Related papers: Reducing roundoff errors in numerical integration …
The Planetary and Lunar ephemerides INPOP10a version has several improvements in the fitting process, the data sets used in the fit and in the general features of the solution. No big change was brought in the dynamics. As a consequence of…
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs…
For the pure biharmonic equation and a biharmonic singular perturbation problem, a residual-based error estimator is introduced which applies to many existing nonconforming finite elements. The error estimator involves the local…
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
In finite element methods (FEMs), the accuracy of the solution cannot increase indefinitely because the round-off error increases when the number of degrees of freedom (DoFs) is large enough. This means that the accuracy that can be reached…
The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…
Recent advances have made numeric debugging tools much faster by using double-double oracles, and numeric analysis tools much more accurate by using condition numbers. But these techniques have downsides: double-double oracles have…
Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless, this…
Algorithms operating on real numbers are implemented as floating-point computations in practice, but floating-point operations introduce roundoff errors that can degrade the accuracy of the result. We propose $\Lambda_{num}$, a functional…
We performed a statistical analysis of the astrometric errors for the major asteroid surveys. We analyzed the astrometric residuals as a function of observation epoch, observed brightness and rate of motion, finding that astrometric errors…
Ground-penetrating radar (GPR) is a mature geophysical method that has gained increasing popularity in planetary science over the past decade. GPR has been utilised both for Lunar and Martian missions providing pivotal information regarding…
Mixed-precision computing has become increasingly important in modern high-performance computing and machine learning applications. When implementing custom mixed-precision functions -- such as fused operators, optimized GPU kernels, or…
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
The apparent close encounters of two satellites in the plane of the sky, called mutual approximations, have been suggested as a different type of astrometric observation to refine the moons' ephemerides. The main observables are the central…
The EPM2011 ephemerides are computed using an updated dynamical model, new values of the parameters, and an extended observation database that contains about 680 000 positional measurements of various types obtained from 1913 to 2011. The…
The problem of exactly summing n floating-point numbers is a fundamental problem that has many applications in large-scale simulations and computational geometry. Unfortunately, due to the round-off error in standard floating-point…
Low precision arithmetic, in particular half precision floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings…
A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…