Optimal linear contractive sequence transformations

AbstractIt is well known that a universal convergence acceleration method can be nonexistent even for some restricted classes of sequences. Thus one can look for contractive sequence transformations. This paper deals with such linear contractive transformations where the coefficients are chosen in an optimal way. The problem leads to a best approximation problem for polynomials in several variables which is completely solved in Section 2. The corresponding optimal linear contractive sequence transformations are then built and studied in Section 3. The fourth section is devoted to synchronous contractive sequence transformations and it opens new ways of research. The last section presents some numerical results illustrating our procedures