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- 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)
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- 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)
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- Milton D. Van Dyke Perturbation methods in fluid mechanics, p. 202. (en)
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- 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)
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- Transformation de Shanks (fr)
- Shanks transformation (en)
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