Newton’s Divided Difference Formula
#include<stdio.h>
#include<conio.h>
int main (void)
{
int i,j,n;
float xp,fp,sum,pi,x[10],f[10],a[10],d[10][10];
printf("Enter the number of data points: ");
scanf("%d",&n);
printf("Enter the value of x: ");
for(i=1;i<=n;i++)
scanf("%f",&x[i]);
printf("Enter the value of f(x): ");
for(i=1;i<=n;i++)
scanf("%f",&f[i]);
for(i=1;i<=n;i++)
d[i][1]=f[i];
for(j=2;j<=n;j++)
{
for(i=1;i<=n-j+1;i++)
d[i][j]=(d[i+1][j-1]-d[i][j-1])/(x[i+j-1]-x[i]);
}
for(j=1;j<=n;j++)
a[j]=d[1][j];
printf("Input the value of xp: ");
scanf("%f",&xp);
sum=a[1];
for(i=2;i<=n;i++)
{
pi=1.0;
for(j=1;j<=i-1;j++)
pi=pi*(xp-x[j]);
sum=sum+a[i]*pi;
}
fp=sum;
printf("\n\nNewton interpolation: \n");
printf("at x = %f is %f ",xp,fp);
getch();
}