Related papers: Lower bounds of the minimum eigenvalue for $M$-mat…
Matrix completion algorithms recover a low rank matrix from a small fraction of the entries, each entry contaminated with additive errors. In practice, the singular vectors and singular values of the low rank matrix play a pivotal role for…
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…
We present improved approximation bounds for the Moore-Penrose inverses of banded matrices, where the bandedness is induced by a metric on the index set. We show that the pseudoinverse of a banded matrix can be approximated by another…
In the paper, the approximate sequence for entropy of some binary hidden Markov models has been found to have two bound sequences, the low bound sequence and the upper bound sequence. The error bias of the approximate sequence is bound by a…
The purpose of this note is twofold: firstly to improve the known results on variation of extreme eigenvalues of birth and death matrices and random walk matrices; and secondly to progress towards the solution of a thirty years old open…
We obtain tight upper and lower bounds to the eigenvalues of an anharmonic oscillator with a rational potential. We compare our bounds with results given by other approaches.
We provide upper and lower bounds on the smallest eigenvalue of grounded Laplacian matrices (which are matrices obtained by removing certain rows and columns of the Laplacian matrix of a given graph). The gap between the upper and lower…
We consider a minimal realization of a rational matrix functions. We perturb the polynomial part and one of the constant matrices from the realization part. We derive explicit computable expressions of backward errors of approximate…
Eigenvalue estimates that are optimal in some sense have self-evident appeal and leave estimators with a sense of virtue and economy. So, it is natural that ongoing searches for effective strategies for difficult tasks such as estimating…
To illustrate that the notion of convergence of submodular function sequences fits reasonably into the limit theory of graphs, we describe several classes of matroids and other submodular setfunctions for which convergence of appropriate…
In this work we review and derive some elementary properties of the discrete renewal sequences based on a positive, finite and integer-valued random variable. Our results consider these sequences as dependent on the probability masses of…
An upper bound on operator norms of compound matrices is presented, and special cases that involve the $\ell_1$, $\ell_2$ and $\ell_\infty$ norms are investigated. The results are then used to obtain bounds on products of the largest or…
This work focuses on the problem of exact model reduction of positive linear systems, by leveraging minimal realization theory. While determining the existence of a positive reachable realization remains in general an open problem, we are…
Traces of inverse powers of a positive definite symmetric tridiagonal matrix give lower bounds of the minimal singular value of an upper bidiagonal matrix. In a preceding work, a formula for the traces which gives the diagonal entries of…
The objective of the matrix selection problem is to select a submatrix $A_{S}\in \mathbb{R}^{n\times k}$ from $A\in \mathbb{R}^{n\times m}$ such that its minimum singular value is maximized. In this paper, we employ the interlacing…
We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we…
In order to prove weak convergence of the periodic multiplicative Selmer algorithm we ensure that the periodicity matrix is positive and establish a relation between its entries and eigenvalues. Since we can imply that the limit of these…
We provide non-asymptotic, relative deviation bounds for the eigenvalues of empirical covariance and Gram matrices in general settings. Unlike typical uniform bounds, which may fail to capture the behavior of smaller eigenvalues, our…
We study the universality of the eigenvalue statistics of the covariance matrices $\frac{1}{n}M^* M$ where $M$ is a large $p\times n$ matrix obeying condition $\bf{C1}$. In particular, as an application, we prove a variant of universality…
In this paper we characterise the indeterminate case by the eigenvalues of the Hankel matrices being bounded below by a strictly positive constant. An explicit lower bound is given in terms of the orthonormal polynomials and we find…