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Implementation

The syntax of the algorithm is:

int Kantorovitch(int Degree,VECTOR &Coeff,REAL Input,double *eps)
with
• Degree: degree of the polynomial
• Coeff: coefficients of the polynomial ordered along increasing degree
• Input: center of the interval in which an unique solution occur
• eps: half width of the solution interval
If this procedure returns 1, then there is an unique solution in the interval [Input-eps,Input+eps]. There is also an implementation of Kantorovitch theorem for interval polynomial:

int Kantorovitch(int Degree,INTERVAL_VECTOR &Coeff,REAL Input,double *eps)
If this procedure returns 1, then any polynomial in the set of interval polynomial has an unique solution in the interval [Input-eps,Input+eps]. There is also an implementation which take into account rounding errors:

int Kantorovitch_Fast_Safe(int Degree,INTERVAL_VECTOR &Coeff,REAL Input,double *eps)
in which "safe" interval value of the coefficients have been pre-computed.

Jean-Pierre Merlet 2012-12-20