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Implementation

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   Contents
Jean-Pierre Merlet 2012-12-20