Keywords: Adomian decomposition method Padé approximants Belov–Chaltikian lattice The nonlinear self-dual network equations Solitary solution a b s t r a c t ADM-Padé technique is a combination of Adomian decomposition method (ADM) and Padé approximants. We solve two nonlinear lattice equations using the technique which gives the approximate solution with higher accuracy and faster convergence ...

This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix and convergence of Padé approximants appears as the strong resolvent convergence of finite matrix approximations to a Jacobi matrix. As a bonus of this, we 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...

We compare Monte Carlo results for the interface tension and interface energy of the 3-dimensional Ising model with Padé and inhomogeneous differential approximants of the low temperature series that was recently extended by Arisue to 17 order in u = exp(−4β). The series is expected to suffer from the roughening singularity at u ≈ 0.196. The comparison with the Monte Carlo data shows that the P...

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. ...

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approxima...

Several existing algorithms for computing the matrix cosine employ polynomial or rational approximations combined with scaling and use of a double angle formula. Their derivations are based on forward error bounds. We derive new algorithms for computing the matrix cosine, the matrix sine, and both simultaneously, that are backward stable in exact arithmetic and behave in a forward stable manner...

Let a(z) be a meromorphic function having in the disk |z| < R precisely λ poles. In this work for the (λ−1)th row of the Padé table of a(z) the set of uniform convergence is explicitly obtained. The present note is a supplement to the previous work of the author (J. Approx. Theory, 123(2003), 160-207). In the theory of uniform convergence of the Padé approximants the principal question is if th...

For a recent new numerical method for computing so-called robust Padé approximants through SVD techniques, the authors gave numerical evidence that such approximants are insensitive to perturbations in the data, and do not have so-called spurious poles, that is, poles with a close-by zero or poles with small residuals. A black box procedure for eliminating spurious poles would have a major impa...

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...