Related papers: Note on improvement precision of recursive functio…
Stochastic rounding (SR) offers an alternative to the deterministic IEEE-754 floating-point rounding modes. In some applications such as PDEs, ODEs and neural networks, SR empirically improves the numerical behavior and convergence to…
Using a perturbation technique, we derive a new approximate filtering and smoothing methodology generalizing along different directions several existing approaches to robust filtering based on the score and the Hessian matrix of the…
The Sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis. Even for other functions, the Sinc approximation works accurately when combined…
As the dimensions and operating voltages of computer electronics shrink to cope with consumers' demand for higher performance and lower power consumption, circuit sensitivity to soft errors increases dramatically. Recently, a new data-type…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
The development of algorithms for automation of subtasks during robotic surgery can be accelerated by the availability of realistic simulation environments. In this work, we focus on one aspect of the realism of a surgical simulator, which…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…
We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is…
Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques…
In \cite{liu2022practical}, a general algorithm is developed to efficiently obtain the best accuracy using the regular refinement. The adaptive refinement allows for obtaining an accuracy with a smaller number of DoFs compared with the…
The goals of this paper are to obtain theoretical models of what happens when a computer calculates the rotation set of a homeomorphism, and to find a good algorithm to perform simulations of this rotation set. To do that we introduce the…
We establish a near-optimality guarantee for the full orthogonalization method (FOM), showing that the overall convergence of FOM is nearly as good as GMRES. In particular, we prove that at every iteration $k$, there exists an iteration…
The widespread adoption of machine learning algorithms necessitates hardware acceleration to ensure efficient performance. This acceleration relies on custom matrix engines that operate on full or reduced-precision floating-point…
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…
Recently we introduced a class of number representations denoted RN-representations, allowing an un-biased rounding-to-nearest to take place by a simple truncation. In this paper we briefly review the binary fixed-point representation in an…
When training neural networks with low-precision computation, rounding errors often cause stagnation or are detrimental to the convergence of the optimizers; in this paper we study the influence of rounding errors on the convergence of the…
Floating-point round-off errors are ubiquitous in numerically intensive programs arising in fields such as scientific computing and optimization. As floating-point errors potentially lead to unexpected and catastrophic program failures, one…
Presented here are algorithms for converting between (decimal) scientific-notation and (binary) IEEE-754 double-precision floating-point numbers. By employing a rounding integer quotient operation these algorithms are much simpler than…
Unitary best approximation to the exponential function on an interval on the imaginary axis has been introduced recently. In the present work two algorithms are considered to compute this best approximant: an algorithm based on rational…
In this work, we deal with an iteration method for approximating a fixed point of a contraction mapping using the Mann's algorithm under functional random errors. We first show its almost complete convergence to the fixed point by mean of…