The error autocorrection effect means that in a calculation all the intermediate errors compensate each other, so the final result is much more accurate than the intermediate results. In this case standard interval estimates (in the framework of interval analysis including the so-called a posteriori interval analysis of Yu. Matijasevich) are too pessimistic. We shall discuss a very strong form ...

Given a function f holomorphic at infinity, the n-th diagonal Padé approximant to f, denoted by [n/n]f, is a rational function of type (n,n) that has the highest order of contact with f at infinity. Nuttall’s theorem provides an asymptotic formula for the error of approximation f− [n/n]f in the case where f is the Cauchy integral of a smooth density with respect to the arcsine distribution on [...

We obtain a result on convergence of Padé approximants for meromorphic functions of Stieltjes type. Connection of Padé approximants with Stieltjes moment problem plays a key role in the proof.

We discuss how to implement an " environmentally friendly " renormalization in the context of finite temperature field theory. Environmentally friendly renormalization provides a method for interpolating between the different effective field theories which characterize different asymptotic regimes. We give explicit two loop Padé resummed results for λφ 4 theory for T > T c. We examine the impli...

This study investigates phonetic factors – vocalic/consonantal context, duration, stress favouring rhotic perception of the lateral approximant in Greek. Nonsense words containing the lateral in different lengths in both intervocalic and internal coda position, alongside similar words containing a rhotic, were presented to Greek listeners for categorisation as /l/ or /r/. Results showed that la...

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...

A new beam propagation method (BPM) is developed based on a direct approximation to the propagator by its [(p-1)/p] Padé approximant. The approximant is simple to construct and has the desired damping effect for the evanescent modes. The method is applied to a tapered waveguide for TM-polarized waves, based on the energy-conserving improvement of the one-way Helmholtz equation. Numerical result...

– Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose a method for semiclassical quantization based upon the Padé approximant to the periodic orbit sums. The Padé approximant allows the re-summation of the typically exponentially divergent periodic orbit terms. The technique does not depend on the existence of a symbolic dynam...