# Steffensen interpolation formula

From Encyclopedia of Mathematics

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) |

#### Comments

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=13445

This article was adapted from an original article by M.K. Samarin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article