Implement the Newton’s interpolation using divided difference table.

#include

#include

#include

void main ()

{

  float x [10], y [10] [10], sum, p, u, temp;

  int i,n,j,k=0,f,m;

  float fact(int);

  clrscr();

  printf("\n How many points?? ");

  scanf("%d",&n);

  for(i=0; i

  {

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

   scanf("%f",&x[i]);

   printf("\n\nenter the value of f(x%d): ",i);

   scanf("%f",&y[k][i]);

  }

  printf("\n\nEnter X for finding f(x): ");

  scanf("%f",&p);

  for(i=1;i

  {

    k=i;

    for(j=0;j

    {

     y[i][j]=(y[i-1][j+1]-y[i-1][j])/(x[k]-x[j]);

     k++;

    }

  }

  printf("\n_____________________________________________________\n");

  printf("\n  x(i)\t   y(i)\t    y1(i)    y2(i)    y3(i)    y4(i)");

  printf("\n_____________________________________________________\n");

  for(i=0;i

  {

    printf("\n %.3f",x[i]);

    for(j=0;j

    {

     printf("   ");

     printf(" %.3f",y[j][i]);

    }

   printf("\n");

  }

  i=0;

  do

  {

   if(x[i]

    k=1;

   else

    i++;

  }while(k != 1);

  f=i;

  sum=0;

  for(i=0;i

  {

   k=f;

   temp=1;

   for(j=0;j

   {

    temp = temp * (p - x[k]);

    k++;

   }

    sum = sum + temp*(y[i][f]);

  }

  printf("\n\n f(%.2f) = %f ",p,sum);

  getch();

}