The computation of an enclosure for the solution of a sparse set of linear equations Ax = b with a thin matrix A and an interval right hand side b is considered. Gaussian elimination works well when the matrix is an M-matrix, but fails when the matrix is a general matrix. This paper illustrates how, for sparse matrices, an ordering intended to reduce the height of the elimination tree (and thus...

Prior treatments of space–time communications in Rayleigh flat fading generally assume that channel coding covers either one fading interval—in which case there is a nonzero “outage capacity”—or multiple fading intervals—in which case there is a nonzero Shannon capacity. However, we establish conditions under which channel codes span only one fading interval and yet are arbitrarily reliable. In...

In this paper analytic hierarchy process (AHP), a well-known approach for handling multi-criteria decision making problems, is discussed. It is based on pairwise comparisons. The methods for deriving the priority vectors from comparison matrices are examined. The existing methods for aggregating the individual comparison matrices into a group comparison matrix are revised. A method for aggregat...

Consider linear systems whose matrix and right-hand side vector depend affine-linearly on parameters varying within prescribed bounds We present some sufficient conditions under which the interval hull (or some bounds) of the solution set of a parametrised interval linear system coincides with the interval hull (or bounds) of the non-parametric interval linear system corresponding to the parame...

In this paper, we import interval method to the iteration for computing Moore-Penrose inverse of the full row (or column) rank matrix. Through modifying the classical Newton iteration by interval method, we can get better numerical results. The convergence of the interval iteration is proven. We also give some numerical examples to compare interval iteration with classical Newton iteration.

Consider linear systems whose matrix and right-hand side vector depend affine-linearly on parameters varying within prescribed bounds We present some sufficient conditions under which the interval hull (or some bounds) of the solution set of a parametrised interval linear system coincides with the interval hull (or bounds) of the non-parametric interval linear system corresponding to the parame...

The paper deals with expressions for the midpoint and the radius of the product of two intervals. Based on these expressions two applications are considered: One leads to an explicit representation of the fixed point of the function [A][x]+ [b] if zero is contained in the interval vector [b] but not in the interior of the entries of the interval matrix [A]. The second application proves the sem...

Methods to compute verified error bounds for the p-norm condition number of a matrix are discussed for p ∈ {1, 2,∞} and the Frobenius norm. We consider the cases of a real or complex, point or interval input matrix. In the latter case the condition number of all matrices within the interval matrix are bounded. A special method for extremely ill-conditioned matrices is derived as well. Numerical...

In this paper Kharitonov's t h e o m for the robust stability of interval polynomials is proved using the second method of Lyapunov. The Hermite matrix is taken as the matrix of the quadratic form which is used as a Lyapunov function to prove Hurwitz stability. It is shown that if the four Hemite matrices correspondii to the four Kharitonov extreme polynomials are positive definite, the Hermite...