A form of notation of the interpolation polynomial obtained from the Stirling interpolation formula by means of the nodes 
at a point 
:
using the relations
After collecting similar terms, the Steffensen interpolation formula can be written in the form
References
| [1] | G.A. Korn, T.M. Korn, "Mathematical handbook for scientists and engineers" , McGraw-Hill (1968) |
The central differences 
, 
(
) are defined recursively from the (tabulated values) 
by the formulas
The Steffensen interpolation formula is also known as Everett's second formula.
References
| [a1] | F.B. Hildebrand, "Introduction to numerical analysis" , McGraw-Hill (1956) pp. 103–105 |
| [a2] | J.F. Steffensen, "Interpolation" , Chelsea, reprint (1950) |
| [a3] | C.-E. Froberg, "Introduction to numerical analysis" , Addison-Wesley (1965) pp. 157 |
How to Cite This Entry:
Steffensen interpolation formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Steffensen_interpolation_formula&oldid=48830
This article was adapted from an original article by M.K. Samarin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098.
See original article
