int Newton_Second_Bound_Interval(int Degree,VECTOR &Coeff,double *bound);with:

`Degree`: degree of the polynomial`Coeff`: the`Degree+1`coefficients of the polynomial in increasing degree`bound`: upper bound on the absolute value of the roots

int Newton_Second_Bound_Inverse_Interval(int Degree,VECTOR &Coeff,double *bound);An upper and lower bound on the absolute value of the roots may be compute by:

int Newton_Second_Bound_Interval(int Degree,VECTOR &Coeff,INTERVAL &Bound);In that case if

Similar procedures exist for interval polynomial:

int Newton_Second_Bound_Interval(int Degree,INTERVAL_VECTOR &Coeff,INTERVAL &Bound); int Newton_Second_Bound_Inverse_Interval(int Degree,INTERVAL_VECTOR &Coeff,INTERVAL &Bound); int Newton_Second_Bound_Interval(int Degree,INTERVAL_VECTOR &Coeff,INTERVAL &L, INTERVAL &U);where

`Bound`: upper or lower bound on the absolute value of the root of the polynomials`L`,`U`: if`L`=[a,b] then the absolute value of the roots of any polynomial in the set is greater than a while some polynomial have root greater than b. Conversely if`U`=[a,b] the absolute value of the roots of any polynomial in the set is lower than b while some polynomial have root lower than a.