  The prediction properties of Aitken's iterated Delta^2 process, Wynn's
epsilon algorithm, and Brezinski's iterated theta algorithm for (formal) power
series are analyzed. As a first step, the defining recursive schemes of these
transformations are suitably rearranged in order to permit the derivation of
accuracy-through-order relationships. On the basis of these relationships, the
rational approximants can be rewritten as a partial sum plus an appropriate
transformation term. A Taylor expansion of such a transformation term, which is
a rational function and which can be computed recursively, produces the
predictions for those coefficients of the (formal) power series which were not
used for the computation of the corresponding rational approximant.
