Further convergence and stability results for the generalized Richardson extrapolation process \(GREP^{(1)}\) with an application to the \(D^{(1)}\)-transformation for infinite integrals
The author studies the convergence and stability properties of a generalized Richardson extrapolation process for the case \(\varphi(t) = \alpha t^{\delta}\) as \(t\to 0+\) in which \(\delta\) is complex when the set of extrapolation points is \(\{t_i=t_0\cdot \omega^i, i=0,1,\dots\}\) with \(\omega\in (0,1)\). He applies this analysis to the D1-transformation of \textit{D. Levin} and \textit{A. Sidi} [Appl. Math. Comput. 9, 175-215 (1981; Zbl 0487.65003)] that is a generalized Richarson extrapolation process. Several numerical examples are given.
scientific article; zbMATH DE number 1398811