Question

Write a computer program using C++ that computes the value of a Lagrange Polynomial and accepts, as input: (n+1) data points (x₀, f(x₀)), (x₁, f(x₁)),...(x_n, f(x_n)).. at value x, which the polynomial is to evaluated. As output, the program should produce a statement that reads, "f(x) = (the value of f(x))". As a test, use the data values (1,2);(-1,1);(0,0);(2,4);(-2,3)

Answer 1

// C++ program that computes the value of a Lagrange Polynomial

#include<bits/stdc++.h>
using namespace std;
int N; //global variable for array size
//interpolation function
// x1 is the new data point whose value is to be evaluated
// n is the no. of known data points
double interpolate(int f[][2], int x1, int n)
{
   double result = 0; // Initialize the result with 0

   for (int i=0; i<n; i++)
   {
       // Compute the terms individually
       double term = f[i][1];
       for (int k=0;k<n;k++)
       {
           if (k!=i)
               term = term*(x1 - f[k][0])/double(f[i][0] - f[k][0]);
       }

       // cumulate terms to find the result
       result += term;
   }

   return result;
}

// main function
int main()
{
   cout<<"Enter size of the input array:";
   cin>>N;
   int f[N][2];
   cout<<"\nEnter data points(as{x,f(x)}):";
   for(int i=0;i<N;i++)
   cin>>f[i][0]>>f[i][1];
cout<<"\nEnter the value of x: ";
int x;
cin>>x;
   cout << "\nValue of f("<<x<<") is : " << interpolate(f, x, N);

/*call our interpolate function with array,value to be calculated and number of known values for interpolation*/
return 0;
}

OUTPUT:

Enter size of the input array:5
Enter data points(as{x,f(x)}):

1 2

-1 1

0 0

2 4

-2 3
Enter the value of x: 2
Value of f(2) is : 4