In this paper for a given prescribed Ritz values that satisfy in the some special conditions, we find a symmetric nonnegative matrix, such that the given set be its Ritz values.

nonnegative matrix factorization (nmf) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. methods in alternating least square (als) approach usually used to solve this non-convex minimization problem.  at each step of als algorithms two convex least square problems should be solved, which causes high com...

it is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. in this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.

We present a model and propose an approach to compute an approximate solution of Fully Fuzzy Linear System $(FFLS)$ of equations in which all the components of the coefficient matrix are either nonnegative or nonpositive. First, in discussing an $FFLS$ with a nonnegative coefficient matrix, we consider an equivalent $FFLS$ by using an appropriate permutation to simplify fuzzy multiplications. T...

In this paper, the nonnegative Q-matrix completion problem is studied. A real n × n matrix is a Q-matrix if for k ∈ {1, . . . , n}, the sum of all k × k principal minors is positive. A digraph D is said to have nonnegative Q-completion if every partial nonnegative Q-matrix specifying D can be completed to a nonnegative Q-matrix. For nonnegative Q-completion problem, necessary conditions and suf...

is known to be stable if and only if ρ(A) < 1. Models of real world dynamical phenomena often involve positive quantities. A dynamical system (1) is called positive if any trajectory of the system starting in the positive orthant R+ remains in R+. In this case, the matrix A has only real positive entries. In many cases, it may be useful to consider systems with a known “nominal” part A and a un...

We consider an adversarially-trained version of the nonnegative matrix factorization, a popular latent dimensionality reduction technique. In our formulation, attacker adds arbitrary bounded norm to given data matrix. design efficient algorithms inspired by adversarial training optimize for dictionary and coefficient matrices with enhanced generalization abilities. Extensive simulations on synt...