Prediction properties of Aitken's iterated Δ2 process, of Wynn's epsilon algorithm, and of Brezinski's iterated theta algorithm
Copyright policy )Prediction properties of Aitken's iterated Δ2 process, of Wynn's epsilon algorithm, and of Brezinski's iterated theta algorithm
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.
34 pages, LaTeX
- University of Regensburg Germany
Extrapolation to the limit, deferred corrections, 41A20 (Primary) 65B05 (Secondary), Applied Mathematics, theta algorithm, epsilon algorithm, Aitken's process, convergence rate, numerical example, Computational Mathematics, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Convergence and divergence of continued fractions
Extrapolation to the limit, deferred corrections, 41A20 (Primary) 65B05 (Secondary), Applied Mathematics, theta algorithm, epsilon algorithm, Aitken's process, convergence rate, numerical example, Computational Mathematics, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Convergence and divergence of continued fractions
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