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wellington36 / extrapolation_methods

Algorithms for accelerating series convergence
https://pypi.org/project/extrapolation
MIT License
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Change the Aitken's transformation #30

Closed wellington36 closed 10 months ago

wellington36 commented 1 year ago

The Aitken's transformation was added in the context of [1], as well as others but looking at some examples with Aitken and Epsilon, we can see certain similarities in some cases:

Figure_1 Figure: Basel problem with error=1e-6

In [2] the Aitken transformation is presented in the form of an extrapolation example. The Epsilon transformation is presented as a generalization of Aitken. Bearing this in mind, it seems better to me to only have one of the two transformations. In this case it seems reasonable to me to add another transformation in place of Aitken. Perhaps from the [2] itself.

Referencies

[1]: Small, C. G. (2010). Expansions and asymptotics for statistics. Chapman & Hall/CRC Mono- graphs on Statistics & Applied Probability. CRC.

[2]: Brezinski, C. and Zaglia, M. R. (2003). Extrapolation Methods: Theory and Practice. Studies in Computational Mathematics 2. North-Holland.

wellington36 commented 10 months ago

In some practical tests (with the Tweedie distribution) it was found that the Ainkten transformation is useful in some cases.