`scipy.optimize._nonlin:BroydenSecond`

Signature

class BroydenSecond(alpha = None, reduction_method = restart, max_rank = None)

Find a root of a function, using Broyden's second Jacobian approximation.

This method is also known as "Broyden's bad method".

This algorithm implements the inverse Jacobian Quasi-Newton update

H_{+} = H + (d x - H df) d f^{†} / (d f^{†} df)

corresponding to Broyden's second method.

The following functions define a system of nonlinear equations

def fun(x):
    return [x[0]  + 0.5 * (x[0] - x[1])**3 - 1.0,
            0.5 * (x[1] - x[0])**3 + x[1]]

✓

A solution can be obtained as follows.

from scipy import optimize
sol = optimize.broyden2(fun, [0, 0])

✓

sol

✗

array([0.84116, 0.15884])