Let A k ; k 0, be a sequence of m m nonnegative matrices and let A(z) = P 1 k=0 A k z k be such that A(1) is an irreducible stochastic matrix. The unique power-bounded solution of the nonlinear matrix equation G = P 1 k=0 A k G k has been shown to play a key role in the analysis of Markov chains of M/G/1 type. Assuming that the matrix A(z) is rational, we show that the solution of this matrix e...

Introduction and notation. The sensitivity of computational problems is a major factor determining the accuracy of computations in machine arithmetic. It may be revealed and taken into account by the methods of perturbation analysis [14, 6]. Below we consider the technique of Lyapunov majorants for perturbation analysis of algebraic matrix equations F (A, X) = 0 arising in science and engineeri...

Let A k ; k 0, be a sequence of mm nonnegative matrices and let A(z) = P 1 k=0 A k z k be such that A(1) is an irreducible stochastic matrix. The unique power-bounded solution of the nonlinear matrix equation G = P 1 k=0 A k G k has been shown to play a key role in the analysis of Markov chains of M/G/1 type. Assuming that the matrix A(z) is rational, we show that the solution of this matrix eq...

We propose a key-frame-based depth propagation method considering movement on the z-axis. First, a homography matrix is obtained through the feature points between points. Through this homography matrix information, a movement of objects or cameras is inferred in the direction of the z axis, thereby creating a depth map that compensates the movement. Then, bilateral filtering is executed to cre...

where z = (x, t) ∈ RN×R and 1 ≤ p0 ≤ N. By convenience, hereafter the term “Kolmogorov equation” will be shortened to KE. We assume the following hypotheses: (H.1) the matrix A0 = (aij)i,j=1,...,p0 is symmetric and uniformly positive definite in R p0 : there exists a positive constant μ such that |η| μ ≤ p0 ∑ i,j=1 aij(z)ηiηj ≤ μ|η|, ∀η ∈ R0 , z ∈ R; (1.2) (H.2) the matrix B ≡ (bij) has constan...

Here V(t,x) = (V1, . . . ,Vn), ρ(t,x) are a vector function and a scalar function which denote the velocity and the density of the medium, G(Z) is an n×n matrix function with the coefficients gi j = gi j(z11, . . . , znn) whose arguments are the coefficients of an n× n matrix Z, Φ is a scalar function, G and Φ are supposed to be smooth, μ > 0. Next, B(V) = zx(0, t,x), where z(τ, t,x) is a solut...

I. Introduction: Multivariate Statistical Analyses comprise a number of statistical methods/tools that may be applied to several fields of empirical investigations. Most of these methods have three characteristics in common: (i) they presume availability of data set, say Z(nxk) (in n observations and k variables; k ≥ 2, n>k), collected from the field (observationally or experimentally); (ii) th...

The 3-entity-type model consists of two relationship matrices, a m× n matrix X and a n× r matrix Y . In the spirit of generalized linear models we define the low rank representations of the relationship matrices to be X ≈ f1(UV T ) and Y ≈ f2(V Z T ) where f1 : R m×n → R and f2 : R n×r → R are the prediction links, and U ∈ R, V ∈ R, and Z ∈ R are the parameters of the model for k ∈ Z. We furthe...

Let A be an n × n complex matrix and 0 ≤ q ≤ 1. The boundary of the q-numerical range of A is the orthogonal projection of a hypersurface defined by the dual surface of the homogeneous polynomial F (t, x, y, z) = det(t In + x(A + A )/2 + y(A−A)/(2i) + z AA). We construct different types of cubic surfaces SF corresponding to the homogeneous polynomial F (t, x, y, z) induced by some 3 × 3 matrice...

We establish structural controllability results for matrix pairs [A, B] where .4=A0+Z piAi, B=B,+Z piB', with tho At, Bi fixed, and the pr free scalar parameters. Tho results characterize structural controllability in several wsys, via, tests involving the cllecking of the rank or the evaluation of the determinant of various constant matrices formed from t,he At, Bi. A number of the result,^ us...