In numerical analysis, Steffensen's method is an iterative method for numerical root-finding named after Johan Frederik Steffensen that is similar to the secant method and to Newton's method. Steffensen's method achieves a quadratic order of convergence without using derivatives, whereas Newton's method converges quadratically but requires derivatives and the secant method does not require derivatives but also converges less quickly than quadratically. Steffensen's method has the drawback that it requires two function evaluations per step, however, whereas Newton's method and the secant method require only one evaluation per step, so it is not necessarily most efficient in terms of computational cost.
Steffensen's method can be derived as an adaptation of Aitken's delta-squared process applied to fixed-point iteration. Viewed in this way, Steffensen's method naturally generalizes to efficient fixed-point calculation in general Banach spaces, whenever fixed points are guaranteed to exist and fixed-point iteration is guaranteed to converge, although possibly slowly, by the Banach fixed-point theorem.