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 Branch among the Nb_Branch that have been found. In Solution we have all the solutions that have been found for the branches when the parameter value was param. The change in the parameter value will be at most sensdelta_param and on exit of the procedure param will be set to the new value. sens indicates the direction of change in the parameter value: +1 for an increase, -1 for a decrease.
This procedure returns: