Bounds for the inverses of generalized Nekrasov matrices

The paper considers upper bounds for the infinity norm of the inverse for matrices in two subclasses of the class of (nonsingular) $H$-matrices, both of which contain the class of Nekrasov matrices. The first one has been introduced recently and consists of the so-called $S$-Nekrasov matrices. For $S$-Nekrasov matrices, the known bounds are improved. The second subclass consists of the so-called QN- (quasi-Nekrasov) matrices, which are defined in the present paper. For QN-matrices, an upper bound on the infinity norm of the inverses is established. It is shown that in application to Nekrasov matrices the new bounds are generally better than the known ones.