A Feasibility Result for Interval Gaussian Elimination Relying on Graph Structure

Abstract

Let A = (a _ij ) ∈ ||R^{nxn n x n} be an interval matrix, i.e. each entry is a compact real interval. ‘Usual’ matrices A ∈ |R^{nxn n x n} with real coefficients will be called point matrices in this paper, and a similar notation and terminology is adopted for vectors. Let b ∈ ||R^{nxn n} be an interval vector. We are interested in computing an interval vector containing the solution set

$$\begin{array}{*{20}{r}} {S : = \{ x \in {\mathbb{R}^n}:there exist a point matrix A \in A } \\ {and a point vector b \in b such that Ax = b\} .} \end{array}$$