aitkens 0.1.0

Aitken's delta-squared acceleration

aitkens

Aitken's delta-squared series acceleration method

J. M. F. Tsang ([e-mail])

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Usage

Given an object xs that can be turned into a one-dimensional numpy array, run:

from aitkens import accelerate

accelerate(xs)

Example: Iterates of $\sqrt{2}$

This example, which is given on the Wikipedia article [1], is actually a poor example since the original iterates converge quadratically, rather than linearly. The accelerated sequence's terms tend to overshoot the true values.

from itertools import accumulate
from aitkens import accelerate

iterates = list(accumulate(
    range(5), lambda x, _: 0.5 * (x + 2/x), initial=1
))
acc = accelerate(iterates)

References

1. https://en.wikipedia.org/wiki/Aitken%27s_delta-squared_process

Licence

This work is licensed under a Creative Commons Attribution 4.0 International License.