Backward Difference Table Generation Using C Programming


Table of Contents

In numerical analysis, Newton's Backward Interpolation formula relies on Backward Difference Table for interpolating intermediate value.

In this program, we are going to generate backward difference table in c programming language.

C Source Code: Backward Difference Table


#include<stdio.h>
#include<conio.h>

int main()
{
 float x[20], y[20][20];
 int i,j, n;
 clrscr();
 /* Input Section */
 printf("Enter number of data?\n");
 scanf("%d", &n);
 printf("Enter data:\n");
 for(i = 0; i < n ; i++)
 {
  printf("x[%d]=", i);
  scanf("%f", &x[i]);
  printf("y[%d]=", i);
  scanf("%f", &y[i][0]);
 }

 /* Generating Backward Difference Table */
 for(i = 1; i < n; i++)
 {
  for(j = n-1; j > i-1; j--)
  {
   y[j][i] = y[j][i-1] - y[j-1][i-1];
  }
 }

 /* Displaying Backward Difference Table */
 printf("\nBACKWARD DIFFERENCE TABLE\n\n");
 for(i = 0; i < n; i++)
 {
  printf("%0.2f", x[i]);
  for(j = 0; j <= i ; j++)
  {
   printf("\t%0.2f", y[i][j]);
  }
  printf("\n");
 }

 getch(); /* Holding Screen */
 return 0;
}

C Output: Backward Difference Table

Enter number of data?
4
Enter data:
x[0]=0
y[0]=1
x[1]=1
y[1]=2
x[2]=2
y[2]=1
x[3]=3
y[3]=10

BACKWARD DIFFERENCE TABLE

0.00    1.00
1.00    2.00    1.00
2.00    1.00    -1.00   -2.00
3.00    10.00   9.00    10.00   12.00