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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| Author: | Mohammad AdmORCiDGND, Jürgen GarloffORCiDGND, 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; Totally nonnegative matrix; Stable polynomial; Quasi-stable polynomial; R-function |
| Issue: | 1 |
| First Page: | 148 |
| Last Page: | 170 |
| Institutes: | Institut für Angewandte Forschung - IAF |
| DDC functional group: | 500 Naturwissenschaften und Mathematik / 510 Mathematik |
| Relevance: | Peer reviewed Publikation in Master Journal List |
| Open Access?: | Nein |
| Licence (English): |  Lizenzbedingungen Elsevier |
