Aitken Interpolation

An algorithm similar to Neville's Algorithm for constructing the Lagrange Interpolating Polynomial. Let $f(x\vert x_0, x_1, \ldots, x_k)$ be the unique Polynomial of $k$th Order coinciding with $f(x)$ at $x_0$, ..., $x_k$. Then

$$\begin{eqnarray*} f(x\vert x_0, x_1)&=&{1\over x_1-x_0}\left\vert\begin{array}{... ...2-x\\ f(x\vert x_0, x_1, x_3) & \!\!x_3-x\end{array}\right\vert. \end{eqnarray*}$$

See also Lagrange Interpolating Polynomial

References

Abramowitz, M. and Stegun, C. 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.