Acceleration results for the vector E-algorithm (Q1187055)

In the last years, many acceleration methods for vector sequences have been published [see e.g. \textit{C. Brezinski} and \textit{Redivo Zaglia}: Extrapolation methods (1991; Zbl 0744.65004)]. In the paper under consideration the author studies an application of the vector \(E\)- algorithm to vector sequences \((S_ n)_ n\) of the type \(S_ n=S+\sum^ \infty_{i=1}a_ ig_ i(n)\), where the components of \((g_ i(n))_ n\) converge linearly, or logarithmically. For each of the two cases several convergence acceleration results are proved. Furthermore, the algorithm is compared with the scalar \(E\)- algorithm, when applied to each component of \((S_ n)_ n\), and some results of numerical tests are given.