Please code in C or C++

Lagrange Interpolation function

Parameters:

n order of polynomial+1

x - where to evaluate xk[n]

x_values fk[n]

Y_value(true value)

double lagrange (int n, double x, double* xk, double* fk) {

int i, k;

double p, lk;

p = 0.0;

for (k=0; k

lk = 1.0;

for (i=0; i

if (i==k)

continue;

/* accumulate Lk(x) */

lk *= (x - xk[i])/(xk[k] - xk[i]); }

/* accumulate the sum */

p += lk*fk[k]; } r

eturn p; }

//To call your function:

for (k=0; k

xk = y[k];

p = lagrange (order+1 , xk, x, f);

Example output:

Lagrange interpolation MENU 1. Function A 2. Function B 3. Quit Enter your choice: 1 WHEN n=5 K Xk P TRUE VALUE ABSOLUTE ERROR 0 -1.0000000 1.4142140 1.414213562 4.38E-07 1 -0.9500000 1.3802810 1.379311422 9.70E-04 2 -0.9000000 1.3468090 1.345362405 1.45E-03 3 -0.8500000 1.3139990 1.312440475 1.56E-03 4 -0.8000000 1.2820420 1.280624847 1.42E-03 5 -0.7500000 1.2511190 1.25 1.12E-03 6 -0.7000000 1.2213990 1.220655562 7.43E-04 7 -0.6500000 1.1930400 1.192686044 3.54E-04 8 -0.6000000 1.1661900 1.166190379 3.79E-07 9 -0.5500000 1.1409860 1.141271221 2.85E-04 10 -0.5000000 1.1175530 1.118033989 4.81E-04 11 -0.4500000 1.0960050 1.09658561 5.81E-04 12 -0.4000000 1.0764470 1.077032961 5.86E-04 13 -0.3500000 1.0589710 1.059481005 5.10E-04 14 -0.3000000 1.0436600 1.044030651 3.71E-04 15 -0.2500000 1.0305840 1.030776406 1.92E-04 16 -0.2000000 1.0198040 1.019803903 9.73E-08

17 -0.1500000 1.0113680 1.011187421 1.81E-04 18 -0.1000000 1.0053150 1.004987562 3.27E-04 19 -0.0500000 1.0016730 1.00124922 4.24E-04 20 0.0000000 1.0004570 1 4.57E-04 21 0.0500000 1.0016730 1.00124922 4.24E-04 22 0.1000000 1.0053150 1.004987562 3.27E-04 23 0.1500000 1.0113680 1.011187421 1.81E-04 24 0.2000000 1.0198040 1.019803903 9.73E-08 25 0.2500000 1.0305840 1.030776406 1.92E-04 26 0.3000000 1.0436600 1.044030651 3.71E-04 27 0.3500000 1.0589710 1.059481005 5.10E-04 28 0.4000000 1.0764470 1.077032961 5.86E-04 29 0.4500000 1.0960050 1.09658561 5.81E-04 30 0.5000000 1.1175530 1.118033989 4.81E-04 31 0.5500000 1.1409860 1.141271221 2.85E-04 32 0.6000000 1.1661900 1.166190379 3.79E-07 33 0.6500000 1.1930400 1.192686044 3.54E-04 34 0.7000000 1.2213990 1.220655562 7.43E-04 35 0.7500000 1.2511190 1.25 1.12E-03 36 0.8000000 1.2820420 1.280624847 1.42E-03 37 0.8500000 1.3139990 1.312440475 1.56E-03 38 0.9000000 1.3468090 1.345362405 1.45E-03 39 0.9500000 1.3802810 1.379311422 9.70E-04 40 1.0000000 1.4142140 1.414213562 4.38E-07 WHEN n=10 display 41 column table WHEN n=15 display 41 column table MENU 1. Function A 2. Function B 3. Quit Enter your choice: 2 WHEN n=5 display 41 column table WHEN n=10 display 41 column table WHEN n=15 display 41 column table MENU 1. Function A 2. Function B 3. Quit Enter your choice: 3 Exit

Problem Description: Use Lagrange interpolation to interpolate the following functions: (a) f(x) = V1 + x2 (b) f(x) = 1 1+25x2 using a set of n+1 regularly spaced nodes computed by the following equation: 2(k - 1) Xk = -1+ -, k = 1,2,3,......, n +1 n Test your generated polynomial with different orders, n= 5, 10, 20 and compute the interpolation polynomial Pn(x) at 41 regularly spaced points. For each value of xk the Lagrange polynomial approximation is output together with the exact /true value from the math library, also output the absolute error. Problem Description: Use Lagrange interpolation to interpolate the following functions: (a) f(x) = V1 + x2 (b) f(x) = 1 1+25x2 using a set of n+1 regularly spaced nodes computed by the following equation: 2(k - 1) Xk = -1+ -, k = 1,2,3,......, n +1 n Test your generated polynomial with different orders, n= 5, 10, 20 and compute the interpolation polynomial Pn(x) at 41 regularly spaced points. For each value of xk the Lagrange polynomial approximation is output together with the exact /true value from the math library, also output the absolute error