Related papers: Quadrature formulas from rational approximations
A brief review of the search for variation of the fine structure constant in quasar absorption spectra is presented. Special consideration is given to the role of atomic calculations in the analysis of the observed data. A range of methods…
Numerical simulations with rigid particles, drops or vesicles constitute some examples that involve 3D objects with spherical topology. When the numerical method is based on boundary integral equations, the error in using a regular…
In the present paper we study high-order cubature formulas for the computation of advection-diffusion potentials over boxes. By using the basis functions introduced in the theory of approximate approximations, the cubature of a potential is…
Highly oscillatory integrals of composite type arise in electronic engineering and their calculations is a challenging problem. In this paper, we propose two Gaussian quadrature rules for computing such integrals. The first one is…
The conception of C- and H-representations of any holomorphic function is further extended to the notions, definitions, lemmas and theorems of the complex integration. On this basis and the introduced notion of a H-plane, generalising the…
We present quadrature schemes to calculate matrices, where the so-called modified Hilbert transformation is involved. These matrices occur as temporal parts of Galerkin finite element discretizations of parabolic or hyperbolic problems when…
This article aims to develop a direct numerical approach to solve the space-fractional partial differential equations (PDEs) based on a new differential quadrature (DQ) technique. The fractional derivatives are approximated by the weighted…
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…
Recursion formulae are derived for the calculation of two centre matrix elements of a radial function in relativistic quantum mechanics. The recursions are obtained between not necessarily diagonal radial eigensates using arbitrary radial…
In the foreseeable future, toolchains for quantum computing should offer automatic means of transforming a high level problem formulation down to a hardware executable form. Thereby, it is crucial to find (multiple) transformation paths…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
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…
The mathematical formulation of Quantum Mechanics is derived from purely operational axioms based on a general definition of "experiment" as a set of transformations. The main ingredient of the mathematical construction is the postulated…
Discrete analogs of extrema of curvature and generalizations of the four-vertex theorem to the case of polygons and polyhedra are suggested and developed. For smooth curves and polygonal lines in the plane, a formula relating the number of…
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…
We present an approach (the biroot method) for nth root approximation that yields closed-form rational functions with coefficients derived from binomial structures, Gaussian functions, or qualifying DAG structures. The method emerges from…
An error analysis for some Newton-Cotes quadrature formulae is presented. Peano-like error bounds are obtained. They are generally, but not always, better than the usual Peano bounds.
In non-equilibrium many-body perturbation theory, Langreth rules are an efficient way to extract real-time equations from contour ones. However, the standard rules are not applicable in cases that do not reduce to simple convolutions and…
The AAA algorithm for rational approximation is employed to illustrate applications of rational functions all across numerical analysis.
A high-order quadrature algorithm is presented for computing integrals over curved surfaces and volumes whose geometry is implicitly defined by the level sets of (one or more) multivariate polynomials. The algorithm recasts the implicitly…