About: Shanks transformation

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In numerical analysis, the Shanks transformation is a non-linear series acceleration method to increase the rate of convergence of a sequence. This method is named after Daniel Shanks, who rediscovered this sequence transformation in 1955. It was first derived and published by R. Schmidt in 1941. Milton D. Van Dyke (1975) Perturbation methods in fluid mechanics, p. 202.

Attributes	Values
rdf:type	software
rdfs:label	Transformation de Shanks (fr) Shanks transformation (en)
rdfs:comment	En analyse numérique, la transformation de Shanks est une méthode non linéaire d'accélération de la convergence de suites numériques. Cette méthode est nommée d'après Daniel Shanks, qui l'exposa en 1955, bien qu'elle ait été étudiée et publiée par R. J. Schmidt dès 1941. C'est une généralisation de l'algorithme Delta-2 d'Aitken. (fr) In numerical analysis, the Shanks transformation is a non-linear series acceleration method to increase the rate of convergence of a sequence. This method is named after Daniel Shanks, who rediscovered this sequence transformation in 1955. It was first derived and published by R. Schmidt in 1941. Milton D. Van Dyke (1975) Perturbation methods in fluid mechanics, p. 202. (en)
foaf:depiction
dcterms:subject	Asymptotic analysis Numerical analysis
Wikipage page ID	21581860 (xsd:integer)
Wikipage revision ID	1066692932 (xsd:integer)
Link from a Wikipage to another Wikipage	Determinant Series acceleration Anderson acceleration Richardson extrapolation Perturbation theory Asymptotic analysis Rate of convergence Numerical analysis Aitken's delta-squared process Daniel Shanks Numerical analysis Padé approximant Fluid mechanics Milton Van Dyke Sequence Non-linear Transient (oscillation) Padé table Sequence transformation
sameAs	Shanks transformation Shanks transformation Shanks transformation Shanks transformation
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cite_journal dbt:Quote_box dbt:Reflist
thumbnail	wiki-commons:Special:FilePath/Shanks_transformation.svg?width=300
align	right (en)
quote	One can calculate only a few terms of a perturbation expansion, usually no more than two or three, and almost never more than seven. The resulting series is often slowly convergent, or even divergent. Yet those few terms contain a remarkable amount of information, which the investigator should do his best to extract. (en) This viewpoint has been persuasively set forth in a delightful paper by Shanks , who displays a number of amazing examples, including several from fluid mechanics. (en)
source	Milton D. Van Dyke Perturbation methods in fluid mechanics, p. 202. (en)
width	60.0 (perCent)
has abstract	En analyse numérique, la transformation de Shanks est une méthode non linéaire d'accélération de la convergence de suites numériques. Cette méthode est nommée d'après Daniel Shanks, qui l'exposa en 1955, bien qu'elle ait été étudiée et publiée par R. J. Schmidt dès 1941. C'est une généralisation de l'algorithme Delta-2 d'Aitken. (fr) In numerical analysis, the Shanks transformation is a non-linear series acceleration method to increase the rate of convergence of a sequence. This method is named after Daniel Shanks, who rediscovered this sequence transformation in 1955. It was first derived and published by R. Schmidt in 1941. One can calculate only a few terms of a perturbation expansion, usually no more than two or three, and almost never more than seven. The resulting series is often slowly convergent, or even divergent. Yet those few terms contain a remarkable amount of information, which the investigator should do his best to extract. This viewpoint has been persuasively set forth in a delightful paper by Shanks (1955), who displays a number of amazing examples, including several from fluid mechanics. Milton D. Van Dyke (1975) Perturbation methods in fluid mechanics, p. 202. (en)
gold:hypernym	Method
prov:wasDerivedFrom	wikipedia-en:Shanks_transformation?oldid=1066692932&ns=0
page length (characters) of wiki page	10899 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Shanks_transformation
is Link from a Wikipage to another Wikipage of	Naval Ordnance Laboratory Series acceleration List of numerical analysis topics Leibniz formula for π Aitken's delta-squared process Daniel Shanks Padé table Sequence transformation
is foaf:primaryTopic of	wikipedia-en:Shanks_transformation

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