Mathc initiation/Fichiers c : c22cd1

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	c3d1.c

/* --------------------------------- */
/* save as c3d1.c                    */
/* --------------------------------- */
#include "x_hfile.h"
#include      "fd.h"
/* --------------------------------- */
int main(void)
{
   int n = 6;

double FirstApproximation = 1.5;

 clrscrn();
 
 printf(" The Newton's method :     \n"
        "                     f(x_n) \n"  
        "     x_n+1 = x_n  - ------- \n"
        "                    f'(x_n) \n"
        "\n\n\n\n\n");
 
 printf(" Use Newton's method to approximate \n" 
        " the largest positive real root of :\n\n" 
        " f : x-> %s\n\n\n" 
        " On a graph of f, you can see that, the largest\n" 
        " positive real root of f is between 1.0 and 2.0.\n\n" 
        " Choose x = %.1f as a first approximation.\n\n", 
          feq,FirstApproximation);
 stop();

 clrscrn();
 
 printf(" The Newton's method :     \n"
        "                     f(x_n) \n"  
        "     x_n+1 = x_n  - ------- \n"
        "                    f'(x_n) \n"
        "\n\n\n");
        
 printf(" As a first approximation x = %.1f \n\n"
        " The Newton's method give :        \n\n",FirstApproximation);
        
 p_Newton_s_Method(FirstApproximation, n, f, Df);
 
 printf(" f(%.15f) = %.15f\n\n",  
              Newton_s_Method(FirstApproximation, n, f, Df)
           ,f(Newton_s_Method(FirstApproximation, n, f, Df)));
 stop();

 return 0;
}
/* ---------------------------------- */
/* ---------------------------------- */

Fichier de commande gnuplot :

# ---------------------
# Copy and past this file into the screen of gnuplot
#
#
set zeroaxis lt 3 lw 1
plot [-2.5:2.5] [-6.:6.]\
         x**3 - 3.0*x + 1.0
reset
# ---------------------

Nous pouvons observer que la plus grande racine est comprise entre 1 et 2. Il faut calculer la racine de cette équation x**3 - 3.0*x + 1.0 = 0. On va donc choisir comme première approximation 1.5. On arrêtera les calculs lorsque l'on aura deux valeurs identiques.

Exemple de sortie écran :

 The Newton's method :     
                     f(x_n) 
     x_n+1 = x_n  - ------- 
                    f'(x_n) 





 Use Newton's method to approximate 
 the largest positive real root of :

 f : x-> x**3 - 3.0*x + 1.0


 On a graph of f, you can see that, the largest
 positive real root of f is between 1.0 and 2.0.

 Choose x = 1.5 as a first approximation.

 Press return to continue. 


*********************

 The Newton's method :     
                     f(x_n) 
     x_n+1 = x_n  - ------- 
                    f'(x_n) 



 As a first approximation x = 1.5 

 The Newton's method give :        

 x[1] = 1.500000000000000
 x[2] = 1.533333333333333
 x[3] = 1.532090643274854
 x[4] = 1.532088886241467
 x[5] = 1.532088886237956
 x[6] = 1.532088886237956


 f(1.532088886237956) = -0.000000000000000

 Press return to continue.