We discuss certain special cases of algebraic approximants that are given as zeroes of so-called effective characteristic polynomials and their generalization to a multiseries setting. These approximants are useful for the convergence acceleration or summation of quantum mechanical perturbation series. Examples will be given and some properties will be discussed.

This paper presents an application of control theory and μ-analysis to stability analysis of optical communication networks. The network transfer matrix representation is used and simplified so that the propagation time-delay is isolated on a link-by-link basis. The optical network stability problem is reformulated as a robust stability problem. Sufficient stability conditions are developed by ...

The univariate theorem of “de Montessus de Ballore” proves the convergence of column sequences of Pad6 approximants for functions f(z) meromorphic in a disk, in case the number of poles of f(z) and their multiplicity is known in advance. We prove here a multivariate analogon for the case of “simple” poles and for the general order Pad& approximants as introduced by Cuyt and Verdonk (1984).

This work is about Frobenius-Padé approximants for series of orthogonal polynomials of dimension d (d ∈ N). Concerning to the series, we give the projection property of partial sums, we show how to compute their coe cients, and how to get the coe cients of the product of a series by a polynomial. Concerning to the approximants we work essentially about their recursive computation. Also, we give...

We present a new set of algorithms for computation of matrix rational interpolants and one-sided matrix greatest common divisors. Examples of these interpolants include Padé approximants, Newton–Padé, Hermite–Padé, and simultaneous Padé approximants, and more generally M-Padé approximants along with their matrix generalizations. The algorithms are fast and compute all solutions to a given probl...

An approximation algorithm is proposed to transform truncated QCD (or QED) series for observables. The approximation is a modification of the Baker–Gammel approximants, and is independent of the renormalization scale (RScl) µ – the coupling parameter α(µ) in the series and in the resulting approximants can evolve according to the perturbative renormalization group equation (RGE) to any chosen l...

Recently it has been pointed out that diagonal Padé approximants to truncated perturbative series in gauge theories have the remarkable property of being independent of the choice of the renormalization scale as long as the gauge coupling parameter α(p2) is taken to evolve according to the one-loop renormalization group equation – i.e., in the large-β0 approximation. In this letter we propose a...

Convergence of diagonal Padé approximants is studied for a class of functions which admit the integral representation F(λ) = r1(λ) R 1 −1 tdσ(t) t−λ + r2(λ), where σ is a finite nonnegative measure on [−1, 1], r1, r2 are real rational functions bounded at ∞, and r1 is nonnegative for real λ. Sufficient conditions for the convergence of a subsequence of diagonal Padé approximants of F on R \ [−1...