Related papers: Efficient evaluation of two-center Gaussian integr…

The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to…

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…

In this article, we explore a series of elementary yet insightful results involving integrals related to Gaussian sums. Using techniques rooted in classical calculus, we derive several identities and evaluate nontrivial definite integrals…

We present an efficient and accurate algorithm for solving the Poisson equation in spherical polar coordinates with a logarithmic radial grid and open boundary conditions. The method employs a divide-and-conquer strategy, decomposing the…

To speed up Gaussian process inference, a number of fast kernel matrix-vector multiplication (MVM) approximation algorithms have been proposed over the years. In this paper, we establish an exact fast kernel MVM algorithm based on exact…

A new estimator for three-center two-particle Coulomb integrals is presented. Our estimator is exact for some classes of integrals and is much more efficient than the standard Schwartz counterpart due to the proper account of distance…

This report mainly focused on the basic concepts and the recovery methods for the random sampling. The recovery methods involve the orthogonal matching pursuit algorithm and the gradient-based total variation strategy. In particular, a fast…

In this paper, we develop simple, yet efficient, procedures for sampling approximations of the two-Parameter Poisson-Dirichlet Process and the normalized inverse-Gaussian process. We compare the efficiency of the new approximations to the…

The reciprocal function, 1/x, is important for many real-time algorithms. It is used in a large variety of algorithms from areas ranging from iterative estimation to machine learning. Many of these algorithms are iterative in nature and…

In this article we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when Gaussian basis set with pseudopotentials are used. The usual algorithm for evaluating exchange matrix scales cubically with the…

The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an…

We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusion in real Hilbert space. The algorithm allows to use the inexact computations of the Lipschitzian and cocoercive…

The interpretation of cosmological observables requires the use of increasingly sophisticated theoretical models. Since these models are becoming computationally very expensive and display non-trivial uncertainties, the use of standard…

We developed a modification to the calculation of the two-point correlation function commonly used in the analysis of large scale structure in cosmology. An estimator of the two-point correlation function is constructed by contrasting the…

We present an efficient quantum algorithm for estimating Gauss sums over finite fields and finite rings. This is a natural problem as the description of a Gauss sum can be done without reference to a black box function. With a reduction…

Efficient Reinforcement Learning usually takes advantage of demonstration or good exploration strategy. By applying posterior sampling in model-free RL under the hypothesis of GP, we propose Gaussian Process Posterior Sampling Reinforcement…

Quasi-2D Coulomb systems are of fundamental importance and have attracted much attention in many areas nowadays. Their reduced symmetry gives rise to interesting collective behaviors, but also brings great challenges for particle-based…

We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…

Two recent landmark experiments have performed Gaussian boson sampling (GBS) with a non-programmable linear interferometer and threshold detectors on up to 144 output modes (see Refs.~\onlinecite{zhong_quantum_2020,zhong2021phase}). Here we…

We develop a functional Stein-Malliavin method in a non-diffusive Poissonian setting, thus obtaining a) quantitative central limit theorems for approximation of arbitrary non-degenerate Gaussian random elements taking values in a separable…