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**Extrapolation methods.**
*(English)*
Zbl 0814.65001

This paper is really an introduction to the book [Extrapolation methods, theory and practice (1991; Zbl 0744.65004)], by the same authors. The paper begins with a discussion of terminology and notation, using Aitken’s method as an example. The sequence transformation for Aitken’s algorithm is then generalized to produce the Shanks transformation, and there is a brief discussion of the \(\varepsilon\)-algorithm for computing the Shanks transformation. This leads to a discussion of the possibility of a universal transformation for accelerating the convergence of all convergent sequences. The concept of remanence is introduced to discuss sets of sequences that are non-accelerable. The paper concludes with some general comments about extrapolation methods and their applications.

Reviewer: A.C.Genz (Pullman)

### MSC:

65B05 | Extrapolation to the limit, deferred corrections |

### Keywords:

epsilon algorithm; convergence acceleration; Aitken’s algorithm; Shanks transformation; remanence; extrapolation methods### Citations:

Zbl 0744.65004
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\textit{C. Brezinski} and \textit{M. Redivo-Zaglia}, Appl. Numer. Math. 15, No. 2, 123--131 (1994; Zbl 0814.65001)

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### References:

[1] | Brezinski, C.; Redivo Zaglia, M., Extrapolation Methods, Theory and Practice (1991), North-Holland: North-Holland Amsterdam · Zbl 0744.65004 |

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