Algorithm for the E-prediction

AbstractWhen the first terms of a sequence are given, a method which gives an approximation of the following ones is called a prediction method. Such methods have already been studied by Allan, Gilewicz, Kiwi, Levin, Prévost, Sidi, Trias, Weissmann, etc.In this paper, we focus on the E-prediction which has been defined and studied by Brezinski and Redivo Zaglia.We obtain a new algorithm generating the E-prediction by using the classical and progressive rules of the E-algorithm. The definition of a prediction method being quite weak, we also talk about consistency in order to appraise the specifications of the E-prediction. At last, some results of consistency are given for a particular case of the E-prediction: the Richardson-prediction