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Newton's Divided Difference Interpolation Formula
![f(x)=f_0+sum_(k=1)^npi_(k-1)(x)[x_0,x_1,...,x_k]+R_n,](/image.pl?url=http%3a%2f%2fmathworld.wolfram.com%2fimages%2fequations%2fNewtonsDividedDifferenceInterpolationFormula%2fNumberedEquation2.svg&f=jpg&w=240)
![[x_1,...]](/image.pl?url=http%3a%2f%2fmathworld.wolfram.com%2fimages%2fequations%2fNewtonsDividedDifferenceInterpolationFormula%2fInline1.svg&f=jpg&w=240)
is a![R_n(x)=pi_n(x)[x_0,...,x_n,x]=pi_n(x)(f^((n+1))(xi))/((n+1)!)](/image.pl?url=http%3a%2f%2fmathworld.wolfram.com%2fimages%2fequations%2fNewtonsDividedDifferenceInterpolationFormula%2fNumberedEquation3.svg&f=jpg&w=240)
.See also
Divided Difference,Finite Difference,Hermite's Interpolating Polynomial,Interpolation,Lagrange Interpolating PolynomialExplore with Wolfram|Alpha
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References
Abramowitz, M. and Stegun, I. A. (Eds.).Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 880, 1972.Hildebrand, F. B.Introduction to Numerical Analysis. New York: McGraw-Hill, pp. 43-44 and 62-63, 1956.Whittaker, E. T. and Robinson, G. "Newton's Formula for Unequal Intervals." §13 inThe Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 24-26, 1967.Referenced on Wolfram|Alpha
Newton's Divided Difference Interpolation FormulaCite this as:
Weisstein, Eric W. "Newton's Divided Difference Interpolation Formula." FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/NewtonsDividedDifferenceInterpolationFormula.html