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LAGRANGE'S INTERPOLATION METHOD FOR FINDING f(X)

Posted By: Shannon Hughes     Category: C Programming     Views: 43713

Write a program of LAGRANGE'S INTERPOLATION METHOD FOR FINDING f(X).

Code for LAGRANGE'S INTERPOLATION METHOD FOR FINDING f(X) in C Programming

#include<stdio.h>
#include<conio.h>
#include<math.h>
void main()
{
  float x[10],y[10],temp=1,f[10],sum,p;
  int i,n,j,k=0,c;
  clrscr();
  printf("\nhow many record you will be enter: ");
  scanf("%d",&n);
  for(i=0; i<n; i++)
  {
   printf("\n\nenter the value of x%d: ",i);
   scanf("%f",&x[i]);
   printf("\n\nenter the value of f(x%d): ",i);
   scanf("%f",&y[i]);
  }
  printf("\n\nEnter X for finding f(x): ");
  scanf("%f",&p);

  for(i=0;i<n;i++)
  {
    temp = 1;
    k = i;
    for(j=0;j<n;j++)
    {
      if(k==j)
      {
        continue;
      }
      else
      {
        temp = temp * ((p-x[j])/(x[k]-x[j]));
      }
    }
    f[i]=y[i]*temp;
  }

  for(i=0;i<n;i++)
  {
     sum = sum + f[i];
  }
  printf("\n\n f(%.1f) = %f ",p,sum);
  getch();
}


/*
______________________________________

OUT PUT
______________________________________

how many record you will be enter: 4


enter the value of x0: 0


enter the value of f(x0): 0


enter the value of x1: 1


enter the value of f(x1): 2


enter the value of x2: 2


enter the value of f(x2): 8


enter the value of x3: 3


enter the value of f(x3): 27


Enter X for finding f(x): 2.5


f(2.5) = 15.312500


*/
  
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Shannon Hughes
Shannon Hughes author of LAGRANGE'S INTERPOLATION METHOD FOR FINDING f(X) is from London, United Kingdom.
 
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Giannis Kostas from Greece Comment on: Aug 09
Hello,
I am new to applied cryptography and I have some questions concerning the above code and in general Lagrange method and crypto. If the points of the polynomial are selected from a Galois Field (e.g. 2^128) will the Lagrange method be able to estimate the right polynomial? I ask that because in your implementation, you used float numbers instead of integers that GF demands. Also, is there significant difference in using integer arithmetic than finite filed arithmetic? And if there is, when is preferred to use one or the other?
Thank you for your time,
Yiannis

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