Given a set of data-points , the Lagrange Interpolating Polynomial is a polynomial of degree , such that it passes through all the given data-points.

It is given as,

where are the data-points.
and,

CODE:

/**********************************
******LAGRANGE INTERPOLATION*******
**********************************/
#include<stdio.h>

/*Function to evaluate Li(x)*/

double Li(int i, int n, double x[n+1], double X){
	int j;
	double prod=1;
    for(j=0;j<=n;j++){
        if(j!=i)
        	prod=prod*(X-x[j])/(x[i]-x[j]);
	}
        return prod;
}

/*Function to evaluate Pn(x) where Pn is the Lagrange interpolating polynomial of degree n*/

double Pn(int n, double x[n+1], double y[n+1], double X){
	double sum=0;
	int i;
    for(i=0;i<=n;i++){
        sum=sum+Li(i,n,x,X)*y[i];
    }
    return sum;
}
main(){
	int i,n;  //n is the degree
	printf("Enter the number of data-points:\n");
	scanf("%d",&n);  //no. of data-points is n+1
	n=n-1;
	//Arrays to store the (n+1) x and y data-points of size n+1
	double x[n+1];
	double y[n+1];
	printf("Enter the x data-points:\n");
	for(i=0;i<n+1;i++){
		scanf("%lf",&x[i]);
	}
	
	printf("Enter the y data-points:\n");
	for(i=0;i<n+1;i++){
		scanf("%lf",&y[i]);
	}
	
	double X;  //value of x for which interpolated value is required
	printf("Enter the value of x for which you want the interpolated value of y(x):\n");
	scanf("%lf",&X);
	printf("The interpolated value is %lf",Pn(n,x,y,X));
}

OUTPUT:

f(x)=1/x

f(x)=x^2

YouTube Tutorial:

Android App:

https://play.google.com/store/apps/details?id=com.bragitoff.lagrangeinterpolatingpolynomial

References and Resources:

http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html
https://en.wikipedia.org/wiki/Lagrange_polynomial
http://wmueller.com/precalculus/families/lagrange.html

Manas Sharma

Ph.D. researcher at Friedrich-Schiller University Jena, Germany. I’m a physicist specializing in computational material science. I write efficient codes for simulating light-matter interactions at atomic scales. I like to develop Physics, DFT, and Machine Learning related apps and software from time to time. Can code in most of the popular languages. I like to share my knowledge in Physics and applications using this Blog and a YouTube channel.

manas.bragitoff.com/