New criteria for identifying H-matrices

In the recent paper of Gan and Huang (Linear Algebra Appl. 374 (2003) 317), several simple criteria, as well as a necessary condition for nonsingular H-matrices, have been obtained. Inspired by this work, we will define several new subclasses of nonsingular H-matrices and give necessary conditions for a matrix to be an H-matrix. Finally, as a result of numerical experiments, we establish relations between defined and some already known subclasses.