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int Kantorovitch(int m,VECTOR (* TheFunction)(VECTOR &),MATRIX (* Gradient)(VECTOR &),
INTERVAL_MATRIX (* Hessian)(int, int, INTERVAL_VECTOR &),VECTOR &Input,double *eps)
- m: number of variables and unknowns
- TheFunction: a procedure to compute the value of the
equations for given values of the unknowns.
This procedure has one arguments which is the
value of the unknowns in vector form
- Gradient: a procedure to compute the Jacobian matrix of
the system in
matrix form. This procedure has one arguments
which is the
value of the unknowns in vector form
- Hessian: a procedure to compute the Hessian for the
equation for interval value input.
This procedure compute the m X n, n Hessian
matrix in interval matrix form.This procedure has
3 arguments l1,l2,X.
The function should return the value of the Hessian of
the equations from l1 to l2
The Hessian of the first equation is stored in
hess(1..n,1...n), the Hessian of
the second equation in
hess(n+1..2n,1..n) and so
on
- Input: the value of the variables which constitute the center
of the convergence ball
Another implementation, consistent with the procedure used in the
general solving algorithm (see section 2.5) is:
int Kantorovitch(int m,
INTERVAL_VECTOR (* TheIntervalFunction)(int,int,INTERVAL_VECTOR &),
INTERVAL_MATRIX (* Gradient)(int, int, INTERVAL_VECTOR &),
INTERVAL_MATRIX (* Hessian)(int, int, INTERVAL_VECTOR &), VECTOR &Input,double *eps)
There is also an implementation of Kantorovitch theorem for univariate
polynomial, see section 5.2.12.
Next: Return code
Up: Kantorovitch theorem
Previous: Mathematical background
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Jean-Pierre Merlet
2012-12-20