Scientific Computing with Python 3

Convergence acceleration

We give an example of application of generators for convergence acceleration. This presentation follows closely the example given by Pramode C.E in Python Generator Tricks (refer [9] for more information).

Note that a generator may take an other generator as an input parameter. For instance, suppose that we have defined a generator that generates the elements of a converging sequence. It is then possible to improve the convergence by an acceleration technique due to Euler and Aitken, often called Aitken’s Δ²-method (Refer [33]). It transforms a sequence s_i into another by defining 

Both sequences have the same limit, but ...