Related papers: ARPIST: Provably Accurate and Stable Numerical Int…
In this paper, we study the efficient numerical integration of functions with sharp gradients and cusps. An adaptive integration algorithm is presented that systematically improves the accuracy of the integration of a set of functions. The…
For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…
Ellipse and ellipsoid fitting has been extensively researched and widely applied. Although traditional fitting methods provide accurate estimation of ellipse parameters in the low-noise case, their performance is compromised when the noise…
A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical…
In many practical applications, spatial data are often collected at areal levels (i.e., block data) and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically…
The computation of global radial basis function (RBF) approximations requires the solution of a linear system which, depending on the choice of RBF parameters, may be ill-conditioned. We study the stability and accuracy of approximation…
Most of existing superpixel methods are designed to segment standard planar images as pre-processing for computer vision pipelines. Nevertheless, the increasing number of applications based on wide angle capture devices, mainly generating…
Translation averaging aims to recover camera locations from pairwise relative translation directions and is a fundamental component of global Structure-from-Motion pipelines. The problem is challenging because direction measurements contain…
We present the 2-point function from Fast and Accurate Spherical Bessel Transformation (2-FAST) algorithm for a fast and accurate computation of integrals involving one or two spherical Bessel functions. These types of integrals occur when…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
The authors present SHarmonic, a new implementation of the spherical harmonics targeted for electronic-structure calculations. Their approach is to use explicit formulas for the harmonics written in terms of normalized Cartesian…
There are many applications in which a bounding sphere containing the given triangle E3 is needed, e.g. fast collision detection, ray-triangle intersecting in raytracing etc. This is a typical geometrical problem in E3 and it has also…
Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially…
We propose a stochastic nonconvex optimization algorithm that achieves almost sure $\tilde{\mathcal{O}}(\epsilon^{-1.5})$ iteration complexity for problems with smooth objective functions and gradients only observable with noise. The…
Classical trust region methods were designed to solve problems in which function and gradient information are exact. This paper considers the case when there are bounded errors (or noise) in the above computations and proposes a simple…
In this paper, we develop an analytical formulation for the Slepian spatial-spectral concentration problem on the sphere for a limited colatitude-longitude spatial region on the sphere, defined as the Cartesian product of a range of…
This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…
In the calculation of thermodynamic properties and three dimensional structures of macromolecules, such as proteins, it is important to have a good algorithm for computing solvent accessible surface area of macromolecules. Here we propose a…
We present $\texttt{cunusht}$, a general-purpose Python package that wraps a highly efficient CUDA implementation of the nonuniform spin-$0$ spherical harmonic transform. The method is applicable to arbitrary pixelization schemes, including…