Shanks transformation

Summary

The Shanks transformation is a nonlinear series acceleration method. Its first-order form takes three consecutive partial sums and returns the limit they would have if the error were exactly geometric. This form coincides with Aitken's delta-squared process. Higher orders $e_k$ use $2k + 1$ terms and model the error as a sum of $k$ geometric sequences. In practice it is computed with Wynn's epsilon algorithm, and applied to the partial sums of a power series it produces Padé approximants.