# C Program to implement the Newton- Gregory forward interpolation

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 .

`/************************************************************ You can use all the programs on  www.c-program-example.com* for personal and learning purposes. For permissions to use the* programs for commercial purposes,* contact [email protected]* To find more C programs, do visit www.c-program-example.com* and browse!* *                      Happy Coding***********************************************************/#include<stdio.h>#include<conio.h>#define MaxN 100#define Order_of_diff 4void 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-arr_x; for(i=0; i<=n-1; i++)  diff_table[i]=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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