A. FDIL (Marrakech) SOME RESULTS ON CONVERGENCE ACCELERATION FOR THE E-ALGORITHM

Abstract. Some new results on convergence acceleration for the E-algorithm which is a general extrapolation method are obtained. A technique for avoiding numerical instability is proposed. Some applica-tions are given. Theoretical results are illustrated by numerical experi-ments. 1. Introduction. The E-algorithm [2], [7] is a general extrapolation process. It depends on some auxiliary sequences (gi(n)), i ≥ 1. For some choices of the auxiliary sequences, one obtains some known convergence acceleration methods (see [2], [3]). When applied to a sequence (sn) o