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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 5, Pages 723–743
DOI: https://doi.org/10.31857/S0044466921050069 (Mi zvmmf11234) 		 
This article is cited in 4 scientific papers (total in 4 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
Citations (4)
DOI: https://doi.org/10.31857/S0044466921050069
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.
Funding agency Grant number
Labex ANR-11-LABX-0007-01
Università di Padova DOR1903575/19
Istituto Nazionale di Alta Matematica "Francesco Severi"
The work of C.B. was supported by the Labex CEMPI (ANR-11-LABX-0007-01). The work of M.R.-Z. was partially supported by the University of Padua, Project 2019 no. DOR1903575/19. M.R.-Z. is member of the INdAM Research group GNCS.
Received: 24.11.2020
Revised: 24.11.2020
Accepted: 14.01.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 5, Pages 699–718
DOI: https://doi.org/10.1134/S0965542521050067
Bibliographic databases:
Document Type: Article
UDC: 519.61
Language: Russian
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
Citation in format AMSBIB
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\vol 61
\issue 5
\pages 723--743
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    • This publication is cited in the following 4 articles:
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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