Related papers: Approximate Translation from Floating-Point to Rea…
Scientific computing applications, such as computational fluid dynamics and climate modeling, typically rely on 64-bit double-precision floating-point operations, which are extremely costly in terms of computation, memory, and energy. While…
Motivated by the importance of floating-point computations, we study the problem of securely and accurately summing many floating-point numbers. Prior work has focused on security absent accuracy or accuracy absent security, whereas our…
Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a theorem prover or proof assistant in a convenient and highly…
In this report, we present a versatile and efficient preconditioned Anderson acceleration (PAA) method for fixed-point iterations. The proposed framework offers flexibility in balancing convergence rates (linear, super-linear, or quadratic)…
In this paper, we demonstrate that in many NP-complete variants of the stable matching problem, such as the Stable Hypergraph Matching problem, the Stable Multicommodity Flow problem, and the College Admission problem with common quotas, a…
Training Deep Neural Networks (DNNs) can be computationally demanding, particularly when dealing with large models. Recent work has aimed to mitigate this computational challenge by introducing 8-bit floating-point (FP8) formats for…
In this work, we propose an extensive numerical study on approximating the absolute value function. The methods presented in this paper compute approximants in the form of rational functions and have been proposed relatively recently, e.g.,…
Reliable numerical computations are central to scientific computing, but the floating-point arithmetic that enables large-scale models is error-prone. Numeric exceptions are a common occurrence and can propagate through code, leading to…
Algebraic Riccati equations (AREs) have been extensively applicable in linear optimal control problems and many efficient numerical methods were developed. The most attention of numerical solutions is the (almost) stabilizing solution in…
Solving continuous variable optimization problems by factorization machine quantum annealing (FMQA) demonstrates the potential of Ising machines to be extended as a solver for integer and real optimization problems. However, the details of…
Numerical data processing is a key task across different fields of computer technology use. However, even simple summation of values is not precise due to the floating point representation use. This paper presents a practical algorithm for…
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…
Rational approximation is a powerful tool to obtain accurate surrogates for nonlinear functions that are easy to evaluate and linearize. The interpolatory adaptive Antoulas--Anderson (AAA) method is one approach to construct such…
A deterministic finite-state automaton (FSA) is an abstract sequential machine that reads the symbols comprising an input word one at a time. An FSA is symmetric if its output is independent of the order in which the input symbols are read,…
In previous work, we proposed a method for leveraging efficient classical simulation algorithms to aid in the analysis of large-scale fault tolerant circuits implemented on hypothetical quantum information processors. Here, we extend those…
Kernel smoothing is a widely used nonparametric method in modern statistical analysis. The problem of efficiently conducting kernel smoothing for a massive dataset on a distributed system is a problem of great importance. In this work, we…
A self-consistent random phase approximation (RPA) is proposed as an effective Hamiltonian method in Light-Front Field Theory (LFFT). We apply the general idea to the light-front massive Schwinger model to obtain a new bound state equation…
The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of…
An improvement on precision of recursive function simulation in IEEE floating point standard is presented. It is shown that the average of rounding towards negative infinite and rounding towards positive infinite yields a better result than…
Interval arithmetic is hardly feasible without directed rounding as provided, for example, by the IEEE floating-point standard. Equally essential for interval methods is directed rounding for conversion between the external decimal and…