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Commit ad8fc1f9 authored by Oliver Sander's avatar Oliver Sander Committed by sander@FU-BERLIN.DE
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Document how the Hessian fd approximation is computed

[[Imported from SVN: r7390]]
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...@@ -146,7 +146,12 @@ public: ...@@ -146,7 +146,12 @@ public:
This default implementation used finite-difference approximations to compute the second derivatives 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: 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, virtual void assembleHessian(const Entity& e,
......
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