This paper presents some practical and guaranteed ways of studying the discrete-time/ continuous-time stability quality of large sparse matrices. The methods use projection techniques for computing an invariant subspace associated with a few outermost eigenvalues (those with largest real parts for the continuous-time case and with largest magnitudes in the discrete-time case). Standard Lyapunov...

Consider a N × n random matrix Yn = (Y n ij ) where the entries are given by Y n ij = σ(i/N,j/n) √ n X ij , the X n ij being centered i.i.d. and σ : [0, 1] 2 → (0,∞) being a continuous function called a variance profile. Consider now a deterministic N×n matrix Λn = ( Λij ) whose non diagonal elements are zero. Denote by Σn the non-centered matrix Yn+Λn. Then under the assumption that limn→∞ N n...

Riassunto: Il lavoro riguarda il processo di convergenza dei paesi appartenenti al partenariato Euro-Mediterraneo nel periodo 1980-1999. Per la misura della convergenza viene proposto un indicatore ed una matrice di “persistenza” che rappresentano, in modo sintetico, il risultato di un algoritmo di classificazione. L’informazione fornita dalla matrice di persistenza viene ridotta successivament...

Pisot numbers, primitive matrices and beta-conjugates. We show that given a Pisot number β, for any integer n large enough, there is a nonnegative primitive square matrix whose order is equal to the degree of β, and the matrix admits β for eingenvalue. Let β = a1/β + a2/β + · · ·+ an/β + · · · be the β-expansion of β. For any Pisot number β, the sequence (an)n≥1 is ultimately periodic i.e., for...

In this paper, we present an upwinding methodology for systems of conservation laws. Our aim is to construct upwind schemes which do not require the extraction of the eigensystem of the jacobian matrix (but just the knowledge of the eigenvalues) and rely on the introduction of an appropriate polynomial approximation. @U @t + @F(U) @x = 0; t > 0; x 2 I R ; (1) avec U(x; t) un etat de l'espace de...

background: sound is one of the most important factors threatening workers’ health. the most efficient and practical method for controlling noise pollution is the use of sound-absorbing materials. impedance tube with two microphones is used to determine the sound absorption coefficients and should be tested periodically for accuracy and efficiency. the purpose of present study was assessing the...

The article presents the general notions and algorithm about the Gauss-Jordan method. An eloquent example is given and the Turbo C program illustrated this method. We conclude that we can obtain by this method the determinant, by simple calculations and reducing the rounding errors Cuvinte cheie: metoda Gauss-Jordan, matricea inversă, limbaj de programare Turbo C, pivot. 1. Noţiuni generale Met...