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arXiv · 2306.05930

Positivity certificates for linear recurrences

Alaa Ibrahim·Bruno Salvy
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Abstract

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.

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Alaa Ibrahim, Bruno Salvy. 2023-06-09. Positivity certificates for linear recurrences. https://doi.org/10.1137/1.9781611977912.37

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