The perturbative series used to extract α s (M τ) from the τ hadronic width exhibits slow convergence. Asymptotic Padé-approximant and Padé summation techniques provide an estimate of these unknown higher-order effects, leading to values for α s (M τ) that are about 10% smaller than current estimates. Such a reduction improves the agreement of α s (M τ) with the QCD evolution of the strong coup...

We present a fraction-free approach to the computation of matrix Padé systems. The method relies on determining a modified Schur complement for the coefficient matrices of the linear systems of equations that are associated to matrix Padé approximation problems. By using this modified Schur complement for these matrices we are able to obtain a fast hybrid fraction-free algorithm for their compu...

The aim of this paper is to introduce a new approximate method, namely the Modified Laplace Padé Decomposition Method (MLPDM) which is a combination of modified Laplace decomposition and Padé approximation to provide an analytical approximate solution to Thomas-Fermi equation. This new iteration approach provides us with a convenient way to approximate solution. A good agreement between the obt...

It is well known that the bilinear transform, or first order diagonal Padé approximation to the matrix exponential, preserves quadratic Lyapunov functions between continuous-time and corresponding discrete-time linear time invariant (LTI) systems, regardless of the sampling time. It is also well known that this mapping preserves common quadratic Lyapunov functions between continuous-time and di...

Matrix Padé approximation is a widely used method for computing matrix functions. In this paper, we apply matrix Padé-type approximation instead of typical Padé approximation to computing the matrix exponential. In our approach the scaling and squaring method is also used to make the approximant more accurate. We present two algorithms for computing A e and for computing At e with many 0 t  re...

We consider multipoint Padé approximation to Cauchy transforms of complex measures. We show that if the support of a measure is an analytic Jordan arc and if the measure itself is absolutely continuous with respect to the equilibrium distribution of that arc with Dini-smooth non-vanishing density, then the diagonal multipoint Padé approximants associated with appropriate interpolation schemes c...

Padé approximant is exploited for an efficient sum-over-poles decomposition of Fermi and Bose functions. The resulting poles are all pure imaginary and can therefore be used to define Padé frequencies, in analogy with the celebrated Matsubara frequencies. The proposed Padé spectrum decomposition is shown to be equivalent to a truncated continued fraction. It converges significantly faster than ...

The three renormalization-group-accessible three-loop coefficients of powers of logarithms within the MS series for the QCD static potential are calculated and compared to values obtained via asymptotic Padé-approximant methods. The leading and next-to-leading logarithmic coefficients are both found to be in exact agreement with their asymptotic Padé-predictions. The predicted value for the thi...

The Padé table of 2F1(a, 1; c; z) is normal for c > a > 0 (cf. [4]). For m ≥ n−1 and c / ∈ Z − , the denominator polynomial Qmn(z) in the [m/n] Padé approximant Pmn(z)/Qmn(z) for 2F1(a, 1; c; z) and the remainder term Qmn(z)2F1(a, 1; c; z)−Pmn(z) were explicitly evaluated by Padé (cf. [2], [6] or [9]). We show that for c > a > 0 and m ≥ n−1, the poles of Pmn(z)/Qmn(z) lie on the cut (1,∞). We d...

We prove that Padé approximants yield increasingly accurate predictions of higher-order coefficients in QCD perturbation series whose high-order behaviour is governed by a renormalon. We also prove that this convergence is accelerated if the perturbative series is Borel transformed. We apply Padé approximants and Borel transforms to the known perturbative coefficients for the Bjorken sum rule. ...