The procedure that allow to determine the next point on a branch is implemented as:

int Certified_Newton(int Nb_Var,int Dimension_Eq,int Nb_Branch,int Branch, INTERVAL_VECTOR (* Func)(int,int,INTERVAL_VECTOR &), INTERVAL_MATRIX (* Gradient)(int, int,INTERVAL_VECTOR &), INTERVAL_MATRIX (* Hessian)(int, int, INTERVAL_VECTOR &), double Accuracy_Var,double Accuracy, double *param,double delta_param,double min_delta_param, int sens,MATRIX &Solution)This procedure determine if it possible to find a new point on the branch numbered

This procedure returns:

- -1, -4: even with a change of the parameter value of
`min_delta_param`we cannot either distinguish two solutions or Kantorovitch has failed to give a positive answer. But this does not mean in general that a singularity occurs. - -2: for systems having more equations than unknowns the solution that has been obtained with Newton for the square system of equations failed to cancel the remaining equations
- -3: Newton has not converged (should not occur)
- -10: singular point
- 1, 2: procedure has succeeded