Please complete the Python 3 code to solve for f(x) = 0 using the Secant method

Question

Please complete the Python 3 code to solve for f(x) = 0 using the Secant method for rootfinding.

Secant method The secant method is similar to Newton's method, but instead of evaluating f'(x) directly, it uses the approximation i-Xi- def secant(f, a, b, tol-1e-10): "Solve f(x) using the secant method" history = [] xlast, flast = b, f(b)[0] # We'LL use x-b as our Last evaluation to initialize x=(a + b) / 2 for i in range(100): # And start with the midpoint as the current guess fx = f(x)[0] history.append((x, if numpy.abs(fx) fx)) tol: break # YOUR CODE HERE #raise NotImplementedError() return numpy.array(history)

Explanation / Answer

# cook your dish here

def secant(f,a,b, TOL=0.001, NMAX=100):

history=[]

xlast,flast=b,f(b)[0]

  

"""

Takes a function f, start values [x0,x1], tolerance value(optional) TOL and

max number of iterations(optional) NMAX and returns the root of the equation

using the secant method.

"""

for i in range(NMAX):

fx=f(x)[0]

history.append(x,fx)

if numpy.abs(fx)<TOL:

break

x = b - f(b)*((b-a)/(f(b)-f(a)))

if x-b < TOL:

return x

else:

a = b

b = x

return numpy.array(history)

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