This modification ensures that at the kth iteration, a bisection step will be performed in at most formula_8 additional iterations, because the above conditions force consecutive interpolation step sizes to halve every two iterations, and after at most formula_8 iterations, the step size will be smaller than formula_3, which invokes a bisection step. Brent proved that his method requires at most "N"2 iterations, where "N" denotes the number of iterations for the bisection method. If the function "f" is well-behaved, then Brent's method will usually proceed by either inverse quadratic or linear interpolation, in which case it will converge superlinearly.