Computation of Padé approximants and continued fractions

摘要

In this paper two methods to compute Padé approximants are given. These methods are based on the interpretation of the ϵ-algorithm of Wynn as the solution of a system of linear equations with an Hankel matrix. Both methods recursively computed a sub-diagonal of the Padé table. The first one gives the values of the approximants (the ϵ-array) while the second provides the coefficient of numerators and denominators. The connection of this method with some polynomials and with continued fractions is studied. This method provides a way to compute recursively a diagonal of the q-d scheme. A variant of the second method can be used to compute the ϵ-array and to settle the topological ϵ-algorithm. The computational aspects of these methods are discussed. Some numerical examples are given.