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Communication Dans Un Congrès Année : 2024

Positivity certificates for linear recurrences

Résumé

We consider linear recurrences with polynomial coefficients of Poincar\'e 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.

Dates et versions

hal-04271203 , version 1 (06-11-2023)

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Alaa Ibrahim, Bruno Salvy. Positivity certificates for linear recurrences. SODA 2024 - ACM-SIAM Symposium on Discrete Algorithms, Jan 2024, Alexandria, Virginia, United States. pp.982-994, ⟨10.1137/1.9781611977912.37⟩. ⟨hal-04271203⟩
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