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Preprints, Working Papers, ... Year : 2006

Partial-Padé prediction

Abstract

When the first terms of a sequence (called sequence to predict) are known, a prediction method is a method which gives us an approximation of the following terms (the so-constructed sequence is called the predicted sequence). In this paper, we expose two prediction methods respectively called εp-prediction which are generalizations of Aitken's ∆ 2-prediction of C. Brezinski and M. Redivo Zaglia [6]-and Padé-prediction of J. Gilewicz [8]-which are very simple to use. In order to choose among the different partial-Padé-predictions, we study some of their properties. However, the most important points of this paper are : • the use of an extrapolation algorithm,(the ε-algorithm) to obtain a prediction algorithm for each partial-Padé-prediction (which avoids to solve a system). • the results about consistency obtained for the partial-Padé-prediction , (i.e. under certain conditions, each term of the predicted sequence converges to the analogous term of the sequence to predict).
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Dates and versions

hal-03663743 , version 1 (10-05-2022)

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Marc Prévost, Denis Vekemans. Partial-Padé prediction. 2006. ⟨hal-03663743⟩
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