RMT-Assignment

FIBONACCI METHOD

#include<stdio.h>
float Fx(float x)
{
   return x*x -2*x;
}
int main()
{
   float n, L, R;
   float X1,X2,F1;
   int x;
   printf("Enter value of N ");
   scanf("%d",&x);
   printf("Enter Lower limits ");
   scanf("%f",&L);
   printf("Enter Upper limits ");
   scanf("%f",&R);
   float Fx1, Fx2;
   
   float F[x+1];
   F[0] = 1;
   F[1] = 1;
   char Q ;
   for (int i = 2; i < x + 1; i++)
   {
      F[i] = F[i-1]+F[i-2];
   }
   printf ("K\t F*\t L\t R\t X1\t X2\t Fx1\t Fx2\tL/R \n"); 
   for(int k = 1; k <=x; k++)
   { 
      F1=F[x-k]/F[x-k+1];
      X2 = L + F1*(R - L);
      X1 = L + R - X2;
      Fx1 = Fx(X1);
      Fx2 = Fx(X2);
      if(Fx1>Fx2)
      {
         Q = 'R';
      }
      if(Fx2>=Fx1)
      {
         Q = 'L';
      }
      if(F1==1)
      printf("%d\t%.2f\t%.2f\t%.2f     \n",k,F1,L,R); 
      else
      printf("%d\t%.2f\t%.2f\t%.2f\t%.2f\t%.2f\t%.2f\t%.2f\t %c\n",k,F1,L,R,X1,X2,Fx1,Fx2,Q); 
      if(Fx1>Fx2)
      {
         L = X1;
      }
      if(Fx2>=Fx1)
      {
         R = X2;
      }
   }
      float xmin = (R + L) / 2;
      float Fxmin = Fx(xmin);
      printf("xmin = %.3f \nfxmin = %.3f\n",xmin,Fxmin);
   return 0;
}

OUTPUT

Enter value of N 5
Enter Lower limits 1 2
Enter Upper limits K     F*      L       R       X1      X2      Fx1     Fx2    L/R 
1       0.63    1.00    2.00    1.38    1.63    -0.86   -0.61    L
2       0.60    1.00    1.63    1.25    1.38    -0.94   -0.86    L
3       0.67    1.00    1.38    1.13    1.25    -0.98   -0.94    L
4       0.50    1.00    1.25    1.13    1.13    -0.98   -0.98    L
5       1.00    1.00    1.13
xmin = 1.063
fxmin = -0.996

GOLDEN SEARCH METHOD

#include<stdio.h>
float Fx(float x)
{
    return x*x - 1.5*x ;
}
int main()
{
    float n, L, R;
    float X1,X2,F1;
    printf("Enter tolerance ");
    scanf("%f",&n);
    printf("Enter Lower limits ");
    scanf("%f",&L);
    printf("Enter Upper limits ");
    scanf("%f",&R);
    float Fx1, Fx2;
    char Q ;
    int k = 0;
    printf("K\t L\t R\t X1\t X2\t Fx1\t Fx2\t L/R \n");
    float L1 = L;
    float R1 = R;
    while((R1-L1)> n)
    {
        R1 = R;
        L1 = L;
        k++;
        F1 = 1 / 1.618;
        X2 = L + F1 * (R - L);
        X1 = L + R - X2;
        Fx1 = Fx(X1);
        Fx2 = Fx(X2);
        if (Fx1 > Fx2)
        Q = 'R';
        if(Fx2>=Fx1)
        Q = 'L';
        if((R-L)<= n){
        printf("%d\t%.2f\t%.2f \n",k,L,R);
        break;
        }
        else
        printf("%d\t%.2f\t%.2f\t%.2f\t%.2f\t%.2f\t%.2f\t %c\n",k,L,R,X1,X2,Fx1,Fx2,Q); 
        if(Fx1>Fx2)
        {
        L = X1;
        }
        if(Fx2>=Fx1)
        {
        R = X2;
        }
    }
        float xmin = (R + L) / 2;
        float Fxmin = Fx(xmin);
        printf("xmin = %.3f \nfxmin = %.3f\n",xmin,Fxmin);
    return 0;  
}

OUTPUT

Enter tolerance 0.15
Enter Lower limits 1 2 
Enter Upper limits K     L       R       X1      X2      Fx1     Fx2     L/R 
1       1.00    2.00    1.38    1.62    -0.16   0.19     L
2       1.00    1.62    1.24    1.38    -0.33   -0.16    L
3       1.00    1.38    1.15    1.24    -0.41   -0.33    L
4       1.00    1.24    1.09    1.15    -0.45   -0.41    L
5       1.00    1.15
xmin = 1.073
fxmin = -0.458