Brezinski, Claude; Zaglia, Michela Redivo Generalizations of aitken’s process for accelerating the convergence of sequences. (English) Zbl 1182.65007 Comput. Appl. Math. 26, No. 2, 171-189 (2007). Summary: When a sequence or an iterative process is slowly converging, a convergence acceleration process has to be used. It consists in transforming the slowly converging sequence into a new one which, under some assumptions, converges faster to the same limit. In this paper, new scalar sequence transformations having a kernel (the set of sequences transformed into a constant sequence) generalizing the kernel of the Aitken’s \(\Delta^{2}\) process are constructed. Then, these transformations are extended to vector sequences. They also lead to new fixed point methods which are studied. Cited in 12 Documents MSC: 65B05 Extrapolation to the limit, deferred corrections Keywords:convergence acceleration; aitken process; extrapolation; fixed point methods PDFBibTeX XMLCite \textit{C. Brezinski} and \textit{M. R. Zaglia}, Comput. Appl. Math. 26, No. 2, 171--189 (2007; Zbl 1182.65007) Full Text: Link