Related papers: Generic Approximation of functions by their pad\'{…
It is known that inner functions exist on strongly pseudoconvex domains. In this paper we will show that they exist on a more general type of domains, including some domains of finite type.
Unlike polynomials, rational functions can represent functions having poles or branch cuts with root-exponential convergence and no Runge phenomenon. Recent developments of the AAA and greedy Thiele algorithms have sparked renewed interest…
We study the convergence of sequences of type I and type II Hermite-Pad\'e approximants for certain systems of meromorphic functions made up of rational modifications of Nikishin systems of functions.
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
The ill-posed analytic continuation problem for Green's functions and self-energies is investigated by revisiting the Pad\'{e} approximants technique. We propose to remedy the well-known problems of the Pad\'{e} approximants by performing…
The advantages and difficulties of application of Pad\'e approximants to two-dimensional regression analysis are discussed. New formulation of residuals is suggested in the method of least squares. It leads to a system of linear equations…
In this paper we obtain several extensions to the quaternionic setting of some results concerning the approximation by polynomials of functions continuous on a compact set and holomorphic in its interior. The results include approximation…
A method for approximating continuous functions $\mathbb{Z}_{p}^{n}\rightarrow\mathbb{Z}_{p}$ by a linear superposition of continuous functions $\mathbb{Z}_{p}\rightarrow\mathbb{Z}_{p}$ is presented and a polynomial regression model is…
We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove…
The vector space of all polynomial functions of degree $k$ on a box of dimension $n$ is of dimension ${n \choose k}$. A consequence of this fact is that a function can be approximated on vertices of the box using other vertices to higher…
Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…
A parquet approximation (generalized ladder diagrams) in matrix models is considered. By means of numerical calculations we demonstrate that in the large $N$ limit the parquet approximation gives an excellent agreement with exact results.
We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply…
Approximate solutions to functional evolution equations are constructed through a combination of series and conjugation methods, and relative errors are estimated. The methods are illustrated, both analytically and numerically, by…
The problem of root mean square approximation of a square integrable function by finite linear combinations of exponential functions is considered. It is subdivided into linear and nonlinear parts. The linear approximation problem is…
A new classification of real functions and other related real objects defined within a compact interval is proposed. The scope of the classification includes normal real functions and distributions in the sense of Schwartz, referred to…
We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…
We shall consider a result of Fel'dman, where a sharp Baker-type lower bound is obtained for linear forms in the values of some E-functions. Fel'dman's proof is based on an explicit construction of Pad\'e approximations of the first kind…
We study AAK as well as Pad\'e approximants to functions f, where f is a sum of a Cauchy transform of a complex measure \mu supported on a real interval included in (-1,1), whose Radon-Nikodym derivative with respect to the arcsine…
In this paper we discuss approximation of partially smooth functions. The problem arises naturally in the study of laminated currents.