From 1ce51ff0a3ffead4775ee5db612e85cf19c6b40e Mon Sep 17 00:00:00 2001 From: gergaud Date: Tue, 10 Nov 2020 12:18:04 +0100 Subject: [PATCH] Coquilles test de convergence dans la doc --- docs/src/Algorithme_de_newton.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/src/Algorithme_de_newton.md b/docs/src/Algorithme_de_newton.md index a65b9ea..f9f2e9d 100644 --- a/docs/src/Algorithme_de_newton.md +++ b/docs/src/Algorithme_de_newton.md @@ -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.