A New Subclass of H-Matrices with Applications

Abstract

The diagonal dominance property has been applied in many different ways and has proven to be very useful in various research areas. Its generalization, also known under the name H-matrix property, can be applied and produce significant benefits in economic theory, environmental sciences, epidemiology, neurology, engineering, etc. For example, it is known that the (local) stability of a (nonlinear) dynamic system is ensured if the (Jacobian) matrix belongs to the H-matrix class, and all its diagonal elements are negative. However, checking the H-matrix property itself is too expensive (from a computational point of view), so it is always worth investing effort in finding new subclasses of H-matrices, defined by relatively simple and practical conditions. Here, we will define a new subclass, which is closely related to the Euclidean vector norm, give some possible applications of this new class, and consider its relationship to some known subclasses.