data. A well known algorithm to compute the eigen…
We propose a second-order accurate method to estimate the eigenvectors of extremely large matrices thereby addressing a problem of relevance to statisticians working in the analysis of very large datasets. More specifically, we show that…
In this paper, we study a mixed variational problem subject to perturbations, where the noise term is modelled by means of a bilinear form that has to be understood to be "small" in some sense. Indeed, we consider a family of such problems…
We give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of…