The Nedrasov property of a matrix is a generalized concept of diagonal dominance. In particular, it comprises usual strict (row-wise) diagonal dominance, irreducible diagonal dominance and Brauer row diagonal dominance. The authors show that the Nekrasov property is invariant to one step of Gaussian elimination without pivoting. They show that this is also true for the class of semistrict diagonally dominant matrices (which are, in fact, special $H$-matrices). The practical implication of these results means that Gaussian elimination without pivoting is feasible for these matrices.
Reviewer: A.Frommer (Wuppertal)