An asymptotically hierarchy-consistent, iterative sequence transformation for convergence acceleration of Fourier series
The author studies the concept of hierarchical consistency in more detail. Its asymptotic variant is used to derive the I transformation. It is shown that the I transformation is a special case of the J transformation. The consequences of this fact are discussed. Also, some basic convergence theory for the I transformation is given. Several numerical examples are given which show that suitable variants of the I transformation are powerful nonlinear convergence accelerators for Fourier series with coefficients of monotonic behavior.
scientific article; zbMATH DE number 1234723
scientific article