Similarities of the integral Padé approximants
A particular selection of Padé type, methods for accelerating the convergence of a sequence of functions is considered. The construction and relationship of Padé type methods with other similar methods are demonstrated. The similarities of the recently introduced methods, namely the integral Padé approximant (IPA), the modified Padé approximant (MPA) together with the well established methods, namely the functional Padé approximant (FPA) and the Aitken \(\Delta^2\) algorithm are illustrated. The IPA is found to be a natural generalisation of Aitken \(\Delta^2\) algorithm. It is stated that the convergence theorem for the IPAs and this theorem is similar to the hybrid FPA.
scientific article; zbMATH DE number 1861331