Generalizations of Aitken's process for accelerating the convergence of sequences

Abstract

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 Δ2 process are constructed. Then, these transformations are extended to vector sequences. They also lead to new fixed point methods which are studied. Copyright © 2007 SBMAC.