Numerical analysis | Asymptotic analysis

Shanks transformation

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. (Wikipedia).

Shanks transformation
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Related pages

Daniel Shanks | Anderson acceleration | Perturbation theory | Sequence transformation | Richardson extrapolation | Numerical analysis | Padé approximant | Padé table | Rate of convergence | Series acceleration | Determinant | Aitken's delta-squared process | Sequence