Self-interlacing polynomials
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866912454542360576 |
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| author | Tyaglov, Mikhail |
| author_facet | Tyaglov, Mikhail |
| contents | We describe a new subclass of the class of real polynomials with real simple roots called self-interlacing polynomials. This subclass is isomorphic to the class of real Hurwitz stable polynomials (all roots in the open left half-plane). In the work, we present basic properties of self-interlacing polynomials and their relations with Hurwitz and Hankel matrices as well as with Stiltjes type of continued fractions. We also establish "self-interlacing" analogues of the well-known Hurwitz and Liénard-Chipart criterions for stable polynomials. A criterion of Hurwitz stability of polynomials in terms of minors of certain Hankel matrices is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1611_09156 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Self-interlacing polynomials Tyaglov, Mikhail Classical Analysis and ODEs 12D10, 26C10, 26C15, 30C15, 15B05 We describe a new subclass of the class of real polynomials with real simple roots called self-interlacing polynomials. This subclass is isomorphic to the class of real Hurwitz stable polynomials (all roots in the open left half-plane). In the work, we present basic properties of self-interlacing polynomials and their relations with Hurwitz and Hankel matrices as well as with Stiltjes type of continued fractions. We also establish "self-interlacing" analogues of the well-known Hurwitz and Liénard-Chipart criterions for stable polynomials. A criterion of Hurwitz stability of polynomials in terms of minors of certain Hankel matrices is established. |
| title | Self-interlacing polynomials |
| topic | Classical Analysis and ODEs 12D10, 26C10, 26C15, 30C15, 15B05 |
| url | https://arxiv.org/abs/1611.09156 |