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Evaluation of the Voigt function, a convolution of a Lorentzian and a Gaussian profile, is essential in various fields such as spectroscopy, atmospheric science, and astrophysics. Efficient computation of the function is crucial, especially…

We present a rational approximation for rapid and accurate computation of the Voigt function, obtained by residue calculus. The computational test reveals that with only $16$ summation terms this approximation provides average accuracy…

The Voigt profile is one of the most used special function in optical spectroscopy. In particle physics a version of this profile which originates from relativistic Breit-Wigner resonance distribution often appears, however, in the…

A variety of "pseudo-Voigt" functions, i.e. a linear combination of the Lorentz and Gauss function (occasionally augmented with a correction term), have been proposed as a closed-form approximation for the convolution of the Lorentz and…

The Voigt profile - a convolution of a Gaussian and a Lorentzian - accurately describes the absorption lines of atomic and molecular gases at low probe powers. Fitting such to experimental spectra yields both the Lorentzian natural…

A Voigt profile function emerges in several physical investigations (e.g. atmospheric radiative transfer, astrophysical spectroscopy, plasma waves and acoustics) and it turns out to be the convolution of the Gaussian and the Lorentzian…

We describe an algorithm to optimally extract individual spectra of blended sources from a long slit spectrum. A semi-analytic model for the spatial profile is used: a Voigt profile for the undersampled core with a numerical correction…

I present a Python package developed for fitting Voigt profiles to absorption lines. The software fits multiple components for various atomic lines simultaneously allowing parameters to be tied and fixed. Moreover, the code is able to…

The Voigt profile is the density obtained from the convolution of a Gaussian and a Cauchy and it is widely used in atomic and molecular spectroscopy. We show that the Voigt profile is a scale mixture of Gaussian distributions, with mixing…

The ongoing optical time-domain astronomy surveys are routinely reporting fifty transient candidates per night. Here, I investigate the demographics of astronomical transients and supernova classifications reported to the Transient Name…

We introduce an algorithm of joint approximation of a function and its first derivative by alternative orthogonal polynomials on the interval [0,1].The algorithm exhibits properties of shape preserving approximation for the function. A weak…

In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…

The broadband line-by-line analysis of radiative transfer in the atmosphere is extremely demanding with regard to computational resources. As a remedy, we present here the calculation of uniform error bounds for approximating the classical…

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,…

We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral…

Opacities of molecules in exoplanet atmospheres rely on increasingly detailed line-lists for these molecules. The line lists available today contain for many species up to several billions of lines. Computation of the spectral line profile…

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…

This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation…

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…

Astrophysics demands higher precision in measurements across photometry, spectroscopy, and astrometry. Several science cases necessitate not only precision but also a high level of accuracy. We highlight the challenges involved,…