NEWTON'S BACKWARD INTERPOLATION FORMULA IN C WITH EXPLANATION

Backward Interpolation.Interpolation is the technique of estimating the value of a function for any intermediate value of the independent variable, while the process of computing the value of the function outside the given range is called extrapolation.

newtons backword interpolation formula



// C Program to interpolate using 
// newton backward interpolation 
#include <stdio.h> 
#include<math.h>
int i,j;
// Calculation of u mentioned in formula 
float backword(float u, int n) 
{ 
 float temp = u; 
 for (i = 1; i < n; i++) 
  temp = temp * (u + i); 
 return temp; 
} 

// Calculating factorial of given n 
int fact(int n) 
{ 
 int f = 1; 
 for ( i = 2; i <= n; i++) 
  f *= i; 
 return f; 
} 

int main() 
{ 
 // number u want to in 
 int n = 5; 
 float x[] = { 2000, 2010, 2020,  2030, 2040 }; 
     
//input 
 float y[n][n]; 
 y[0][0] = 654; 
 y[1][0] = 76; 
 y[2][0] = 83; 
 y[3][0] = 93; 
 y[4][0] = 105; 


 for (i = 1; i < n; i++) { //finding table
  for ( j = n - 1; j >= i; j--) 
   y[j][i] = y[j][i - 1] - y[j - 1][i - 1]; 
 } 


 for ( i = 0; i < n; i++) { //displlaying table
  for ( j = 0; j <= i; j++) 
   printf("%f ", y[i][j] );
  printf("\n");
   
 } 

 
 float value = 2035; //value of unknown

//finding sum 
 float sum = y[n - 1][0]; 
 float u = (value - x[n - 1]) / (x[1] - x[0]); 
 for ( i = 1; i < n; i++) { 
  sum = sum + (backword(u, i) * y[n - 1][i]) / 
         fact(i); 
 } 

 printf("\n Value at =%f is=%f ",value,sum);
  printf("\n"); 
 return 0; 
} 

OUTPUT 

want to run this program ?

click here to run this online 

#this progaran is running through theCODECHEF IDE

• Facebook
• Twitter
• Google+
• Pinterest

PLZ... Share This Site To Your Contacts.....










• share our blog
• please don't forget to share our blog and also subscribe to our youtube channel.. click here to subscribe our youtube channel
• click here to  follow our Facebook page




With regards

Team EveTech