Work

A study of the validity of Oppenheim's inequality for Hurwitz matrices associated with Hurwitz polynomials

Year: 2024

Type: article

Abstract: In this paper, Hurwitz polynomials, i.e., real polynomials whose roots are located in the open left half of the complex plane, and their associated Hurwitz matrices are considered. New formulae for the principal minors of Hurwitz matrices are presented which lead to ($ i $) a new criteria for deciding whether a polynomial is Hurwitz, ($ ii $) an inequality of a type of Oppenheim's inequality for the Hurwitz matrices up to order $6 $, and ($ iii $) a necessary and sufficient condition for the Hadamard square root of Hurwitz polynomials of degree five to be Hurwitz.

Source: Electronic Journal of Linear Algebra

DOI: 10.13001/ela.2024.8371

Authors: Fatimah Alsaafin, Doaa Al-Saafin, Jürgen Garloff

Institutions: University of Konstanz, HTWG Hochschule Konstanz - Technik, Wirtschaft und Gestaltung

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4401752294

FWCI: 0.201

Cites: 14

Cited by: 1

Related to: 10