Reference no: EM132212262

Question :

Write a Python procedure to approximate the Gaussian function exp(-(x/3)² ) in the range -8 ? +8 using Chebyshev polynomials.

The Chebyshev module is as follows:

import numpy as np

import matplotlib.pyplot as plt

def chebyshev(x,n):
x2 = x**2
if n == 0:
return x*0.+1.0
elif n == 1:
return x
elif n == 2:
return 2*x2 - 1.0
elif n ==3:
return (4*x2-3)*x
elif n == 4:
return (8*x2 - 8)*x2 + 1.0
elif n == 5:
return ((16*x2 -20)*x2 + 5)*x
elif n == 6:
return ((32*x2-48)*x2 + 18)*x2 - 1
elif n == 7:
return (((64*x2 - 112)*x2 + 56)*x2 -7)*x
elif n == 8:
return (((128*x2 - 256)*x2 + 160)*x2 -32)*x2 + 1
elif n == 9:
return ((((256*x2 - 576)*x2 + 432)*x2 - 120)*x2 + 9)*x
elif n == 10:
return ((((512*x2 - 1280)*x2 + 1120)*x2 - 400)*x2 + 50)*x2 - 1.0
elif n == 11:
return (((((1024*x2 - 2816)*x2 + 2816)*x2 - 1232)*x2 + 220)*x2 -11)*x
else:
print( "Chebyshev order must be in range 0..11 value give is ")
exit()

if __name__ == '__main__':
x = np.linspace(-1,1.0,100)
plt.figure(1)
for i in range(12):
a = chebyshev(x,i)
plt.plot(x,a)

plt.show()