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Improvement of the function evaluation and of the Jacobian

An improved value of the Jacobian is obtained by taking account its derivative in the procedure:

 
INTERVAL_MATRIX Compute_Best_Gradient_Interval(int Dimension,
                    int Dimension_Eq,
                    INTERVAL_MATRIX (* Gradient)(int, int, INTERVAL_VECTOR &), 
                    INTERVAL_MATRIX (* Hessian)(int, int, INTERVAL_VECTOR &), 
                    INTERVAL_VECTOR &Input,
                    int Exact,INTERVAL_MATRIX &InGrad)
where

To compute only the best value of the jacobian element at l-th row nad j-th column you may use:

 
INTERVAL Compute_Best_Gradient_Interval_line(int l,int j,int Dim,
                    int Dimension_Eq,
                    INTERVAL_MATRIX (* Gradient)(int, int, INTERVAL_VECTOR &), 
                    INTERVAL_MATRIX (* Hessian)(int, int, INTERVAL_VECTOR &), 
                    INTERVAL_VECTOR &Input,int Exact)

We may also obtain the best interval evaluation of the equations through the procedure

 
INTERVAL_VECTOR Compute_Interval_Function_Gradient(int Dimension,
                    int Dimension_Eq,
                    INTERVAL_VECTOR (* TheIntervalFunction)(int,int,INTERVAL_VECTOR &), 
                    INTERVAL_MATRIX (* Gradient)(int, int, INTERVAL_VECTOR &), 
                    INTERVAL_MATRIX (* Hessian)(int, int, INTERVAL_VECTOR &), 
                    INTERVAL_VECTOR &Input, int Exact)



Jean-Pierre Merlet 2012-12-20