Ariel Kellison
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Mechanizing Olver's Error Arithmetic Open
We mechanize the fundamental properties of a rounding error model for floating-point arithmetic based on relative precision, a measure of error proposed as a substitute for relative error in rounding error analysis. A key property of relat…
Bean: A Language for Backward Error Analysis Open
Backward error analysis offers a method for assessing the quality of numerical programs in the presence of floating-point rounding errors. However, techniques from the numerical analysis literature for quantifying backward error require su…
Bean: A Language for Backward Error Analysis Open
Backward error analysis offers a method for assessing the quality of numerical programs in the presence of floating-point rounding errors. However, techniques from the numerical analysis literature for quantifying backward error require su…
Type-Based Approaches to Rounding Error Analysis Open
This dissertation explores the design and implementation of programming languages that represent rounding error analysis through typing. In the first part of this dissertation, we demonstrate that it is possible to design languages for for…
Numerical Fuzz: A Type System for Rounding Error Analysis Open
Algorithms operating on real numbers are implemented as floating-point computations in practice, but floatingpoint operations introduce roundoff errors that can degrade the accuracy of the result. We propose , a functional programming lang…
The First Tri-Lab Workshop on Formal Verification: Capabilities, Challenges, Research Opportunities, and Exemplars Open
The First Tri-Lab Workshop on Formal Verification was held in Santa Fe, New Mexico, on December 5th, 2023. This workshop gathered staff from Sandia, Los Alamos, and Lawrence Livermore National Laboratories and NASA’s Jet Propulsion Laborat…
VCFloat2: Floating-Point Error Analysis in Coq Open
The development of sound and efficient tools that automatically perform floating-point round-off error analysis is an active area of research with applications to embedded systems and scientific computing. In this paper we describe VCFloat…
Towards Verified Rounding Error Analysis for Stationary Iterative Methods Open
Iterative methods for solving linear systems serve as a basic building block for computational science. The computational cost of these methods can be significantly influenced by the round-off errors that accumulate as a result of their im…
Global stochastic optimization of stellarator coil configurations Open
In the construction of a stellarator, the manufacturing and assembling of the coil system is a dominant cost. These coils need to satisfy strict engineering tolerances, and if those are not met the project could be cancelled as in the case…
A Machine-Checked Direct Proof of the Steiner-Lehmus Theorem Open
A direct proof of the Steiner-Lehmus theorem has eluded geometers for over 170 years. The challenge has been that a proof is only considered direct if it does not rely on reductio ad absurdum. Thus, any proof that claims to be direct must …
On Expanding Standard Notions of Constructivity Open
Brouwer developed the notion of mental constructions based on his view of mathematical truth as experienced truth. These constructions extend the traditional practice of constructive mathematics, and we believe they have the potential to p…