Steffensen's method: Difference between revisions

Revision as of 18:11, 13 July 2008

Revision as of 02:34, 15 July 2008

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:<math>f(u)- f(v)=L(u,v)\ (u-v) \,</math>&nbsp;.

In the original form (given in the section above), where the function <math>f\ </math> simply takes in and produces real numbers, the operators are ''divided differences''. In the general form, the operators <math>L\ </math> are the analogue of divided differences in the [[Banach space]].

Steffensen's method is then very similar to the Newton's method, except that it uses the divided difference<math>L(f(x),x)\ </math> instead of the derivative <math>Df(x)\ </math>. It is thus defined by