Related papers: An adaptive gaussian quadrature for the Voigt func…
The specification of a covariance function is of paramount importance when employing Gaussian process models, but the requirement of positive definiteness severely limits those used in practice. Designing flexible stationary covariance…
We present a new version of the fast Gauss transform (FGT) for discrete and continuous sources. Classical Hermite expansions are avoided entirely, making use only of the plane-wave representation of the Gaussian kernel and a 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.…
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…
This work presents a method of computing Voigt functions and their derivatives, to high accuracy, on a uniform grid. It is based on an adaptation of Fourier-transform based convolution. The relative error of the result decreases as the…
In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss-Hermite quadrature by exploiting its relationship with the normal distribution. The proposed quadrature is not Gaussian, but…
Time-slicing has emerged as a strategy for incorporating semiclassical propagation into real-time path integral formulation and recovering full quantum dynamics. A central step is the decomposition of a time-evolved wave function into a…
In this work we propose and analyze a Hessian-based adaptive sparse quadrature to compute infinite-dimensional integrals with respect to the posterior distribution in the context of Bayesian inverse problems with Gaussian prior. Due to the…
Gaussian building blocks are essential for photonic quantum information processing, and universality can be practically achieved by equipping Gaussian circuits with adaptive measurement and feedforward. The number of adaptive steps then…
The Voigt profile is the density obtained from the convolution of a Gaussian and a Cauchy and it is widely used in atomic and molecular spectroscopy. We show that the Voigt profile is a scale mixture of Gaussian distributions, with mixing…
Highly oscillatory integrals of composite type arise in electronic engineering and their calculations is a challenging problem. In this paper, we propose two Gaussian quadrature rules for computing such integrals. The first one is…
A variety of problems in computational physics and engineering require the convolution of the heat kernel (a Gaussian) with either discrete sources, densities supported on boundaries, or continuous volume distributions. We present a unified…
A Voigt profile function emerges in several physical investigations (e.g. atmospheric radiative transfer, astrophysical spectroscopy, plasma waves and acoustics) and it turns out to be the convolution of the Gaussian and the Lorentzian…
We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an…
This work deals with uncertainty quantification for a generic input distribution to some resource-intensive simulation, e.g., requiring the solution of a partial differential equation. While efficient numerical methods exist to compute…
In this paper, we obtain various series and asymptotic expansions involving the modified Bessel function of the second kind for the normal inverse Gaussian cumulative distribution function. The new expansions accelerate computations,…
Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…
We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly…
We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical…
Graph states are the backbone of measurement-based continuous-variable quantum computation. However, experimental realisations of these states induce Gaussian measurement statistics for the field quadratures, which poses a barrier to obtain…