Acceleration property for the E-algorithm and an application to the summation of series
The E-algorithm is the most general sequence transformation actually known, since it contains as particular cases almost all the sequence transformations discovered so far: Richardson polynomial extrapolation, Shanks’ transformation, summation processes, Germain-Bonne transformation, Levin’s generalized transformations, the processp and rational extrapolation. In  some results concerning the columns of the E-algorithm were proved. In this paper, by adding conditions about determinants, we prove that the diagonal of this algorithm also accelerates the convergence of the initial sequence.
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