Related papers: Quadrature formulas from rational approximations
These notes build an introduction to Convolution Quadrature techniques applied to linear convolutions and convolution equations with a bias to problems related to wave propagation. The notes are self-contained and emphasize algorithmic…
Cubature formulas, asymptotically optimal with respect to accuracy, are derived for calculating multidimensional weakly singular integrals. They are used for developing a universal code for calculating capacitances of conductors of…
In this contribution we deal with Gaussian quadrature rules based on orthogonal polynomials associated with a weight function $w(x)= x^{\alpha} e^{-x}$ supported on an interval $(0,z)$, $z>0.$ The modified Chebyshev algorithm is used in…
It is known that difference equations generated as the Newton-Raphson iteration for quadratic equations are solvable in closed form, and the solution can be constructed from linear three-term recurrence relations with constant coefficients.…
We discuss the advantages of using the approximate quantum Fourier transform (AQFT) in algorithms which involve periodicity estimations. We analyse quantum networks performing AQFT in the presence of decoherence and show that extensive…
Cubature formulas, asymptotically optimal with respect to accuracy, are derived for calculating multidimensional weakly singular integrals. They are used for developing a universal code for calculating capacitances of conductors of…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
The plane-wave approximation is widely used in the practical calculations concerning neutrino oscillations. A simple derivation of this approximation starting from the neutrino wave-packet framework is presented.
In molecular physics, it is often necessary to average over the orientation of molecules when calculating observables, in particular when modelling experiments in the liquid or gas phase. Evaluated in terms of Euler angles, this is closely…
The papers shows an algorithm to search for approximations of reals to rationals of the form a/b^2 that runs on \sqrt(b) polynomial time steps.
This paper presents a new approach in application of the Fourier transform to the complex error function resulting in an efficient rational approximation. Specifically, the computational test shows that with only $17$ summation terms the…
We consider the problem of numerically computing a critical point of a functional $J\colon M\rightarrow R$ where $M$ is a Riemannian manifold. Due to local quadratic convergence a popular choice to solve this problem is the geometric Newton…
Recently, Gautschi introduced so-called generalized Gauss-Radau and Gauss-Lobatto formulae which are quadrature formulae of Gaussian type involving not only the values but also the derivatives of the function at the endpoints. In the…
A novel artificial neural network method is proposed for solving Cauchy inverse problems. It allows multiple hidden layers with arbitrary width and depth, which theoretically yields better approximations to the inverse problems. In this…
Potential theory for rational approximation is reviewed by means of examples computed with the AAA algorithm.
A period of a rational integral is the result of integrating, with respect to one or several variables, a rational function over a closed path. This work focuses particularly on periods depending on a parameter: in this case the period…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
The structural properties of square-shoulder fluids are derived from the use of the rational function approximation method. The computation of both the radial distribution function and the static structure factor involves mostly analytical…
In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy-Riemann equations. Our method allows to…
Quaternions often appear in wide areas of applied science and engineering such as wireless communications systems, mechanics, etc. It is known that are two types of non-isomorphic generalized quaternion algebras, namely: the algebra of…