相关论文: Robust Pade approximants may have spurious poles

For a recent new numerical method for computing so-called robust Pad\'e 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…

In the work it is shown that not all limit points of poles of the Pad\'e approximants for the last intermediate row are obstructions for poinwise convergence of the whole row to an approximable function. The corresponding examples are…

We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a…

A method is suggested for treating the well-known deficiency in the use of Pade approximants that are well suited for approximating rational functions, but confront problems in approximating irrational functions. We develop the approach of…

We explain that, like the usual Pad\'e approximants, the barycentric Pad\'e approximants proposed recently by Brezinski and Redivo-Zaglia can diverge. More precisely, we show that for every polynomial P there exists a power series S, with…

The origin of the spurious poles of the gauge field propagators in the temporal axial and the null-plane gauges is discussed. The conclusion is that these poles do not require any special prescription. They are a manifestation of the fact…

Results of analysis of correctness and limitations of the classical Coupled Cavity Model are presented in the paper. It is shown that in the case of an infinite chain of resonators, there are spurious solutions of the characteristic…

The perturbative series used to extract $\alpha_s(M_\tau)$ from the $\tau$ hadronic width exhibits slow convergence. Asymptotic Pade-approximant and Pade summation techniques provide an estimate of these unknown higher-order effects,…

We show that badly approximable vectors are exactly those that cannot, for any inhomogeneous parameter, be inhomogeneously approximated at every monotone divergent rate. This implies in particular that Kurzweil's Theorem cannot be…

In this article, we show how the theory of rough paths can be used to provide a notion of solution to a class of nonlinear stochastic PDEs of Burgers type that exhibit too high spatial roughness for classical analytical methods to apply. In…

We address surface soliton complexes formed at the edge of annular guiding structures containing several concentric rings. Such soliton complexes feature a -phase difference between neighboring spots. It is shown that the multipole-mode…

In this note we consider asymptotics of the multipoint Pad\'e approximants to Cauchy integrals of analytic non-vanishing densities defined on a Jordan arc connecting $ -1 $ and $ 1 $. We allow for the situation where the (symmetric) contour…

We consider the problem of finding approximate analytical solutions for nonlinear equations typical of physics applications. The emphasis is on the modification of the method of Pad\'e approximants that are known to provide the best…

We study diagonal multipoint Pad\'e approximants to sums of a Cauchy transform of a complex measure and a rational function. The measure is assumed to have compact regular support included into the real line and an argument of bounded…

We show that there exists a geodesic spanner with almost linear number of edges.

We present a critical analysis of Pade-based methods for the unitarization of low energy amplitudes. We show that the use of certain Pade Approximants to describe the resonance region may lead to inaccurate determinations. In particular, we…

We study the stability of non compact steady and expanding gradient Ricci solitons. We first show that strict linear stability implies dynamical stability. Then we give various sufficient geometric conditions ensuring the strict linear…

Stationary droplets simulated by multi-phase lattice Boltzmann methods lead to spurious velocities around them. In this article I report the origin of these spurious velocities for one example and show how they can be avoided.

Given non-collinear points a_1, a_2, a_3, there is a unique compact, say \Delta, that has minimal logarithmic capacity among all continua joining a_1, a_2, and a_3. For h be a complex-valued non-vanishing Dini-continuous function on \Delta,…

The interaction of both scalar and counter-rotating polarized steady state pulses (SSP) is studied numerically for a medium characterized by nonlinear susceptibilities of the third and the fifth order (a cubic-quintic medium…