Aitken's Delta Squared Process

An Algorithm which extrapolates the partial sums $s_n$ of a Series $\sum_n a_n$ whose Convergence is approximately geometric and accelerates its rate of Convergence. The extrapolated partial sum is given by

$${s_n}'\equiv s_{n+1} - {{(s_{n+1}-s_n)^2}\over {s_{n+1}-2 s_n +s_{n-1}}}.$$

See also Euler's Series Transformation

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 18, 1972.

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. 160, 1992.