CERTAIN MODIFICATIONS OF AITKEN'S ACCELERATOR FOR SLOWLY CONVERGENT SEQUENCES

Abstract

The paper presents three modifications of the Aitken accelerator for slowly or irregularly convergent sequences. The first proposal, based on backward extension of a sequence, is particularly useful if a small number of regular sequence terms is known. The next two procedures - integral exponential and hyperbolic - can be applied to sequences with irregular or disturbed convergence. Numerical examples show essential error reduction of the limit of sequences under consideration.