On Descartes' rule of signs for hyperbolic polynomials
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | |
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| _version_ | 1866909063606960128 |
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| author | Kostov, Vladimir Petrov |
| author_facet | Kostov, Vladimir Petrov |
| contents | We consider univariate real polynomials with all roots real and with two sign changes in the sequence of their coefficients which are all non-vanishing. One of the changes is between the linear and the constant term. By Descartes' rule of signs, such degree $d$ polynomials have $2$ positive and $d-2$ negative roots. We consider the sequences of the moduli of their roots on the real positive half-axis. When the moduli are distinct, we give the exhaustive answer to the question at which positions can the moduli of the two positive roots be. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02307 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Descartes' rule of signs for hyperbolic polynomials Kostov, Vladimir Petrov Classical Analysis and ODEs We consider univariate real polynomials with all roots real and with two sign changes in the sequence of their coefficients which are all non-vanishing. One of the changes is between the linear and the constant term. By Descartes' rule of signs, such degree $d$ polynomials have $2$ positive and $d-2$ negative roots. We consider the sequences of the moduli of their roots on the real positive half-axis. When the moduli are distinct, we give the exhaustive answer to the question at which positions can the moduli of the two positive roots be. |
| title | On Descartes' rule of signs for hyperbolic polynomials |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2304.02307 |