Extrapolation methods
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.
scientific article; zbMATH DE number 699074