Nekrasov type matrices and upper bounds for their inverses

The paper considers the so-called $P$-Nekrasov and $\{P_1, P_2\}$-Nekrasov matrices, defined in terms of permutation matrices $P, P_1, P_2$, which generalize the well-known notion of Nekrasov matrices. For such matrices $A$, available upper bounds on $\|A^{-1}\|_\infty$ are recalled, and new upper bounds for the $P$-Nekrasov and $\{P_1, P_2\}$-Nekrasov matrices are suggested. It is shown that the latter bound generally improves the earlier bounds, as well as the bound for the inverse of a $P$-Nekrasov matrix and the classical bound for the inverse of a strictly diagonally dominant matrix.