if __name__ == "__main__":
N = 9 # number of points
interval = [-5, 5]
cheb_zeros = chebyshev(interval[0], interval[1],
N) # retrieve the chebyshev zeros
values = [f(x) for x in cheb_zeros] # calculate the function for the zeros
print("The interpolation points are as follows:")
print(cheb_zeros)
print("Respectively, the function value at these points are:")
print(values)
P = pb1.newton_interpolation(values, cheb_zeros)
X = cheb_zeros
print("This gives the following interpolation polynomial:")
pb1.print_polynomial(P, X)
max_diff = 0
max_x = 0
poly_values = zeros(1001)
x = linspace(interval[0], interval[1], 1001)
for i in range(1001):
x_coord = x[i]
y_coord = pb1.get_value_of_polynomial(P, X, x_coord)
fx = f(x_coord)
if abs(fx - y_coord) > max_diff:
zeros(upper_bound+1 - lower_bound)]
for N in N_values: # Loop as required by problem
max_error = [0, 0, 0] # Used store the maximum error of each interpolation
max_x = [0, 0, 0] # Used to store the abscicas at which the maximum error occurs
# Generating the ordinates and absciccas
interval = [-5, 5]
spacing = 10 / N
points = [interval[0] + spacing / 2 + spacing * m for m in range(N)] # creates the absiccas
values = [f(x) for x in points] # creates the ordinates
# Newton approximation:
newton_poly = pb1.newton_interpolation(values, points) # This gives us our newton_polynomial
# Newton with Chebyshev zeros:
cheb_zeros = pb2.chebyshev(-5, 5, N) # Retrieves the Chebyshev zeros
cheb_values = [f(x) for x in cheb_zeros] # Retrieves the ordinates for the Chebyshev zeros
cheb_newton_poly = pb1.newton_interpolation(cheb_values, cheb_zeros) # Generates polynomial
spline_coeff = pb3.SplineCoefficients(points, values) # Returns our spline interpolation coefficients
x = linspace(interval[0], interval[1], 1001)
for i in range(1001): # We loop through the 1001 points
x_coord = x[i]
# We evaluate all of the approximations at the iteration absica and store it in an array
