Related papers: A Rational Approximant for the Digamma Function
The main purpose of the paper is to present some powerful data on the advantage of the rational approximation procedure based on Hermite-Pad\'e polynomials over the Pad\'e approximation procedure. The first part of the paper is devoted to…
In this paper, we develop a new neural network family based on power series expansion, which is proved to achieve a better approximation accuracy in comparison with existing neural networks. This new set of neural networks embeds the power…
Sequence transformations are valuable numerical tools that have been used with considerable success for the acceleration of convergence and the summation of diverging series. However, our understanding of their theoretical properties is far…
In this paper we study linear and non-linear Fourier-Pad\'e approximation for Angelesco systems of functions. This construction is similar to that of Hermite-Pad\'e approximation. Instead of considering power series expansions of the…
One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…
In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…
Transcendental functions, such as exponentials and logarithms, appear in a broad array of computational domains: from simulations in curvilinear coordinates, to interpolation, to machine learning. Unfortunately they are typically expensive…
The use of separable approximations is proposed to mitigate the curse of dimensionality related to the approximation of high-dimensional value functions in optimal control. The separable approximation exploits intrinsic decaying sensitivity…
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
In \cite{5} we proved that generically functions defined in any open set can be approximated by a sequense of their pad\'{e} approximants, in the sense of uniform convergence on compacta. In this paper we examine a more particular space,…
It is well known that rational approximation theory involves degenerate hypergeometric functions and, in particular, the Pad\'e approximation of the exponential function is closely related to Kummer hypergeometric functions. Recently, in…
We construct a new type of convergent, and asymptotic, representations, dyadic expansions. Their convergence is geometric and the region of convergence often extends from infinity down to $0^+$. We show that dyadic expansions are…
Purpose of writing this paper is to solve a transcendental function containing a product of a variable and its double exponential by a unique method of approximation. If the value of the said product is given, then its inverse function is…
A method is suggested allowing for the improvement of accuracy of self-similar factor and root approximants, constructed from asymptotic series. The method is based on performing a power transform of the given asymptotic series, with the…
We propose a novel approach for parameterizing the luminosity distance, based on the use of rational "Pad\'e" approximations. This new technique extends standard Taylor treatments, overcoming possible convergence issues at high redshifts…
We prove simultaneous universal Pad\'{e} approximation for several universal Pad\'{e} approximants of several types. Our results are generic in the space of holomorphic functions, in the space of formal power series as well as in a subspace…
We reconsider the Euler-Lagrange equation for the Skyrme model in the hedgehog ansatz and study the analytical properties of the solitonic solution. In view of the lack of a closed form solution to the problem, we work on approximate…
A finite sum of exponential functions may be expressed by a linear combination of powers of the independent variable and by successive integrals of the sum. This is proved for the general case and the connection between the parameters in…
Rational best approximations (in a Chebyshev sense) to real functions are characterized by an equioscillating approximation error. Similar results do not hold true for rational best approximations to complex functions in general. In the…
We construct a new type of convergent asymptotic representations, dyadic factorial expansions. Their convergence is geometric and the region of convergence can include Stokes rays, and often extends down to 0^+. For special functions such…