# Everett interpolation formula

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A method of writing the interpolation polynomial obtained from the Gauss interpolation formula for forward interpolation at with respect to the nodes , that is,  without finite differences of odd order, which are eliminated by means of the relation Adding like terms yields Everett's interpolation formula (1)

where and (2) Compared with other versions of the interpolation polynomial, formula (1) reduces approximately by half the amount of work required to solve the problem of table condensation; for example, when a given table of the values of a function at is to be used to draw up a table of the values of the same function at , , where is an integer, the values for are computed be means of the formula and is used to find both values .

In manual calculation, in the case it is advisable to approximate the coefficient of in (2) by and instead of to compute The parameter can be chosen, for example, from the condition that the principal part of where has a minimum value. In this case .

How to Cite This Entry:
Everett interpolation formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Everett_interpolation_formula&oldid=18723
This article was adapted from an original article by M.K. Samarin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article