Related papers: On the global error committed when evaluating the …

Researchers have widely used exploratory factor analysis (EFA) to learn the latent structure underlying multivariate data. Rotation and regularised estimation are two classes of methods in EFA that they often use to find interpretable…

Millisecond focal plane telemetry is now becoming practical due to a new generation of near-IR detector arrays with sub-electron noise that are capable of kHz readout rates. Combining these data with those simultaneously available from the…

In recent years, half precision floating-point arithmetic has gained wide support in hardware and software stack thanks to the advance of artificial intelligence and machine learning applications. Operating at half precision can…

This article deals with quantitative error analysis resulting from ellipsometric data obtained from measurement on curved surfaces including the influence of non-collimated beams. Numerical model based on the combination of geometrical and…

This work concerns the numerical analysis of the linear elasticity problem with a Robin boundary condition on a smooth domain. A finite element discretization is presented using high-order curved meshes in order to accurately discretize the…

This paper deals with the evaluation of double line integrals of the squared exponential covariance function. We propose a new approach in which the double integral is reduced to a single integral using the error function. This single…

A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…

It is well known that phase function methods allow for the numerical solution of a large class of oscillatory second order linear ordinary differential equations in time independent of frequency. Unfortunately, these methods break down in…

Traditionally Bayesian decision-theoretic design of experiments proceeds by choosing a design to minimise expectation of a given loss function over the space of all designs. The loss function encapsulates the aim of the experiment, and the…

Huber loss, its asymmetric variants and their associated functionals (here named Huber functionals) are studied in the context of point forecasting and forecast evaluation. The Huber functional of a distribution is the set of minimizers of…

We investigate the proximal map for the weighted mean absolute error function. An algorithm for its efficient and vectorized evaluation is presented. As a demonstration, this algorithm is applied as part of a checkerboard algorithm to solve…

This study investigates component wise estimation of ordered variances of scale mixture of two normal distributions. For this study two special loss functions are considered namely squared error loss function and entropy loss function. We…

This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…

Gradient descent is a widely used iterative algorithm for finding local minima in multivariate functions. However, the final iterations often either overshoot the minima or make minimal progress, making it challenging to determine an…

Wave breaking is a critical process in the upper ocean: an energy sink for the surface wave field and a source for turbulence in the ocean surface boundary layer. We apply a novel multi-layer numerical solver resolving upper-ocean dynamics…

In this paper we define a small variation of the Taylor method and a formula for the global error of this new numerical method that allows us to keep track of the round-off error and does not require previous knowledge of the exact…

We introduce the variational filtering EM algorithm, a simple, general-purpose method for performing variational inference in dynamical latent variable models using information from only past and present variables, i.e. filtering. The…

We present a computational and statistical approach for fitting isotonic models under convex differentiable loss functions. We offer a recursive partitioning algorithm which provably and efficiently solves isotonic regression under any such…

We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…

Numerical approximation of the long time behavior of a stochastic differential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical…