C Program to implement the Newton- Gregory forward interpolation. Newtons – Gregory forward difference formula is a finite difference identity capable of giving an interpolated value between the tabulated points {fk} in terms of the first value f0 and powers of the forward difference Δ. In this program we used the multidimensional arrays and arrays in c. Read more about C Programming Language .

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#include<stdio.h>

#include<conio.h>

#define MaxN 100

#define Order_of_diff 4

void main ()

{

float arr_x[MaxN+1], arr_y[MaxN+1], numerator=1.0, denominator=1.0, x, y, p, h, diff_table[MaxN+1][Order_of_diff+1];

int i,j,n,k;

clrscr();

printf("Enter the value of n n");

scanf("%d",&n);

printf("Enter the values of x and y");

for(i=0; i<=n; i++)

scanf("%f%f", &arr_x[i], &arr_y[i]);

printf("Enter the value of x at which value of y is to be calculated");

scanf("%f", &x);

h=arr_x[1]-arr_x[0];

for(i=0; i<=n-1; i++)

diff_table[i][1]=arr_y[i+1]-arr_y[i];/*Creating the difference table and calculating first order differences*/

for(j=2; j<=Order_of_diff; j++)/*Calculating higher order differences*/

for(i=0; i<=n-j; i++)

diff_table[i][j]=diff_table[i+1][j-1] - diff_table[i][j-1];

i=0;

while(!(arr_x[i]>x)) /* Finding x0 */

i++;

i--;

p=(x-arr_x[i])/h;

y=arr_y[i];

for (k=1; k<=Order_of_diff; k++)

{

numerator *=p-k+1;

denominator *=k;

y +=(numerator/denominator)*diff_table[i][k];

}

printf("When x=%6.1f, y=%6.2fn",x, y);

getch();

}

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