Backward Differences Generation For Interpolation

C Program for backward differences generation for interpolation

#include

#include

#include

#include

void main()

{

double y[20], x[20];

int I,j,k,num;

printf("\n Backward differences generation for interpolation");

printf("\n\n Enter the value of x and y(x) ");

scanf("%d",&num);

for(i=0;i

{

printf("\n Enter value of x %d:",i);

scanf("%lf”,&x[i]);

printf("\n Enter value of y %d:",i);

scanf("%lf",&y[i][0]);

}

k=0;

for(j=1;j

{

k++;

for(i=num;i>=k;i--)

{

y[i][j]=y[i][j-1]-y[i-1][j-1];

}

}

k=num;\

printf("\n Backward difference table\n");

printf("\n\tx\ty\tDy\tD2y\tD3y\tD4y\tD5y\tD6y\n");

for(i=0;i

{

printf("\nx%d=%4.2lf",I,x[i]);

for(j=0;j

{

printf("\t%4.2lf",y[i][j]);

}

printf("\n");

}

}

Output

Backward differences generation for interpolation

Enter the value of x and y =f(x):3

Enter value of x0:1

Enter value of x0:1

Enter value of x1:2

Enter value of x1:2

Enter value of x2:3

Enter value of x2:3

The backward difference table is as follows

X       y        Dy     D2y   D3y   D4y   D5y   D6y

X0     =1.00          1.00

X1     =2.00          2.00            1.00

X2     =3.00          3.00            1.00            0.00

C Program for backward differences generation for interpolation

#include

#include

#include

#include

 void main()

{

   double y[20][20], x[20];

   int i, j, k, num;

   printf("\nBackwad differences generation for Interpolation");

   printf("\n\nEnter the value of x and y = f(x)");

   scanf("%d", &num);

    for (i = 0; i < num; i++)

    {

      printf("\nEnter value of x%d : ", i);

      scanf("%lf", &x[i]);

      printf("\nEnter value of y%d : ", i);

      scanf("%lf", &y[i][0]);

    }

   k = 0;

   for (j = 1; j < num; j++)

   {

      k++;

      for (i = num - 1; i >= k; i--)

      {

         y[i][j] = y[i][j - 1] - y[i - 1][j - 1];

      }

   }

   k = num;

   printf("\nBackward Difference Table\n");

   printf("\n\tx\ty\tDy\tD2y\tD3y\tD4y\tD5y\tD6y\n");

   for (i = 0; i < num; i++)

   {

      printf("\nx%d    = %4.2lf", i, x[i]);

      for (j = 0; j < i + 1; j++)

     {

         printf("\t%4.2lf ", y[i][j]);

      }

      printf("\n");

   }

}

Output

Backwad differences generation for Interpolation

Enter the value of x and y = f(x) : 3

Enter value of x0 : 1

Enter value of y0 : 1

Enter value of x1 : 2

Enter value of y1 : 2

Enter value of x2 : 3

Enter value of y2 : 3

The backward difference table is as follows . . .

x    y    Dy    D2y    D3y    D4y    D5y    D6y

x0    = 1.00    1.00

x1    = 2.00    2.00     1.00

x2    = 3.00    3.00     1.00     0.00