Total nonnegativity of finite Hurwitz matrices and root location of polynomials
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2017
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918073691275264 |
|---|---|
| author | Adm, Mohammad Garloff, Jürgen Tyaglov, Mikhail |
| author_facet | Adm, Mohammad Garloff, Jürgen Tyaglov, Mikhail |
| contents | In 1970, B.A. Asner, Jr., proved that for a real quasi-stable polynomial, i.e., a polynomial whose zeros lie in the \emph{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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1711_04651 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Total nonnegativity of finite Hurwitz matrices and root location of polynomials Adm, Mohammad Garloff, Jürgen Tyaglov, Mikhail Classical Analysis and ODEs 15B48, 26C10 (Primary), 15A18, 15B05, 93D20 (Secondary) In 1970, B.A. Asner, Jr., proved that for a real quasi-stable polynomial, i.e., a polynomial whose zeros lie in the \emph{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. |
| title | Total nonnegativity of finite Hurwitz matrices and root location of polynomials |
| topic | Classical Analysis and ODEs 15B48, 26C10 (Primary), 15A18, 15B05, 93D20 (Secondary) |
| url | https://arxiv.org/abs/1711.04651 |