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This article is cited in 3 scientific papers (total in 3 papers)
General numerical methods
A survey of Shanks' extrapolation methods and their applications
C. Brezinskia, M. Redivo-Zagliab a Université de Lille, CNRS, UMR 8524 – Laboratoire Paul Painlevé, Lille, France
b Università degli Studi di Padova, Dipartimento di Matematica "Tullio Levi-Civita", Padova, Italy
Abstract:
When a sequence or a series of scalars, vectors, matrices, tensors, is converging slowly to its limit, it can be transformed, by a sequence transformation, into a new sequence or a set of new sequences, which under some assumptions converges faster to the same limit. Such a transformation can even be applied to diverging sequences or series, thus providing its analytic continuation. Shanks’ transformation is a well known sequence transformation for accelerating the convergence of scalar sequences. In this survey, we explain its development, its various extensions, and its implementation. Several applications illustrate its effectiveness.
Key words:
acceleration methods, sequence transformations, Shanks' transformation, Padé approximation, tensor.
Received: 24.11.2020 Revised: 24.11.2020 Accepted: 14.01.2021
Citation:
C. Brezinski, M. Redivo-Zaglia, “A survey of Shanks' extrapolation methods and their applications”, Zh. Vychisl. Mat. Mat. Fiz., 61:5 (2021), 723–743; Comput. Math. Math. Phys., 61:5 (2021), 699–718
Linking options:
https://www.mathnet.ru/eng/zvmmf11234 https://www.mathnet.ru/eng/zvmmf/v61/i5/p723
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