A New Subclass of H-Matrices with Applications

Dragana Cvetković, Đorđe Vukelić and Ksenija Doroslovački ()
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Dragana Cvetković: Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia
Đorđe Vukelić: Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia
Ksenija Doroslovački: Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia

Mathematics, 2024, vol. 12, issue 15, 1-15

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.

Keywords: H-matrices; spectrum localization; stability of dynamical systems; norm bounds of the inverse (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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