divided difference interpolation formula

Newton’s divided difference interpolation formula is the analogue of the Gregory-Newton and Taylor seriesMathworldPlanetmath for divided differencesDlmfMathworldPlanetmath.

If f is a real function and x0,x1, is a sequence of distinct real numbers, then we have, for any integer n>0,


where the remainder can be expressed either as


or as


where η lies between the smallest and the largest of x,x0,,xn.

Remark. If f is a polynomial of degree n, then R vanishes.

Title divided difference interpolation formula
Canonical name DividedDifferenceInterpolationFormula
Date of creation 2013-03-22 16:19:13
Last modified on 2013-03-22 16:19:13
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 8
Author CWoo (3771)
Entry type Theorem
Classification msc 39A70