Séminaire LSC: Newton-Raphson iteration for Cartesian differential categories

Zeinab Galal

Date(s) : 15/02/2024   iCal
11 h 00 min - 12 h 30 min

Interactions between derivatives and fixpoints have many important
applications in both computer science and mathematics. In this talk, I will
present a categorical framework to combine fixpoints with derivatives for
Cartesian differential categories with a fixpoint operator by introducing an
additional axiom relating the derivative of a fixpoint with the fixpoint of
the derivative. The standard examples of Cartesian differential categories
where we can compute fixpoints provide canonical models of this notion. As an
application, I will show how this framework is a suitable setting to formalize
the Newton-Raphson optimization for fast approximation of fixpoints and extend
it to higher order languages. This is based on joint work with Jean-Simon
Pacaud Lemay.

Site Sud, Luminy, TPR2, Amphithéâtre Herbrand 130-134 (1er étage)


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