[Python] Where does SciPy's adaptive step size method for finite differences originate?

Inside the KrylovJacobian class from SciPy, there is this method:

def _update_diff_step(self):
mx = abs(self.x0).max()
mf = abs(self.f0).max()
self.omega = self.rdiff * max(1, mx) / max(1, mf)


which would be the same as:



This modifies the step size that the finite difference method uses, however, I cannot find the origin of this expression, or why it works.

Does anybody know the source of this method or the reasoning behind it?

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