IN C LANGUAGE!

Create a program that interpolate a polynomial using lagrange interpolation by satisfying all these requirement:

a.Using function:

double lagrange(double x_int[ ], double y_int[ ], int n, double x) which calculates the value of the n-th order lagranges polynomial Pn(x) defined for the set of nodes , for a given value of x.

b. Create an input file interpolation_data.ini on the disk containing :

5 // order of P n (x)

0.0 1.0 // x_int(0) , y_int(0)

1.0 3.0

3.0 -2.0

5.0 -5.0

8.0 -1.0

10.0 2.0 // x_int(n) , y_int(n)

c. In the main function, write the following actions:

? It opens and reads the file interpolation_data.ini

? It calculates the interpolation polynomial at 101 equally spaced points in the closed interval [x(0),x(n)].

? It opens and writes the output disk file interpolation_results.dat in the following manner:

......................................

(0), y (0), n), y(n) (0), y (0), n), y(n)