`scipy.optimize._nonlin:BroydenFirst`

Signature

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

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

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

This algorithm implements the inverse Jacobian Quasi-Newton update

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

which corresponds to Broyden's first Jacobian update

J_{+} = J + (df - J d x) d x^{†} / d x^{†} d x

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.broyden1(fun, [0, 0])

✓

sol

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