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Aitken Interpolation

Aitken interpolation is an algorithm similar to Neville's algorithm for constructing the Lagrange interpolating polynomial. Let f(x|x_0,x_1,...,x_k) be the unique polynomial of kth polynomial order coinciding with f(x) at x_0, ..., x_k. Then

f(x|x_0,x_1)=1/(x_1-x_0)|f_0 x_0-x; f_1 x_1-x|
(1)
f(x|x_0,x_2)=1/(x_2-x_0)|f_0 x_0-x; f_2 x_2-x|
(2)
f(x|x_0,x_1,x_2)=1/(x_2-x_1)|f(x|x_0,x_1) x_1-x; f(x|x_0,x_2) x_2-x|
(3)
f(x|x_0,x_1,x_2,x_3)=1/(x_3-x_2)|f(x|x_0,x_1,x_2) x_2-x; f(x|x_0,x_1,x_3) x_3-x|.
(4)

See also

Lagrange Interpolating Polynomial

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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. 879, 1972.Acton, F. S. Numerical Methods That Work, 2nd printing. Washington, DC: Math. Assoc. Amer., pp. 93-94, 1990.Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, p. 102, 1992.

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Aitken Interpolation

Cite this as:

Weisstein, Eric W. "Aitken Interpolation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AitkenInterpolation.html

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