Analytical and numerical studies of the convergence behavior of the j transformation

A new nonlinear sequence transformation, the iterative j transformation, was proposed recently by the author (1993). For this transformation, a derivation based on the method of hierarchical consistency, alternative recursive representations, general properties, an explicit expression for the kernel, model sequences, and its relation to other sequence transformations have been given (the author, 1994). The j transformation is of similar generality as the well-known E algorithm (Brezinski, 1980; Hهvie, 1979). In the present contribution, some results on convergence acceleration properties of the j transformation are proved. Numerical test results are presented which show that the j transformation is a very powerful computational tool for convergence acceleration, extrapolation, and summation of divergent series.