The reason why the Newton's method complains eventually

Here we are trying to find solutions to the system: F=0. That is
Newton's method leads to the following iterations:
xn+1= xn-(DFxn)-1. F(xn).
The iteration process breaks down when DFxn ,which is the same as the hessian matrix of f at xn , has rank less than three. Recall that we are approching the singular curves on which the hessian matrices have rank deficiency. So the Newton's method complains eventually.
Chia-Hsing Nien <>
Last modified: Tue May 28 13:25:43 1996