Acceleration of Superlinearly Convergent Sequences

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Abstract

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

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