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Ajout dans la doc des tests d'arret

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gergaud 2020-11-10 11:44:54 +01:00
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docs/src/Algorithme_de_newton.md
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@ -46,5 +46,10 @@ une approximation de la solution du problème ``\min _{x \in \mathbb{R}^{n}} f(x
b. Mise à jour : ``x_{k+1} = x_{k}+ d_{k} , k = k + 1`` b. Mise à jour : ``x_{k+1} = x_{k}+ d_{k} , k = k + 1``
#### 2.Retourner : ``x_{k}``. #### 2.Retourner : ``x_{k}``.
## Tests de convergence
1. ``\|\nabla f(\beta^{(k+1)})\|$ petit : $\|\nabla f(\beta^{(k+1)})\| \leq \max(\texttt{Tol\_rel}\|\nabla f(\beta^{(0)})\|,\texttt{Tol\_als})``;
2. Evolution de ``f(\beta^{(k+1)})`` petit : ``|f(\beta^{(k+1)}) - f(\beta^{(k)})| \leq \max(\texttt{Tol\_rel}|f(\beta^{(k)})|,\texttt{Tol\_als})``
3. Evolution du pas ``d^{(k)}=\beta^{(k+1)}-\beta^{(k)}`` petit : ``\|\beta^{(k+1)}-\beta^{(k)}\| \leq \max(\texttt{Tol\_rel}\|\beta^{(k)}\|,\texttt{Tol\_als})``
4. Le nombre d'itération maximal est atteint.