An efficient convergence test for the fixed point method
The fixed point method consists to find the solution of F(X)=X.
One can not get fixed with the convergence condition |F'(X)|<1 because if the function has an optimum then |F'(X)|=0 even if the solution is not yet reached.
We introduce an efficient convergence test with the condition:
|Xn+1 - Xn| ≤ epsilon1 And |F(Xn+1)-Xn+1| ≤ epsilon2