Similarities of the integral Padé approximants

摘要

We consider a particular selection of Padé type methods for accelerating the convergence of sequence of functions. The construction and relationship of Padé type methods with other similar methods are demonstrated. We illustrate 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 Δ2 algorithm. The IPA is found to be a natural generalisation of Aitken Δ2 algorithm. Also we state the convergence theorem for the IPAs and this theorem is similar to the hybrid FPA.