Related papers: Combining Tools for Optimization and Analysis of F…
Matrix-vector multiplication forms the basis of many iterative solution algorithms and as such is an important algorithm also for hierarchical matrices which are used to represent dense data in an optimized form by applying low-rank…
Combinatorial interaction testing has been addressed as an effective software testing technique recently. It shows its ability to reduce the number of test cases that have to be considered for software-under-test by taking the combinations…
In this paper, we present an automated technique SWATI: Synthesizing Wordlengths Automatically Using Testing and Induction, which uses a combination of Nelder-Mead optimization based testing, and induction from examples to automatically…
BOAT is a free cross-platform software for statistical data analysis and numerical computing. Thanks to its multiple-precision floating point engine, it allows arbitrary-precision calculations, whose digits of precision are only limited by…
From a theoretical point of view, finding the solution set of a system of inequalities in only two variables is easy. However, if we want to get rigorous bounds on this set with floating point arithmetic, in all possible cases, then things…
In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional…
In recent years, machine learning (ML) and neural networks (NNs) have gained widespread use and attention across various domains, particularly in transportation for achieving autonomy, including the emergence of flying taxis for urban air…
To obtain accurate results in numerical computation, high-precision arithmetic is a straightforward approach. However, most processors lack hardware support for floating-point formats beyond double precision (FP64). Double-word arithmetic…
The discrete dipole approximation (DDA) is a widely used and versatile numerical method for solving electromagnetic scattering by arbitrarily shaped objects. Despite its popularity, quantitative comparisons between independent…
In recent years, half precision floating-point arithmetic has gained wide support in hardware and software stack thanks to the advance of artificial intelligence and machine learning applications. Operating at half precision can…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
Bayesian optimization works effectively optimizing parameters in black-box problems. However, this method did not work for high-dimensional parameters in limited trials. Parameters can be efficiently explored by nonlinearly embedding them…
Multi-term floating-point addition appears in vector dot-product computations, matrix multiplications, and other forms of floating-point data aggregation. A critical step in multi-term floating point addition is the alignment of fractions…
Quantum algorithms to solve practical problems in quantum chemistry, materials science, and matrix inversion often involve a significant amount of arithmetic operations which act on a superposition of inputs. These have to be compiled to a…
New regulations are imposing noise emissions limitations for the aviation industry which are pushing researchers and engineers to invest efforts in studying the aeroacoustics phenomena. Following this trend, an in-house computational fluid…
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…
Recent advances in 3D Gaussian Splatting (3DGS) have focused on accelerating optimization while preserving reconstruction quality. However, many proposed methods entangle implementation-level improvements with fundamental algorithmic…
Hyperparameter optimization and neural architecture search can become prohibitively expensive for regular black-box Bayesian optimization because the training and evaluation of a single model can easily take several hours. To overcome this,…
The Viterbi algorithm is a key operator for structured sequence inference in modern data systems, with applications in trajectory analysis, online recommendation, and speech recognition. As these workloads increasingly migrate to…
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…