For some constant α_0, α(f, z)<α_0 implies that z is an approximate zero of f, where α(f, z) = ( left bracketing bar f(z) right bracketing bar )/( left bracketing bar f'(z) right bracketing bar ) sup_(k>1) ( left bracketing bar (f^(k)(z))/(k!f'(z)) right bracketing bar )^(1/(k - 1)). Smale found a constant α≈0.130707 for the test, and this value was subsequently improved to α_0 = 3 - 2sqrt(2)≈0.171573 by Wang and Han, and further improved by Wang and Zhao (Wang and Zhao 1995; Petković et al. 1997, p. 2).
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