Abstract
We show that almost all vector extrapolation methods posses the property of quasilinearity (that is, translativity and homogeneity). We give a necessary and sufficient condition for the property of translativity. This condition is applied to some vector extrapolation methods, in particular the H-algorithm, the E-algorithm, and certain polynomial extrapolation methods. An application of this condition to convergence acceleration is also given and applied to Henrici's transformation and to the vector generalization of the E-algorithm given by Wimp.
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