Program to understand and use Lagrange’s Interpolation for a polynomial to determine functional value of data

Lagrange’s Interpolation for a polynomial is used to determine nature of a polynomial with its degree based upon number of input values. As a polynomial is constructed, it is matched for the given data value to verify or to compute its functional value. This is all done by programming for Lagrange’s Polynomial.

/* To calculate the functional value using Lagrange’s Interpolation */

#include

#include

#include

#include

void main()

{

double n, a, k, value, x[10], f[10], p[10];

clrscr();

cout<<“Enter the no of data:\t”;

cin>>n;

cout<<<<“Enter the input values:\t”;

for(int i=1;i<=n;i++)

{

cin>>x[i];

cout<<<“\t”;

}

cout<<<<“Enter the respective functional values:\t”;

for(i=1;i<=n;i++)

{

cin>>f[i];

cout<<<“\t”;

}

cout<<<“Supply the data whose functional value is to be determined:\t”;

cin>>a;

for(k=1;k<=n;k++)

{

p[k]=1.0;

for(i=1;i<=n;i++)

{

if(i!=k)

p[k]=p[k]*(a-x[i])/(x[k]-x[i]);

}

}

value=0.0;

for(i=1;i<=n;i++)

{

value=value+(p[i]*f[i]);

}

cout<<<<“Required functional value for “<<<” is “<<<“.”;

getch();

}

*To understand and use Lagrange’s Interpolation for a polynomial to determine functional value of data in C++ Programming Language for Numerical Methods for Engineering Students*