Wikipedia:
Steffensen's method
Steffensen's method is an iterative process achieving quadratic convergence without employing derivatives.
Generalised definition
![x_{k+1} = x_k + [I - F(f(x_k), x_k)]^{-1}(f(x_k) - x_k) \,](http://content.answers.com/main/content/wp/en/math/f/3/8/f387b1c92b4ecf5d0bf7eb253be89626.png)
for a mapping f on a Banach space X and F(x',x") a family of bounded linear operators associated with x' and x", having the properties
and
This process, given a sufficiently good initial approximation, converges quadratically to a fixed point.
References
- On Steffensen's Method L. W. Johnson; D. R. Scholz SIAM Journal on Numerical Analysis, Vol. 5, No. 2. (Jun., 1968), pp. 296-302. Stable URL: [1]
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