The condition number of a polynomial may be defined either
as the ratio lowest root over largest root or as the ratio
over
where
are the roots of the
polynomial. In the later case the condition number has a value between
0 and 1.
The minimal and maximal values of the condition number of a parametric
polynomial in both form may be calculated using the procedure:
int ALIAS_Min_Max_CN(int Degree, int Nb_Parameter,INTERVAL_VECTOR (* TheCoeff)(INTERVAL_VECTOR &), int Nb_Constraints,INTEGER_VECTOR &Type_Eq, int (* TheMatrix)(INTERVAL_VECTOR &, INTERVAL_MATRIX &), int Has_Matrix, INTERVAL_VECTOR (* IntervalFunction)(int,int,INTERVAL_VECTOR &), int Has_Gradient, INTERVAL_MATRIX (* Gradient)(int, int,INTERVAL_VECTOR &), INTERVAL & TheDomain,INTERVAL_VECTOR & TheDomain_Parameter, int Type, int Nb_Points,int Absolute, int rand,int Iteration, double Accuracy_Variable,double Accuracy,double AccuracyM, INTERVAL &Lowest,INTERVAL &Highest, INTERVAL_MATRIX &Place,int Stop, double *Seuil, int (* Solve_Poly)(double *, int *,double *), int (* Simp_Proc)(INTERVAL_VECTOR &))where the arguments are identical than for the previous procedure except for: