C Program Of NA Using Divide Deference

/* Newton Divided difference formula */
# include <stdio.h>
# include <conio.h>
# define MAX 20
void main()
{
int i,j,n;
float x[MAX],fx[MAX][MAX],xp,u,sum=0;
printf("Newton Divided Difference formula \n");
printf("Enter No. of data points : ");
scanf("%d",&n);
printf("Enter values of X and f(x) set by set each at once \n");
for(i=1;i<=n;i++)
scanf("%f%f",&x[i],&fx[i][1]);
printf("Enter value of X at which interpolation is required : ");
scanf("%f",&xp);
for(i=2;i<=n;i++)
for(j=1;j<=n-i+1;j++)
fx[j][i]=(fx[j+1][i-1]-fx[j][i-1])/(x[j+i-1]-x[j]);
printf("-------------------------------------------------------------------\n");
printf("X F(x) ");
for(i=1;i<n;i++)
printf("y%d ",i);
printf("\n-----------------------------------------------------------------\n");
for(i=1;i<=n;i++)
{
printf("%4.2f\t ",x[i]);
for(j=1;j<=n-i+1;j++)
printf("%4.2f ",fx[i][j]);
printf("\n");
}
printf("\n-----------------------------------------------------------------\n");
sum=fx[1][1];
for(i=2;i<=n;i++)
{
u=1;
for(j=1;j<i;j++)
u=u*(xp-x[j]);
u=u*fx[1][i];
sum=sum+u;
}
printf("For %3.2f Interpolated value = %4.2f",xp,sum);
getch();
}
OUTPUT
Newton Divided Difference formula
Enter No. of data points : 5
Enter values of X and f(x) set by set each at once
-1 3
0 -6
3 39
6 822
7 1611
Enter value of X at which interpolation is required : 4
------------------------------------------------------------------------------
X F(x) y1 y2 y3 y4
-----------------------------------------------------------------------------
-1.00 3.00 -9.00 6.00 5.00 1.00
0.00 -6.00 15.00 41.00 13.00
3.00 39.00 261.00 132.00
6.00 822.00 789.00
7.00 1611.00
-----------------------------------------------------------------------------
For 4.00 Interpolated value = 138.00