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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
Citations:
Zbl 0744.65004
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References:
[1] Brezinski, C.; Redivo Zaglia, M., Extrapolation methods, theory and practice, (1991), North-Holland Amsterdam · Zbl 0744.65004
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