Related papers: Global approximations to the error function of rea…
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…
We present a rational approximation for the Dawson's integral of real argument and show how it can be implemented for accurate and rapid computation of the Voigt function at small $y < < 1$. The algorithm based on this approach enables…
This paper proposes a unique optimization approach for estimating the minimax rational approximation and its application for evaluating matrix functions. Our method enables the extension to generalized rational approximations and has the…
State-of-the-art static analysis tools for verifying finite-precision code compute worst-case absolute error bounds on numerical errors. These are, however, often not a good estimate of accuracy as they do not take into account the…
Accurate yet efficient computation of the Voigt and complex error function is a challenge since decades in astrophysics and other areas of physics. Rational approximations have attracted considerable attention and are used in many codes,…
Factorization of polynomials is one of the foundations of symbolic computation. Its applications arise in numerous branches of mathematics and other sciences. However, the present advanced programming languages such as C++ and J++, do not…
In the present paper, we propose a block variant of the extended Hessenberg process for computing approximations of matrix functions and other problems producing large-scale matrices. Applications to the computation of a matrix function…
Given the importance of floating-point~(FP) performance in numerous domains, several new variants of FP and its alternatives have been proposed (e.g., Bfloat16, TensorFloat32, and Posits). These representations do not have correctly rounded…
In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…
The reciprocal function, 1/x, is important for many real-time algorithms. It is used in a large variety of algorithms from areas ranging from iterative estimation to machine learning. Many of these algorithms are iterative in nature and…
We investigate the proximal map for the weighted mean absolute error function. An algorithm for its efficient and vectorized evaluation is presented. As a demonstration, this algorithm is applied as part of a checkerboard algorithm to solve…
Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic, adaptive algorithm for approximating the solution to a…
Approximate computing has shown to provide new ways to improve performance and power consumption of error-resilient applications. While many of these applications can be found in image processing, data classification or machine learning, we…
We describe a procedure based on the iteration of an initial function by an appropriated operator, acting on continuous functions, in order to get a fixed point. This fixed point will be a calibrated subaction for the doubling map on the…
In a general setting, we study a posteriori estimates used in finite element analysis to measure the error between a solution and its approximation. The latter is not necessarily generated by a finite element method. We show that the error…
Variational Bayes (VB) has shown itself to be a powerful approximation method in many application areas. This paper describes some diagnostics methods which can assess how well the VB approximates the true posterior, particularly with…
We consider the error due to a single bit-flip in a floating point number. We assume IEEE 754 double precision arithmetic, which encodes binary floating point numbers in a 64-bit word. We assume that the bit-flip happens randomly so it has…
Static analysis by abstract interpretation aims at automatically proving properties of computer programs. To do this, an over-approximation of program semantics, defined as the least fixpoint of a system of semantic equations, must be…
In this paper I consider the applications of several kinds of approximations of real functions to the problem of verified computation (reliable computing) of the range of implicitly defined real function $x_{n+1} = G(x_{1}, ..., x_{n}),$…
A new sampling methodology based on incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the…