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.

Let A be a nonnegative square matrix whose symmetric part has rank one. Tournament matrices are of this type up to a positive shift by 1/2I . When the symmetric part of A is irreducible, the Perron value and the left and right Perron vectors of L(A, α) = (1 − α)A+ αAt are studied and compared as functions of α ∈ [0, 1/2]. In particular, upper bounds are obtained for both the Perron value and it...

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...

This paper is concerned with properties of the algebraic degree of the Laplace–Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator, how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polyno...

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...

This paper is concerned with the relative perturbation theory and its entrywise relatively accurate numerical solutions of an M -matrix Algebraic Riccati Equations (MARE) XDX −AX −XB + C = 0 by which we mean the following conformally partitioned matrix ( B −D −C A ) is a nonsingular or an irreducible singular M -matrix. It is known that such an MARE has a unique minimal nonnegative solution Φ. ...

In this paper, we discuss convergence of the extrapolated iterative methods for solving singular linear systems. A general principle of extrapolation is presented. The semiconvergence of an extrapolated method induced by a regular splitting and a nonnegative splitting is proved whenever the coe cient matrix A is a singular M -matrix with ‘property c’ and an irreducible singular M -matrix, respe...