To Construct the New Data Points Using Gauss's Backward Method of Interpolation - C Data Structure

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Description

To Construct the New Data Points Using Gauss's Backward Method of Interpolation

Demo Code

#include <stdio.h>
#define MAX 20/*from   ww w. j  a v  a  2  s .c  o  m*/

void main()
{
  int i, j, terms=10;
  
  float ax[MAX], ay[MAX], x, y = 0, h, p;
  
  float diff[MAX][5], y1, y2, y3, y4;

  printf("\nEnter the values of x upto 2 decimal points.\n");
  
  for (i=0; i<terms; i++) {
    printf("Enter the value of x%d: ", i+1);
    scanf("%f",&ax[i]);
  }
  printf("\nNow enter the values of y upto 4 decimal points.\n");
  
  for (i=0; i < terms; i++) {
    printf("Enter the value of y%d: ", i+1);
    scanf("%f", &ay[i]);
  }
  
  x = 20;
  
  h = ax[1] - ax[0];
  
  for(i=0; i < terms-1; i++)
    diff[i][1] = ay[i+1] - ay[i];
  
  for(j=2; j <= 4; j++)
    for(i=0; i < terms-j; i++)
      diff[i][j] = diff[i+1][j-1] - diff[i][j-1];
  
  i = 0;
  do {
    i++;
  } while (ax[i] < x);
  i--;
  p = (x - ax[i]) / h;
  y1 = p * diff[i-1][1];
  y2 = p *(p+1) * diff[i-1][2]/2;
  y3 = (p+1) * p * (p-1) * diff[i-2][3]/6;
  y4 = (p+2) * (p+1) * p * (p-1) * diff[i-3][4]/24;
  y = ay[i] + y1 + y2 + y3 + y4;
  printf("\nFor x = %6.2f,      y = %6.4f ", x, y);

}

Result


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