Brezinski, C.; Redivo-Zaglia, M. Extrapolation methods. (English) Zbl 0814.65001 Appl. Numer. Math. 15, No. 2, 123-131 (1994). 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) Cited in 26 Documents 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 PDF BibTeX XML Cite \textit{C. Brezinski} and \textit{M. Redivo-Zaglia}, Appl. Numer. Math. 15, No. 2, 123--131 (1994; Zbl 0814.65001) Full Text: DOI OpenURL References: [1] Brezinski, C.; Redivo Zaglia, M., Extrapolation Methods, Theory and Practice (1991), North-Holland: North-Holland Amsterdam · Zbl 0744.65004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.