Related papers: Rational Hermite-Pad\'e Approximants vs Pad\'e App…
Generic approximation of entire functions by their Pad\'{e} approximants has been achieved in the past (\cite{3}). In the present article we obtain generic approximation of holomorphic functions on arbitrary open sets by sequences of their…
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…
Generalizations of the Hermite polynomials to many variables and/or to the complex domain have been located in mathematical and physical literature for some decades. Polynomials traditionally called complex Hermite ones are mostly…
We construct explicitly Pad\'e approximations of the second kind for a special class of G-functions. These are then applied to prove a Baker-type lower bound for linear forms in the p-adic values of these functions. Moreover, we consider…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given…
Polynomials known as Multiple Orthogonal Polynomials in a single variable are polynomials that satisfy orthogonality conditions concerning multiple measures and play a significant role in several applications such as Hermite-Pad\'e…
Numerical approximate computation can solve large and complex problems fast. It has the advantage of high efficiency. However it only gives approximate results, whereas we need exact results in many fields. There is a gap between…
Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of…
We obtain strong and uniform asymptotics in every domain of the complex plane for the scaled polynomials $a (3nz)$, $b (3nz)$, and $c (3nz)$ where $a$, $b$, and $c$ are the type II Hermite-Pad\'e approximants to the exponential function of…
We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace…
The paper presents linear integral predictors for continuous time high-frequency signals with a a finite spectrum gap. The predictors are based on approximation of a complex valued periodic exponential (complex sinusoid) by rational…
We show that Hermite's approximations to values of the exponential function at given algebraic numbers are nearly optimal when considered from an adelic perspective. We achieve this by taking into account the ratio of these values whenever…
The cosmography known as the Pad\'{e} polynomials has been widely used in the reconstruction of luminosity distance, and the orders of Pad\'{e} polynomials influence the reconstructed result derived from Pad\'{e} approximation. In this…
Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…
This paper presents a novel method for polynomial approximation (Hermite approximation) using the fusion of value and derivative information. Therefore, the least-squares error in both domains is simultaneously minimized. A covariance…
Because of the high approximation power and simplicity of computation of smooth radial basis functions (RBFs), in recent decades they have received much attention for function approximation. These RBFs contain a shape parameter that…
We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.
A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…
We show that Hermite's approximations to values of the exponential function at given algebraic numbers are nearly optimal when considered from an adelic perspective. We achieve this by taking into account the ratio of these values whenever…