Implementation

The Cassini bounds may be obtained with the procedure:

 
int Cassini_Simplification(INTERVAL_MATRIX &A,int Size, 
                  int Type_Matrix, INTERVAL &Input)

where

• A: the matrix
• Size: the dimension of the matrix
• Type: 0 if the matrix is not available, 2 if the matrix is symmetrical, 1 otherwise
• Input: an estimation of the bounds of the roots

The procedure will return -1 if there is no intersection between Input and the Cassini bounds, 1 if there Input has been improved, 0 otherwise.

This procedure may also be called with:

 
int Cassini_Simplification(int (* TheMatrix)(INTERVAL_VECTOR &, INTERVAL_MATRIX &),
      INTERVAL_VECTOR &Param,int Size, int Type_Matrix, INTERVAL &Input)

where TheMatrix is a procedure that compute the elements of the matrix according to the interval value of the parameters Param.