As is well known, an irreducible nonnegative matrix possesses a uniquely determined Perron vector. As the main result of this paper we give a description of the set of Perron vectors of all the matrices contained in an irreducible nonnegative interval matrix A. This result is then applied to show that there exists a subset A∗ of A parameterized by n parameters (instead of n2 ones in the descrip...

We present and explore the behaviour of a branch-and-bound algorithm for calculating valid bounds on the k-th largest eigenvalue of a symmetric interval matrix. Branching on the interval elements of the matrix takes place in conjunction with the application of Rohn’s method (an interval extension of Weyl’s theorem) in order to obtain valid outer bounds on the eigenvalues. Inner bounds are obtai...

The differentiation matrix for a Daubechies-based wavelet basis defined on an interval will be constructed. It will be shown that the differentiation matrix based on the currently available boundary constructions does not maintain the superconvergence encountered under periodic boundary conditions. BJgy .. .. . .. .A0000 w__ •t!ar ~'..,-

and Applied Analysis 3 Let a and b be two cost intervals, and the minimum cost interval is to be chosen. i If the decision maker DM is optimistic, then he/she will prefer the interval with maximum width along with the risk of more uncertainty giving less importance. ii If DM is pessimistic, then he/she will pay more attention on more uncertainty. That is, on the right hand points of the interva...

Using a generalized Riccati transformation, some new oscillation criteria of linear second order matrix differential system with damping are built by the method of integral average. These results are based on the information on a sequence of subintervals of [t0,∞). 2000 Mathematics Subject Classification: 34C10.

Explicit formulae for the inverse of an interval matrix of the form [I − ∆, I + ∆] (where I is the unit matrix) are proved via finding explicit solutions of certain nonlinear matrix equations.

The purpose of this paper is to inquire the connection between maximal inner interval estimates of the solution sets to interval linear system and solutions of the dualization equation in Kaucher interval arithmetic. The results of our work are as follows: 1) a criterion of inner interval estimate of the solution set, 2) a criterion for a solution of dualization equation to be a maximal inner i...

Matrix game theory is concerned with how two players make decisions when they are faced with known exact payoffs. The aim of this paper is to develop a simple and an effective linear programming method for solving matrix games in which the payoffs are expressed with intervals. Because the payoffs of the matrix game are intervals, the value of the matrix game is an interval as well. Based on the...

Explicit formulae for the inverse of an interval matrix of the form [I − ∆, I + ∆] (where I is the unit matrix) are proved via finding explicit solutions of certain nonlinear matrix equations.