A New Extended Padé Approximation and Its Application

Abstract EN

We extend ordinary Padé approximation, which is based on a set of standard polynomials as {1,x,…,xn}, to a new extended Padé approximation (Müntz Padé approximation), based on the general basic function set {1,xλ,x2λ,…,xnλ} (0<λ≤1) (the particular case of Müntz polynomials) using general Taylor series (based on fractional calculus) with error convergency.

The importance of this extension is that the ordinary Padé approximation is a particular case of our extended Padé approximation.

Also the parameterization (λ is the corresponding parameter) of new extended Padé approximation is an important subject which, obtaining the optimal value of this parameter, can be a good question for a new research.