Related papers: Gaussian Quadrature Rule using {\epsilon}-Quasiort…
We introduce simple quadrature rules for the family of nonparametric nonconforming quadrilateral element with four degrees of freedom. Our quadrature rules are motivated by the work of Meng {\it et al.} \cite{meng2018new}. First, we…
The classical quadratic Gauss sum can be thought of as an exponential sum attached to a quadratic form on a cyclic group. We introduce an equivariant version of Gauss sum for arbitrary finite quadratic forms, which is an exponential sum…
This article is an abridged and commented translation into Spanish of the 1815 memoir where Gauss introduced the quadrature rules now associated with his name. Gauss' work does not resemble at all the stardard text-book treatment of…
In order to approximate the integral $I(f)=\int_a^b f(x) dx$, where $f$ is a sufficiently smooth function, models for quadrature rules are developed using a given {\it panel} of $n (n\geq 2)$ equally spaced points. These models arise from…
It is shown that quadrature formulas in many different applications can be derived from rational approximation of the Cauchy transform of a weight function. Since rational approximation is now a routine technology, this provides an easy new…
We analyse the Gaussian wave packet transform. Based on the Fourier inversion formula and a partition of unity, which is formed by a collection of Gaussian basis functions, a new representation of square-integrable functions is presented.…
We present a systematic computational framework for generating positive quadrature rules in multiple dimensions on general geometries. A direct moment-matching formulation that enforces exact integration on polynomial subspaces yields…
In a recently developed approximation technique for quantum field theory the standard one-loop result is used as a seed for a recursive formula that gives a sequence of improved Gaussian approximations for the generating functional. In this…
In quantum computation with continous-variable systems, quantum advantage can only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian unitary evolutions and measurements suited for computation are challenging to…
A novel recurrence formula for moments with respect to M\"{u}ntz-Legendre polynomials is proposed and applied to construct a numerical method for solving generalized Gauss quadratures with power function weight for M\"{u}ntz systems. These…
Bayesian quantum estimation provides a robust framework for quantum technologies, especially in scenarios with limited data and minimal prior information. Yet, its application to continuous-variable Gaussian systems has remained limited and…
A method is introduced for approximate marginal likelihood inference via adaptive Gaussian quadrature in mixed models with a single grouping factor. The core technical contribution is an algorithm for computing the exact gradient of the…
Closed formulae for all Gaussian or optimal, 1-parameter quadrature rules in a compact interval [a, b] with non uniform, asymmetric subintervals, arbitrary number of nodes per subinterval for the spline classes $S_{2N, 0}$ and $S_{2N+1,…
This article is concerned with a new method for the approximate evaluation of Fourier sine and cosine transforms. We develop and analyse a new quadrature rule for Fourier sine and cosine transforms involving transforming the integral to one…
We introduce two versions of a new sketch for approximately embedding the Gaussian kernel into Euclidean inner product space. These work by truncating infinite expansions of the Gaussian kernel, and carefully invoking the…
Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set…
Gauss-Legendre quadrature and the trapezoidal rule are powerful tools for numerical integration of analytic functions. For nearly singular problems, however, these standard methods become unacceptably slow. We discuss and generalize some…
We embark in a program of studying the problem of better approximating surfaces by triangulations(triangular meshes) by considering the approximating triangulations as finite metric spaces and the target smooth surface as their…
A new method to represent and approximate rotation matrices is introduced. The method represents approximations of a rotation matrix $Q$ with linearithmic complexity, i.e. with $\frac{1}{2}n\lg(n)$ rotations over pairs of coordinates,…
In the area of statistical planning, there is a large body of theoretical knowledge and computational experience concerning so-called optimal approximate designs of experiments. However, for an approximate design to be executed in practice,…