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Prediction properties of some extrapolation methods. (English) Zbl 0619.65001

Convergence acceleration methods consist in the construction of a sequence converging faster than the initial sequence. Each member of the new sequence is a guess for the limit and it is computed from a restricted number of terms of the initial sequence. It is shown herein how convergence acceleration methods can be used to predict the next (unknown) term of the initial sequence instead of its limit. Particular emphasis on Aitken’s \(\Delta^ 2\) process and the E-algorithm is placed.

MSC:

65B05 Extrapolation to the limit, deferred corrections
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References:

[1] Brezinski, C., A general extrapolation algorithm, Numer. math., 35, 175-187, (1980) · Zbl 0444.65001
[2] Brezinski, C., The Mühlbach – neville – aitken algorithm and some extensions, Bit, 20, 444-451, (1980) · Zbl 0462.65006
[3] Brezinski, C., Error control in convergence acceleration processes, IMA J. numer. anal., 3, 65-80, (1983) · Zbl 0515.65004
[4] Gilewicz, J., Numerical detection of the best Padé approximant and determination of the Fourier coefficients of insufficiently sampled functions, (), 99-103
[5] Havie, T., Generalized neville type extrapolation schemes, Bit, 19, 204-213, (1979) · Zbl 0404.65001
[6] Mühlbach, G., Neville – aitken algorithm for interpolation by functions of Chebyshev systems in the sense of Newton and in generalized sense of Hermite, (), 200-212
[7] Sidi, A.; Levin, D., Prediction properties of the t-transformation, SIAM J. numer. anal., 20, 589-598, (1983) · Zbl 0521.65002
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