On the composition of exponentials and the numerical integration of differential equations on manifolds (Adrien Busnot Laurent, INRIA Rennes)

28.10.2025 14:00

The composition of matrix exponentials is well understood through the BCH formula and the use of the inverse differential of the exponential map dexp^{-1}. We will consider a similar problem from the geometric perspective with the composition of geodesic exponential, defined by a general affine connection. Using geometric arguments, we describe the Taylor expansion of the equivalent of dexp^{-1}, a geometric BCH formula, and apply the approach for the creation of numerical integrators on manifolds, equipped with any geometry. The approach is motivated by ongoing works on stochastic numerics on manifolds.

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre