On Matrices with Only One Non-SDD Row

The class of H-matrices, also known as Generalized Diagonally Dominant (GDD) matrices, plays an important role in many areas applied linear algebra, well a wide range applications, such dynamical analysis complex networks that arise ecology, epidemiology, infectology, neurology, engineering, economy, opinion dynamics, and other fields. To conclude the particular system is (locally) stable, it sufficient to prove corresponding (Jacobian) matrix H-matrix with negative diagonal entries. In practice, however, very difficult determine whether non-singular or not, so valuable investigate subclasses H-matrices which are defined by relatively simple practical criteria. Many have recently been discussed detail demonstrating benefits they can provide, though one subclass has not fully exploited until now. aim this paper attract attention discuss its relation more investigated classes, while showing main advantage, based on simplicity elegance. This new approach, we presenting paper, will be compared existing ones, three possible spectrum localization; maximum norm estimation inverse point, block case; error for LCP problems. conclusion importance our approach grows dimension.