Series Acceleration

Build Status	Coverage	Documentation	Social

This package aims to provide methods to estimate the limite of infinite series from a finite set of samples.

Documentation

One first constructs a helper for one of the methods and then calls the sum function with the series and this helper. Due to performance reasons, it can be advantageous to use the sum function, expecting an array of partial sums instead.

using SeriesAcceleration

range = 1:10              # specify the minimum number of summands before to fit
exps   = 0:4               # exponents to fit
rh = Richardson(range, exps)  # Richardson starting with 1 summands and using 5 exponents
series = 1 ./ (1:100) .^ 2
res_1 = esum(rh, series)
res_2 = esum_c(rh, cumsum(series))

Status

ToDo's

bunch of convenience wrapper functions (for example in-place construction of helpers).
Documentation structure

Overview

Methods currently implemented are:

Method	Status	Algorithms	References
Richardson	mostly done	Matrix Invers, Direct a_0	1,2
Shanks	todo
Levin	todo

References

1: Bender, C. M., & Orszag, S. A. (1999). Advanced Mathematical Methods for Scientists and Engineers I. Springer New York. https://doi.org/10.1007/978-1-4757-3069-2

2: Rohringer, G., & Toschi, A. (2016). Impact of nonlocal correlations over different energy scales: A dynamical vertex approximation study. Physical Review B, 94(12). https://doi.org/10.1103/physrevb.94.125144