Generalizations of Aitken's process for a certain class of sequences

In this paper, we construct several sequence transformations whose kernels contain sequences of the form ^Sn=S+^anλn, n=0,1,..., where S and λ are unknown parameters, and (^an) is a known sequence. These transformations generalize Aitken's ^Δ2 process. We provide certain sufficient conditions under which one of our transformations accelerates the convergence of certain types of sequences. Finally, we illustrate these theoretical results through several numerical experiments using diverging and converging sequences.