相关论文: The Fourier expansion approximation for high-accur…
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…
The Voigt profile is important for spectroscopy, astrophysics, and many other fields of physics, but is notoriously difficult to compute. McLean et al. [J. Electron Spectrosc. & Relat. Phenom., 1994] have proposed an approximation using a…
This paper presents a novel method of approximating the scalar Wiener-Hopf equation; and therefore constructing an approximate solution. The advantages of this method over the existing methods are reliability and explicit error bounds.…
We derive and showcase a novel approach to approximating Fourier transforms in higher dimensions, focusing specifically on the case of 2D radially concentrated ('ring-like') functions. We first reduce the problem to that of evaluating the…
Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier…
We investigate the variable-exponent Abel integral equations and corresponding fractional Cauchy problems. The main contributions of the work are enumerated as follows: (i) We develop an approximate inversion technique for variable-exponent…
An algorithm for computing the incomplete gamma function $\gamma^*(a,z)$ for real values of the parameter $a$ and negative real values of the argument $z$ is presented. The algorithm combines the use of series expansions, Poincar\'e-type…
We describe a systematic expansion for full QCD. The leading term in the expansion gives the valence approximation. The expansion reproduces full QCD if an infinite number of higher terms are included.
Unitary best approximation to the exponential function on an interval on the imaginary axis has been introduced recently. In the present work two algorithms are considered to compute this best approximant: an algorithm based on rational…
The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given…
It is shown that the real part of the complementary error function is bounded below by 1 in the subset of the complex plane where the principal argument is between $3\pi/4$ and $5\pi/4$. This improves a previous result asserting that the…
In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…
In this paper we derive a new recovery procedure for the reconstruction of extended exponential sums of the form $y(t) = \sum_{j=1}^{M} \left( \sum_{m=0}^{n_j} \, \gamma_{j,m} \, t^{m} \right) {\mathrm e}^{2\pi \lambda_j t}$, where the…
Random Fourier Features (RFF) is among the most popular and broadly applicable approaches for scaling up kernel methods. In essence, RFF allows the user to avoid costly computations on a large kernel matrix via a fast randomized…
We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…
Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational…
Instead of sampling a function at a single point, average sampling takes the weighted sum of function values around the point. Such a sampling strategy is more practical and more stable. In this note, we present an explicit method with an…
We introduce an efficient method for computing the Stekloff eigenvalues associated with the Helmholtz equation. In general, this eigenvalue problem requires solving the Helmholtz equation with Dirichlet and/or Neumann boundary condition…