Related papers: Reducing roundoff errors in numerical integration …

Orbital solutions for binary or multiple stellar systems that combine astrometry (e.g., position angles and angular separations) with spectroscopy (radial velocities) have important advantages over astrometric-only or spectroscopic-only…

We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…

If an orbit is fitted from combined RV and astrometric data, the orbit should be physically consistent with both data sets. The Keplerian orbit of a planet is a highly nonlinear function of seven parameters. The astrometric orbit problem…

In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical…

In this paper, we consider matrix completion with absolute deviation loss and obtain an estimator of the median matrix. Despite several appealing properties of median, the non-smooth absolute deviation loss leads to computational challenge…

Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…

Earth imaging satellites are a crucial part of our everyday lives that enable global tracking of industrial activities. Use cases span many applications, from weather forecasting to digital maps, carbon footprint tracking, and vegetation…

In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition techniques. Our approach involves a dual application of a basic…

Many algorithms feature an iterative loop that converges to the result of interest. The numerical operations in such algorithms are generally implemented using finite-precision arithmetic, either fixed- or floating-point, most of which…

The knowledge of the orbit or the ephemeris uncertainty of asteroid presents a particular interest for various purposes. These quantities are for instance useful for recovering asteroids, for identifying lost asteroids or for planning…

Longitudinal models with dynamics governed by differential equations may require numerical integration alongside parameter estimation. We have identified a situation where the numerical integration introduces error in such a way that it…

Software methods introduced for automated design of approximate implementations of arithmetic circuits rely on fast and accurate evaluation of approximate candidate implementations. To accelerate the evaluation of circuit error, we propose…

We accelerated an {\it ab-initio} QMC electronic structure calculation by using GPGPU. The bottleneck of the calculation for extended solid systems is replaced by CUDA-GPGPU subroutine kernels which build up spline basis set expansions of…

This paper considers a probabilistic model for floating-point computation in which the roundoff errors are represented by bounded random variables with mean zero. Using this model, a probabilistic bound is derived for the forward error of…

Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…

Detecting binary black holes in interferometer data requires an accurate knowledge of the orbital phase evolution of the system. From the point of view of data analysis one also needs fast algorithms to compute the templates that will…

Interval arithmetic is a simple way to compute a mathematical expression to an arbitrary accuracy, widely used for verifying floating-point computations. Yet this simplicity belies challenges. Some inputs violate preconditions or cause…

Given the stringent requirements of energy efficiency for Internet-of-Things edge devices, approximate multipliers, as a basic component of many processors and accelerators, have been constantly proposed and studied for decades, especially…

Techniques that rigorously bound the overall rounding error exhibited by a numerical program are of significant interest for communities developing numerical software. However, there are few available tools today that can be used to…

Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…