Treffer: A necessary and sufficient criterion to guarantee feasibility of the interval Gaussian algorithm for a class of matrices

Let \([A]\) denote an interval of matrices in \(\mathbb{R}^{n\times n}\), let \([b]\) denote an interval of vectors in \(\mathbb{R}^ n\). In view of the equation \(A\cdot x = b\) with \(A \in [A]\) and \(b \in [b]\) one is interested in the solution set \(S:=\{x\mid x\in \mathbb{R}^ n, \exists A \in [A], b \in [b]: A\cdot x\}= b\). The well-known interval Gaussian algorithm (IGA) for solving \(A\cdot x = b\) either produces an interval \([x]\) which contains the solution set \(S\) or it is not feasible (i.e. encounters division by 0). The authors present for a special class of intervals of matrices a necessary and sufficient condition for the feasibility of the interval Gaussian algorithm.