A contribution to the feasibility of the interval Gaussian algorithm (Q811945)

The author studies feasibility of the interval Gaussian algorithm for solving interval linear systems \([A]x=[b]\) in the case of generalized diagonally dominant matrices; an interval matrix \([A]\) is called generalized diagonally dominant if it satisfies \(\langle[A]\rangle x\geq 0\) for some \(x>0\), where \(\langle[A]\rangle\) is the comparison matrix. It is proved that for an irreducible generalized diagonally dominant interval matrix, the interval Gaussian algorithm is feasible if and only if the signs of the entries of the midpoint matrix follow certain pattern.