Abstract
We consider transformations which accelerate convergence in some specified classes of convergent sequences. As an asymptotic measure of acceleration we introduce the order of transformation. We find a sharp upper bound on the order and show the explicit form of transformations of maximal order. We consider also the efficiency of transformations for fast convergent sequences. As a special case we find that the Germain-Bonne version of Richardson extropolation has maximal order for linearly convergent sequences.
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