Convergence Acceleration of Vector Sequences by Vector Padé Approximation

Abstract

By making use of vector Padé approximants, a method for accelerating the convergence of vector sequences is derived. The method obtained includes the well known Henrici transformation as a special case. A main character of the method is that it can use partial vector components to accelerate convergence of the whole vector sequence. Results about the efficacy of the method are established. An algorithm and some numerical examples are given.