Positivity certificates for linear recurrences
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916093798383616 |
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| author | Ibrahim, Alaa Salvy, Bruno |
| author_facet | Ibrahim, Alaa Salvy, Bruno |
| contents | We consider linear recurrences with polynomial coefficients of Poincaré type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity of solutions provided the initial conditions satisfy a precisely defined genericity condition. For positive sequences, the algorithm produces a certificate of positivity that is a data-structure for a proof by induction. This induction works by showing that an explicitly computed cone is contracted by the iteration of the recurrence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_05930 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Positivity certificates for linear recurrences Ibrahim, Alaa Salvy, Bruno Symbolic Computation Discrete Mathematics 05A20, 11B37, 39A06, 68V05 F.2.2; G.2.1; I.1.2 We consider linear recurrences with polynomial coefficients of Poincaré type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity of solutions provided the initial conditions satisfy a precisely defined genericity condition. For positive sequences, the algorithm produces a certificate of positivity that is a data-structure for a proof by induction. This induction works by showing that an explicitly computed cone is contracted by the iteration of the recurrence. |
| title | Positivity certificates for linear recurrences |
| topic | Symbolic Computation Discrete Mathematics 05A20, 11B37, 39A06, 68V05 F.2.2; G.2.1; I.1.2 |
| url | https://arxiv.org/abs/2306.05930 |