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}} in practical use the secant method actually converges faster than Steffensen's method, when both algorithms succeed: The secant method achieves a factor of about   {{nobr|{{math|(1.6){{sup|2}}   ≈   2.6}} times}}   as many digits for every two steps (two function evaluations), compared to Steffensen's factor of   {{math|2}}   for every one step (two function evaluations).
Similar to most other [[Root-finding algorithm#Iterative methods|iterative root-finding algorithms]], the crucial weakness in Steffensen's method is choosing a "sufficiently close" starting value <math>\ x_0 ~.</math> If the value of <math>\ x_0\ </math> is not "close enough" to the actual solution <math>\ x_\star\ ,</math> the method may fail, and the sequence of values <math>\ x_0, \, x_1, \, x_2, \, x_3, \, \dots\ </math> may either erratically flip-flop between two (or more) extremes, or diverge to infinity, or both.
==Derivation using Aitken's delta-squared process==
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