New classes of nonsingular matrices and upper bounds for their inverses

The paper introduces new classes of nonsingular matrices, which extend some known subclasses of the class of nonsingular $\mathcal{H}$-matrices, such as the Nekrasov, $Q$-Nekrasov, $\{P_1,P_2\}$-Nekrasov, and DZ matrices. For matrices in the classes introduced, upper bounds for $\|A^{-1}\|_\infty$ are derived (in a unified manner) and shown to improve the known bounds for matrices from the corresponding subclasses of nonsingular $\mathcal{H}$-matrices.