Levin-type transformations

Summary

Levin-type transformations are nonlinear series acceleration methods that use explicit estimates of the remainder of a series. They assume that the error of the $n$-th partial sum is a known estimate $\omega_n$ times a slowly varying correction. They eliminate this correction exactly when it is a polynomial in $1/(n + \beta)$. Levin's $t$- and $u$-transformations take $\omega_n$ from the terms of the series. They work well both for alternating series and for many series with terms of one sign. They can also assign values to some divergent series.