Pade and Pade-Type Approximation for 2π-Periodic L~p Functions

摘要

The numerical evaluation of a 2π-periodic L~p function by its Fourier series expansion may become a difficult task whenever only a few coefficients of this series are known or it converges too slowly. In this paper we propose a general method to evaluate such any function, by means of composed Pade-type approximants. The definition, the main ideas, and the properties of the approximants will be given. After having done this successfully, we will consider several concrete examples and a theoretical application to the convergence acceleration problem of functional sequences.