Acceleration of superlinearly convergent sequences

Abstract

A method analogous to the Aitken extrapolation is proposed to accelerate the convergence of sequences of real or complex numbers with asymptotic behavior where ei is the error of the ith element of the sequence, dj≥1 for all 1≤j≤r, and ∑dj > 1. The R-order of the resulting sequences is computed using methods which are also of independent interest.