Pad e-type approximants and errors of Pad e approximants

A family of Pad e-type approximants for accelerating the convergence of sequences

We describe a collection of Pad e-type methods for accelerating the convergence of sequence of functions. The construction and connections of Pad e’s methods with other similar methods are given. We examine the e ectiveness of these new methods, namely integral Pad e approximant, modi ed Pad e approximant and squared Pad e approximant together with the well-established methods, namely functiona...

The diagonal of the Pad e table andthe approximation of the Weyl functionof second order di erence

We study connections between diagonal Pad e approximants and spectral properties of second order diierence operators with complex coeecients. In a rst part, we identify the diagonal of the Pad e table with a particular diierence operator which is shown to have maximal resolvent set. The spectrum of an asymptotically periodic complex diierence operator is given, and we prove convergence on the r...

Pad E Type Approximants with Preassigned Zeros

Integral Representation of the Error and AsymptoticError

In this paper we will give an integral representation of the error for the generalized Pad e type approximants deened in 2]. We will deduce some asymptotic upper bounds on the error of sequences of these approximants. As applications, we will consider functions deened by their expansions in some families of classical orthogonal polynomials and obtain for the corresponding approximants some resu...

Comparison of acceleration techniques of analytical methods for solving differential equations of integer and fractional order

The work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on Homotopy analysis method  and Adomian decomposition method for solving  differential equations of integer and fractional orders.