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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^'=s_(n+1)-((s_(n+1)-s_n)^2)/(s_(n+1)-2s_n+s_(n-1)).

See also

Euler's Series Transformation

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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. 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.

Referenced on Wolfram|Alpha

Aitken's Delta-Squared Process

Cite this as:

Weisstein, Eric W. "Aitken's Delta-Squared Process." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AitkensDelta-SquaredProcess.html

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