We give an estimate for the relative change in the eigenvalues, as well as bounds on the angles between the perturbed and unperturbed eigenvectors. This class includes componentwise, or more generally 'localized', relative perturbations of Laplacians. We show that the estimate is optimal up to ...
Deconvolution Density Estimation on the Space of Positive Definite Symmetric Matrices We develop a nonparametric estimator for the density function of a random sample of positive definite matrices. Our estimator is based on the Helgason-Fourier transform and its inversion, the natural tools for analysis...
A note on the Frobenius conditional number with positive definite matrices In this article, we focus on the lower bounds of the Frobenius condition number. Using the generalized Schwarz inequality, we present some lower bounds for... H Li,Z Gao,Z Di - 《Journal of Inequalities & Applications...
For M-matrices A and weak regular splittings there exist well-known comparison theorems. Here, we give a comparison theorem for splittings of Hermitian positive definite matrices. Furthermore, we establish a comparison theorem for multisplittings of a Hermitian positive definite matrix....
This paper deals with the eigenproblem of positive definite matrices. A numerical algorithm, to find the largest eigenvalues of a full positive definite matrix using Householder reflections, is described. The proposed algorithm can be used to find all the eigenvalues of a symmetric matrix or at lea...
Our technique is based on the Bhaskar and Lakshmikantham coupled fixed point theorem. Results A new result on the existence of a unique positive definite solution is derived. An iterative method is constructed to compute the unique positive definite solution. Finally, some numerical examples are us...
An iterative method for solving large linear systems with sparse symmetric positive definite matrices on massively parallel computers is suggested. The met... LY Kolotilina,AY Yeremin - 《International Journal of High Speed Computing》 被引量: 171发表: 2012年 Newton Sketch: A Linear-time Optimiza...
A note on regularity and positive definiteness of interval matrices We present a sufficient regularity condition for interval matrices which generalizes two previously known ones. It is formulated in terms of positive defin... R Farhadsefat,T Lotfi,J Rohn - 《Central European Journal of Mathematics...
Negative Definite Functions on the Space of Infinite Hermitian Matrices In this paper we investigate a Lévy–Khinchin type integral formula of negative definite functions defined over the Olshanski spherical pair of infinite h... Bouali,Mohamed - 《Complex Analysis & Operator Theory》 被引量: 0发...
(a,b) Adjacency matrices with μ 0 = 0.1 ; (c,d) Adjacency matrices with μ 0 = 0.2 . In all scenarios, the experiments were replicated 50 times and the variation in the average values of NMI and AR with respect to μ 0 for the different methods are reported in Figure 5a–f. ...