Question

Make a program for LAGRANGE INTERPOLATION METHOD using C++ program and can be evaluated both polynomial and Transcendental Functions.

Answer 1

In this C++ program, x and y are two array for storing x data and y data respectively. xp is interpolation point given by user and output of Lagrange interpolation method is obtained in yp.

#include<iostream>
#include<conio.h>

using namespace std;

int main()
{
         float x[100], y[100], xp, yp=0, p;
         int i,j,n;

         /* Input Section */
         cout<<"Enter number of data: ";
         cin>>n;
         cout<<"Enter data:"<< endl;
         for(i=1;i<=n;i++)
         {
                  cout<<"x["<< i<<"] = ";
                  cin>>x[i];
                  cout<<"y["<< i<<"] = ";
                  cin>>y[i];
         }
         cout<<"Enter interpolation point: ";
         cin>>xp;

         /* Implementing Lagrange Interpolation */
         for(i=1;i<=n;i++)
         {
                  p=1;
                  for(j=1;j<=n;j++)
                  {
                           if(i!=j)
                           {
                                p = p* (xp - x[j])/(x[i] - x[j]);
                           }
                  }
                  yp = yp + p * y[i];
         }
         cout<< endl<<"Interpolated value at "<< xp<< " is "<< yp;

         return 0;
}