Séminaire LSC: Newton-Raphson iteration for Cartesian differential categories
Date(s) : 15/02/2024 iCal
11h00 - 12h30
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.
Emplacement
I2M Luminy - TPR2, Amphithéâtre Herbrand 130-134 (1er étage)
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