diff --git a/dune/gfe/localgeodesicfestiffness.hh b/dune/gfe/localgeodesicfestiffness.hh index b91bcc2081d8ec4eb61b1c8dabd8325961b2a397..7e332e90723ca6e318917f1d9457cf99bdca51b2 100644 --- a/dune/gfe/localgeodesicfestiffness.hh +++ b/dune/gfe/localgeodesicfestiffness.hh @@ -146,7 +146,12 @@ public: This default implementation used finite-difference approximations to compute the second derivatives The formula for the Riemannian Hessian has been taken from Absil, Mahony, Sepulchre: - 'Optimization algorithms on matrix manifolds', page 107 + 'Optimization algorithms on matrix manifolds', page 107. There it says that + \f[ + \langle Hess f(x)[\xi], \eta \rangle + = \frac 12 \frac{d^2}{dt^2} \Big(f(\exp_x(t(\xi + \eta))) - f(\exp_x(t\xi)) - f(\exp_x(t\eta))\Big)\Big|_{t=0}. + \f] + We compute that using a finite difference approximation. */ virtual void assembleHessian(const Entity& e,