Commonly used techniques to study non-perturbative aspects of the strong interactions have a deep connection with rational approximants, and in particular with Padé approximants to meromorphic functions. However, only recently this connection has been acknowledged and efforts at fully exploiting it are only starting. In this article I will briefly review the most prominent techniques used in no...

Using sequence transformation and extrapolation algorithms for the prediction of further sequence elements from a finite number of known sequence elements is a topic of growing importance in applied mathematics. For a short introduction, see the book of Brezinski and Redivo Zaglia 1, Section 6.8 . We mention theoretical work on prediction properties of Padé approximants and related algorithms l...

We apply the technique of self-similar exponential approximants based on successive truncations of continued exponentials to reconstruct functional laws of the quasi-exponential class from the knowledge of only a few terms of their power series. Comparison with the standard Padé approximants shows that, in general, the self-similar exponential approximants provide significantly better reconstru...

We prove that the Nevalinna-Pick algorithm provides different homeomorphisms between certain topological spaces of measures, analytic functions and sequences of complex numbers. This algorithm also yields a continued fraction expansion of every Schur function, whose approximants are identified. The approximants are quotients of rational functions which can be understood as the rational analogs ...

In a recent paper (Beghi, Lepschy & Viaro (1997) IEEE Transactions on Circuits and System-I, 44, 824}828) a procedure for obtaining proper rational approximants of the transfer function of a delay was suggested. We study a generalization of the feedback problem posed in the cited paper and obtain its general solution. Explicit computations of the generalized approximants are obtained in terms o...

Quadratic Shafer approximants and their generalization to higher degree polynomials called Hermite-Padé approximants have been successfully used in quantum mechanics for calculation of exponentially small escape rates. In this paper we test quadratic Shafer approximants in representing growth rates typical for equatorial atmosphere. One of the characteristic features of the equatorial Kelvin wa...

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...

Rational and algebraic Pad e approximants are applied to MMller-Plesset (MP) perturbation expansions of energies for a representative sample of atoms and small molecules. These approximants can converge to the full connguration-interaction result even when partial summation diverges. At order MP2 (the rst order beyond the Hartree-Fock approximation) best results are obtained from the rational 0...

In order to reduce the Gibbs phenomenon exhibited by the partial Fourier sums of a periodic function f , defined on [−π, π], discontinuous at 0, Driscoll and Fornberg considered so-called singular Fourier-Padé approximants constructed from the Hermite-Padé approximants of the system of functions (1, g1(z), g2(z)), where g1(z) = log(1 − z) and g2(z) is analytic, such that Re (g2(e)) = f(t). Conv...