Related papers: Precision Arithmetic: A New Floating-Point Arithme…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our…
Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing…
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today.…
This paper proposes a parametric error analysis method for Goldschmidt floating point division, which reveals how the errors of the intermediate results accumulate and propagate during the Goldschmidt iterations. The analysis is developed…
If the non-zero finite floating-point numbers are interpreted as point intervals, then the effect of rounding can be interpreted as computing one of the bounds of the result according to interval arithmetic. We give an interval…
We propose a novel foundation for calculus that focuses on the notion of approximations while avoiding the use of limits altogether. Continuity is defined as approximation at a point, while differentiability is defined as approximation with…
Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE754 Standard. In this context, an elementary brick of…
We consider rate swaps which pay a fixed rate against a floating rate in presence of bid-ask spread costs. Even for simple models of bid-ask spread costs, there is no explicit strategy optimizing an expected function of the hedging error.…
Uncertainty propagation in non-linear dynamical systems has become a key problem in various fields including control theory and machine learning. In this work we focus on discrete-time non-linear stochastic dynamical systems. We present a…
Debugging accumulation of floating-point errors is hard; ideally, computer should track it automatically. Here we consider twofold approximation of an exact real with value + error pair of floating-point numbers. Normally, value + error sum…
Much recent research is devoted to exploring tradeoffs between computational accuracy and energy efficiency at different levels of the system stack. Approximation at the floating point unit (FPU) allows saving energy by simply reducing the…
In this paper, a new ridge-type shrinkage estimator for the precision matrix has been proposed. The asymptotic optimal shrinkage coefficients and the theoretical loss were derived. Data-driven estimators for the shrinkage coefficients were…
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…
Conformal prediction is a framework for providing prediction intervals with distribution-free validity, guaranteeing predictive coverage for data drawn from any distribution. Its two main variants are full conformal prediction and split…
In this paper, we address the efficient implementation of moving horizon state estimation of constrained discrete-time linear systems. We propose a novel iteration scheme which employs a proximity-based formulation of the underlying…
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…
We describe various issues caused by the lack of round-to-nearest mode in the \textit{gcc} compiler implementation of the fixed-point arithmetic data types and operations. We demonstrate that round-to-nearest is not performed in the…
Geometric predicates are a basic ingredient to implement a vast range of algorithms in computational geometry. Modern implementations employ floating point filtering techniques to combine efficiency and robustness, and state-of-the-art…
We derive the general analytical expressions for the statistical uncertainties of cumulants up to fourth order including an efficiency correction. The analytical expressions have been tested with a toy Monte Carlo model analysis. An…