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Coquilles test de convergence dans la doc

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gergaud 2020-11-10 12:18:04 +01:00
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docs/src/Algorithme_de_newton.md
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@ -48,8 +48,8 @@ une approximation de la solution du problème ``\min _{x \in \mathbb{R}^{n}} f(x
## Tests de convergence
1. ``\|\nabla f(\beta^{(k+1)})\|$ petit : $\|\nabla f(\beta^{(k+1)})\| \leq \max(\texttt{Tol\_rel}\|\nabla f(\beta^{(0)})\|,\texttt{Tol\_als})``;
2. Evolution de ``f(\beta^{(k+1)})`` petit : ``|f(\beta^{(k+1)}) - f(\beta^{(k)})| \leq \max(\texttt{Tol\_rel}|f(\beta^{(k)})|,\texttt{Tol\_als})``
3. Evolution du pas ``d^{(k)}=\beta^{(k+1)}-\beta^{(k)}`` petit : ``\|\beta^{(k+1)}-\beta^{(k)}\| \leq \max(\texttt{Tol\_rel}\|\beta^{(k)}\|,\texttt{Tol\_als})``
1. Convergence, ``\|\nabla f(x^{(k+1)})\|$ petit : $\|\nabla f(x^{(k+1)})\| \leq \max(\texttt{Tol\_rel}\|\nabla f(x^{(0)})\|,\texttt{Tol\_abs})``
2. Stagnation de ``x_k``, ``d^{(k)}=x^{(k+1)}-x^{(k)}`` petit : ``\|x^{(k+1)}-x^{(k)}\| \leq \max(\texttt{Tol\_rel}\|x^{(k)}\|,\texttt{Tol\_abs})``
3. Stagnation de ``f`` : ``|f(x^{(k+1)}) - f(x^{(k)})| \leq \max(\texttt{Tol\_rel}|f(x^{(k)})|,\texttt{Tol\_abs})``
4. Le nombre d'itération maximal est atteint.