Bruno Salvy: Algorithms proving inequalities of sequences – lecture 1 скачать в хорошем качестве

Bruno Salvy: Algorithms proving inequalities of sequences – lecture 1

We have long known how to prove identities between sequences defined by linear recurrences with polynomial coefficients, but the development of algorithms proving inequalities is relatively recent. Inequalities, or even simply positivity, are actually delicate questions related to problems whose decidability is still unknown, even for recurrences with constant coefficients. This course will present recent algorithms that cover a large class of linear recurrences. These algorithms construct proofs by induction that take the form of cones that are stable by an underlying recurrence operator. The existence and construction of such cones rely on an extension of the classical Perron- Frobenius theory to matrices leaving a cone invariant. The more recent parts of the course are based on joint work with Alaa Ibrahim. Recording during the thematic meeting : «Francophone Computer Algebra Days» the March 02, 2026 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area