Aitken's delta-squared process

Aitken's delta-squared process, also called Aitken extrapolation, is a series acceleration method used to speed up the rate of convergence of a sequence. It is named after Alexander Aitken, who introduced the method in 1926 as part of an extension to Bernoulli's method. It is most useful for accelerating a sequence that is converging linearly. A precursor form was known to Seki Kowa, who lived from 1642 to 1708, and was applied by him to the rectification of the circle, that is, to the calculation of pi.