Steffensen's method: Difference between revisions

Revision as of 09:42, 4 July 2025

Revision as of 09:43, 4 July 2025

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{{short description|Newton-like root-finding algorithm that does not use derivatives}}

In [[numerical analysis]], '''Steffensen's method''' is an [[iterative method]] named after [[Johan Frederik Steffensen]] for numerical [[root-finding method|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 [[derivative]]s, whereas the more familiar Newton's method also 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, whereas the secant method requires only one evaluation per step, so it is not necessarily most efficient in terms of [[computational cost]], depending on the number of iterations each requires. Newton's method also requires evaluating two functions per step – for the function and for its derivative – and its computational cost varies between being the same as Steffensen's method (for most functions, where calculation of the derivative is just as computationally costly as the original function).{{efn|