Total nonnegativity of finite Hurwitz matrices and root location of polynomials

  • In 1970, B.A. Asner, Jr., proved that for a real quasi-stable polynomial, i.e., a polynomial whose zeros lie in the closed left half-plane of the complex plane, its finite Hurwitz matrix is totally nonnegative, i.e., all its minors are nonnegative, and that the converse statement is not true. In this work, we explain this phenomenon in detail, and provide necessary and sufficient conditions for a real polynomial to have a totally nonnegative finite Hurwitz matrix.

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Metadaten
Author:Mohammad Adm, Jürgen GarloffGND, Mikhail TyaglovGND
URN:urn:nbn:de:bsz:kon4-opus4-14614
DOI:https://doi.org/10.1016/j.jmaa.2018.06.065
ISSN:0022-247X
ISSN:1096-0813
Parent Title (English):Journal of Mathematical Analysis and Applications
Volume:467
Publisher:Elsevier
Document Type:Article
Language:English
Year of Publication:2018
Release Date:2019/01/11
Tag:Hurwitz matrix; Quasi-stable polynomial; R-function; Stable polynomial; Totally nonnegative matrix
Issue:1
First Page:148
Last Page:170
Institutes:Institut für Angewandte Forschung - IAF
DDC functional group:500 Naturwissenschaften und Mathematik / 510 Mathematik
Open Access?:Nein
Relevance:Peer reviewed Publikation in Thomson-Reuters-Listung
Licence (English):License LogoLizenzbedingungen Elsevier