Oct 14, 2011

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 .

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#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;

 printf("Enter the value of n \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);

 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];

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

 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=%6.2f\n",x, y);

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