Related papers: Stable High Order Quadrature Rules for Scattered D…
We develop efficient numerical integration methods for computing an integral whose integrand is a product of a smooth function and the Gaussian function with a small standard deviation. Traditional numerical integration methods applied to…
We provide explicit expressions for quadrature rules on the space of $C^1$ quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention…
The main purpose of scattering experiments is to unveil the underlying structure of the colliding particles and their interaction. Typically one measures scattering observables (cross sections and polarizations) at discrete angles and…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
A novel method is proposed to infer Bayesian predictions of computationally expensive models. The method is based on the construction of quadrature rules, which are well-suited for approximating the weighted integrals occurring in Bayesian…
Scientific machine learning for inferring dynamical systems combines data-driven modeling, physics-based modeling, and empirical knowledge. It plays an essential role in engineering design and digital twinning. In this work, we primarily…
We propose a new class of high-order time-marching schemes with dissipation user-control and unconditional stability for parabolic equations. High-order time integrators can deliver the optimal performance of highly-accurate and robust…
The goal of the present paper is to understand the impact of numerical schemes for the reconstruction of data at cell faces in finite-volume methods, and to assess their interaction with the quadrature rule used to compute the average over…
Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…
We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…
In this technical note, we explain how to construct Gaussian quadrature rules for efficiently and accurately computing integrals of S(x)f(x) where S(x) is the solar irradiance function tabulated in the ASTM standard and f(x) is an arbitary…
We empirically study sorting in the evolving data model. In this model, a sorting algorithm maintains an approximation to the sorted order of a list of data items while simultaneously, with each comparison made by the algorithm, an…
Many modern datasets don't fit neatly into $n \times p$ matrices, but most techniques for measuring statistical stability expect rectangular data. We study methods for stability assessment on non-rectangular data, using statistical learning…
The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function on a uniform grid to scattered data quasi-interpolation. It is shown that high order…
We introduce a new type of quadrature, known as approximate Gaussian quadrature (AGQ) rules using {\epsilon}-quasiorthogonality, for the approximation of integrals of the form \int f(x)d \alpha(x). The measure {\alpha}(\cdot) can be…
In this paper we obtain $L^1$-weighted norms of classical orthogonal polynomials (Hermite, Laguerre and Jacobi polynomials) in terms of the zeros of these orthogonal polynomials; these expressions are usually known as quadrature rules. In…
In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…
The purpose of this work is to introduce a strategy for determining the nodes and weights of a low-cardinality positive cubature formula nearly exact for polynomials of a given degree over spherical polygons. In the numerical section we…
We present convergence theory for corrected quadrature rules on uniform Cartesian grids for functions with a point singularity. We begin by deriving an error estimate for the punctured trapezoidal rule, and then derive error expansions. We…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…