A new subclass of H-matrices

Class of H-matrices plays an important role in various scientific disciplines, in economics, for example. However, this class could be used in order to get various benefits in other linear algebra fields, like determinant estimation, Perron root estimation, eigenvalue localization, improvement of convergence area of relaxation methods, etc. For that reason, it seems important to find a subclass of H-matrices, as wide as possible, and expressed by explicit conditions, involving matrix elements only. One step forward in this direction, starting from Gudkov matrices, from one side, and S-SDD matrices, from the other side, will be presented in this paper.