Inflation and Newton scheme

For the distance equations we use a specific procedure for the inflation method (see section 3.1.6). Indeed in that case it is possible to calculate directly the diameter of the largest ball centered at an approximation of a solution that contains one and only one solution. The procedure is:

 
int ALIAS_Epsilon_Inflation(int Dimension,int Dimension_Eq,
      INTEGER_MATRIX &APOW,MATRIX &ACONS,
      VECTOR &LI,
      int NB_EQV,int NB_VARV,MATRIX &AVARV,
      VECTOR &Amid,
      INTERVAL_VECTOR &P,
      INTERVAL_VECTOR &PP1,
      int type,double epsilon,
      int (* Simp_Proc)(INTERVAL_VECTOR &))

We have also a specific implementation of the Newton scheme:

 
int Newton_Fast(int Dimension,int Dimension_Eq,
                   INTEGER_MATRIX &APOW,MATRIX &ACONS,VECTOR &LI,
                   int NB_EQV,int NB_VARV,MATRIX &AVARV,
                   VECTOR &Input,double Accuracy,int Max_Iter,VECTOR &Residu)