A New Criterion to Guarantee the Feasibility of the Interval Gaussian Algorithm
Andreas Frommer, Giovanna Castro Lemos Mayer · SIAM Journal on Matrix Analysis and Applications · 1993
The main subject of this paper is the interval Gaussian algorithm, which produces an interval Vector $[ x ]^G $ analogously to its well-known counterpart in classical numerical analysis. Criteria are derived to guarantee the existence of $[ x ]^G $ if the $n \times n$ interval matrix $[ A ]$ is degenerate to a point matrix or if its comparison matrix $\langle [ A ] \rangle$ is irreducible and diagonally dominant. While in the first case all classical criteria of feasibility apply, the second case yields to a criterion which seems to be new. A way to construct matrices such that $[ x ]^G $ does not exist, although it does for each matrix $\tilde A \in [ A ]$, is also indicated.