A family of Padé-type approximants for accelerating the convergence of sequences

We describe a collection of Padé-type methods for accelerating the convergence of sequence of functions. The construction and connections of Padéʹs methods with other similar methods are given. We examine the effectiveness of these new methods, namely integral Padé approximant, modified Pade approximant and squared Padé approximant together with the well-established methods, namely functional Pade approximant and classical Padé approximant, for approximating the characteristic value and corresponding characteristic function. Estimates of characteristic value and characteristic function derived using integral Pade approximants are found to be substantially more accurate than other similar methods.