Related papers: Reducing roundoff errors in numerical integration …
We present a detailed study of roundoff errors in probabilistic floating-point computations. We derive closed-form expressions for the distribution of roundoff errors associated with a random variable, and we prove that roundoff errors are…
In this paper we develop the first fine-grained rounding error analysis of finite element (FE) cell kernels and assembly. The theory includes mixed-precision implementations and accounts for hardware-acceleration via matrix multiplication…
This research explores the enhancement of lunar landing precision through an advanced structured light system, integrating machine learning, Iterative Learning Control (ILC) and Structured Illumination Microscopy (SIM) techniques. By…
Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speed-ups and lower storage cost if applied appropriately. The growing interest in…
This paper introduces a new computational methodology for determining a-posteriori multi-objective error estimates for finite-element approximations, and for constructing corresponding (quasi-)optimal adaptive refinements of finite-element…
We describe an algorithm for long-term planetary orbit integrations, including the dominant post-Newtonian effects, that employs individual timesteps for each planet. The algorithm is symplectic and exhibits short-term errors that are…
This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been…
This paper presents almanac and ephemeris message representation for lunar navigation satellites supporting the Lunar Augmented Navigation System (LANS). The proposed method combines osculating orbital elements, Chebyshev polynomials, and…
Floating point error is an inevitable drawback of embedded systems implementation. Computing rigorous upper bounds of roundoff errors is absolutely necessary to the validation of critical software. This problem is even more challenging when…
Elementary function calls are a common feature in numerical programs. While their implementions in library functions are highly optimized, their computation is nonetheless very expensive compared to plain arithmetic. Full accuracy is,…
Systematic errors are inevitable in most measurements performed in real life because of imperfect measurement devices. Reducing systematic errors is crucial to ensuring the accuracy and reliability of measurement results. To this end,…
In this work, we provide energy-efficient architectural support for floating point accuracy. Our goal is to provide accuracy that is far greater than that provided by the processor's hardware floating point unit (FPU). Specifically, for…
We consider the computation of the matrix logarithm by using numerical quadrature. The efficiency of numerical quadrature depends on the integrand and the choice of quadrature formula. The Gauss--Legendre quadrature has been conventionally…
Accurate error estimation is crucial in model order reduction, both to obtain small reduced-order models and to certify their accuracy when deployed in downstream applications such as digital twins. In existing a posteriori error estimation…
The most critical component of any adaptive numerical quadrature routine is the estimation of the integration error. Since the publication of the first algorithms in the 1960s, many error estimation schemes have been presented, evaluated…
We introduce new rounding methods to improve the accuracy of finite precision quantum arithmetic. These quantum rounding methods are applicable when multiple samples are being taken from a quantum program. We show how to use multiple…
Higher-order radiative corrections play an important role in precision studies of the electroweak and Higgs sector, as well as for the detailed understanding of large backgrounds to new physics searches. For corrections beyond the one-loop…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
Floating-point arithmetic performance determines the overall performance of important applications, from graphics to AI. Meeting the IEEE-754 specification for floating-point requires that final results of addition, subtraction,…
A longstanding problem related to floating-point implementation of numerical programs is to provide efficient yet precise analysis of output errors. We present a framework to compute lower bounds on largest absolute roundoff errors, for a…