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Thiele's Interpolation Formula

Let rho be a reciprocal difference. Then Thiele's interpolation formula is the continued fraction

f(x)=f(x_1)+(x-x_1)/(rho(x_1,x_2)+)(x-x_2)/(rho_2(x_1,x_2,x_3)-f(x_1)+) (x-x_3)/(rho_3(x_1,x_2,x_3,x_4)-rho(x_1,x_2)+...).

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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. 881, 1972.Milne-Thomson, L. M. The Calculus of Finite Differences. London: Macmillan, 1951.

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Thiele's Interpolation Formula

Cite this as:

Weisstein, Eric W. "Thiele's Interpolation Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ThielesInterpolationFormula.html

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