Two recent approaches [4, 14] in subspace identification problems require the computation of the R factor of the QR factorization of a block–Hankel matrix H , which, in general has a huge number of rows. Since the data are perturbed by noise, the involved matrix H is, in general, full rank. It is well known that, from a theoretical point of view, the R factor of the QR factorization of H is equ...

The convergence of Markov chain–based Monte Carlo linear solvers using the Ulam– von Neumann algorithm for a linear system of the form x = Hx + b is investigated in this paper. We analyze the convergence of the Monte Carlo solver based on the original Ulam–von Neumann algorithm under the conditions that ‖H‖ < 1 as well as ρ(H) < 1, where ρ(H) is the spectral radius of H. We find that although t...

It is well-known that the Schur complement of a strictly diagonally dominant matrix is strictly diagonally dominant, too. Also, if a matrix is an H-matrix, then its Schur complement is an H-matrix, too. Recent research showed that the same type of statement holds for some special subclasses of H-matrices, see, for example, Liu et al. (2004). The aim of this paper is twofold: first, to show that...

The genus Hypericum is one of the most important medicinal plants that contain 17 species in Iran, three of them are endemics. This paper reports the essential oil composition of eight Hypericum species from Iran. The essential oil analysis of a number of the studied plants has already been reported but their report from Iran may be valuable for scientists.  Samples collected from different pla...

Let M(A) denote the comparison matrix of a square H-matrix A, that is, M(A) is an M-matrix. Hmatrices such that their comparison matrices are non-singular are well studied in the literature. In this paper, we study characterizations of H-matrices with either singular or non-singular comparison matrices. The spectral radius of the Jacobi matrix of M(A) and the generalized diagonal dominance prop...

We introduce a fast algorithm for entrywise evaluation of the Gauss--Newton Hessian (GNH) matrix fully connected feed-forward neural network. The has precomputation step and sampling step. While it generally requires $\mathcal{O}(Nn)$ work to compute an entry (and entire column) in GNH network with $N$ parameters $n$ data points, our reduces cost $\mathcal{O}(n+d/\epsilon^2)$ work, where $d$ is...

matrix metalloproteinases (mmps) are a family of neutral proteinases that are important in normal development, cellular differentiation or migration, angiogenesis, neurogenesis, wound repair, and a wide range of pathological processes such as oxidative stress and neuroinflammation. mmps have been demonstrated to increase the permeability of the blood–brain barrier (bbb) by degrading the compone...

The NP-hard Distinct Vectors problem asks to delete as many columns as possible from a matrix such that all rows in the resulting matrix are still pairwise distinct. Our main result is that, for binary matrices, there is a complexity dichotomy for Distinct Vectors based on the maximum (H) and the minimum (h) pairwise Hamming distance between matrix rows: Distinct Vectors can be solved in polyno...

Stress is a centrality measure determined by the shortest paths passing through given vertex. Noting that adjacency matrix playing an important role in finding distance and number of between pair vertices, interesting expression also algorithm are presented to find stress using matrix. The results suitably adopted obtain betweenness measure. Further extended cases Cartesian product G□H graphs, ...

A (semistability) factor [semifactor] of a matrix AE r: nn is a positive definite [positive semidefinite] matrix H such that AH + HA* is positive semidefinite. We give three proofs to show that if A has a semistability factor then it cannot be unique. We give necessary and sufficient conditions for a matrix H to be a (semi)factor of a given matrix. We also determine the dimension of the cone of...