Related papers: Empirical Research and Automatic Processing Method…
In various applications, computers are required to compute approximations to univariate elementary and special functions such as $\exp$ and $\arctan$ to modest accuracy. This paper proposes a new heuristic for automating the design of such…
We have devised a simple numerical technique to treat rugged data points that arise due to the insufficient gain setting error (or quantization error) of a digital instrument. This is a very wide spread problem that all experimentalists…
The goal of program repair is to automatically fix programs to meet a specification. We propose a new specification mechanism, direct manipulation, in which the programmer can visualize the trace of a buggy program on a failing input and…
In this article, we introduce a new technique for precision tuning. This problem consists of finding the least data types for numerical values such that the result of the computation satisfies some accuracy requirement. State of the art…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Combinatorial optimisation is the practice of selecting the best constituent…
Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of…
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…
A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…
Gradient approximations are a class of numerical approximation techniques that are of central importance in numerical optimization. In derivative-free optimization, most of the gradient approximations, including the simplex gradient,…
We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce…
Fixpoints are ubiquitous in computer science and when dealing with quantitative semantics and verification one often considers least fixpoints of (higher-dimensional) functions over the non-negative reals. We show how to approximate the…
Block Floating Point (BFP) arithmetic is currently seeing a resurgence in interest because it requires less power, less chip area, and is less complicated to implement in hardware than standard floating point arithmetic. This paper explores…
The differences between the sets in which ideal arithmetics takes place and the sets of floating point numbers are outlined. A set of classical problems in correct numerical evaluation is presented, to increase the awareness of newcomers to…
We propose a new instruction (FPADDRE) that computes the round-off error in floating-point addition. We explain how this instruction benefits high-precision arithmetic operations in applications where double precision is not sufficient.…
Black-box Large Language Models (LLMs) provide practical and accessible alternatives to other machine learning methods, as they require minimal labeled data and machine learning expertise to develop solutions for various decision making…
Floating-point addition on a finite-precision machine is not associative, so not all mathematically equivalent summations are computationally equivalent. Making this assumption can lead to numerical error in computations. Proper ordering…
Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring…
Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the…
We propose an implementation of symplectic implicit Runge-Kutta schemes for highly accurate numerical integration of non-stiff Hamiltonian systems based on fixed point iteration. Provided that the computations are done in a given floating…
Floating-point program errors can lead to severe consequences, particularly in critical domains such as military applications. Only a small subset of inputs may induce substantial floating-point errors, prompting researchers to develop…