相关论文: Comments on the Voigt function implementation in t…
The aim of this paper is to apply an original computation method due to Malesevic and Makragic [5] to the problem of approximating some trigonometric functions. Inequalities of Wilker-Cusa-Huygens are discussed, but the method can be…
It is known that the computation of the Voigt/complex error function is problematic for highly accurate and rapid computation at small imaginary argument $y << 1$, where $y = \operatorname{Im} \left[ z \right]$. In this paper we consider an…
We evaluate an adaptive gaussian quadrature integration scheme that will be suitable for the numerical evaluation of generalized redistribution in frequency functions. The latter are indispensable ingredients for "full non-LTE" radiation…
Accurate relative spectrophotometry is critical for many science applications. Small wavelength scale residuals in the flux calibration can significantly impact the measurements of weak emission and absorption features in the spectra. Using…
In this work we present a simple approximation for the Voigt/comp-lex error function based on fitting with set of the exponential functions of form ${\alpha _n}{\left| t \right|^n}{e^{ - {\beta _n}\left| t \right|}}$, where ${\alpha _n}$…
We introduce a Bayesian approach for modeling Voigt profiles in absorption spectroscopy and its implementation in the python package, BayesVP, publicly available at https://github.com/cameronliang/BayesVP. The code fits the absorption line…
The knowledge of the exact structure of the optical system PSF enables a high-quality image reconstruction in fluorescence microscopy. Accurate PSF models account for the vector nature of light and the phase and amplitude modifications.…
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…
A rapidly convergent series, based on Taylor expansion of the imaginary part of the complex error function, is presented for highly accurate approximation of the Voigt/complex error function with small imaginary argument (Y less than 0.1).…
We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…
In this work we show how to perform a rapid computation of the Voigt/complex error over a single domain by vectorized interpolation. This approach enables us to cover the entire set of the parameters $x,y \in \mathbb{R}$ required for the…
The fitting of spectral lines is a common step in the analysis of line observations and simulations. However, the observational noise, the presence of multiple velocity components, and potentially large data sets make it a non-trivial task.…
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…
In this work, we develop a method for rational approximation of the Fourier transform (FT) based on the real and imaginary parts of the complex error function \[ w(z) = e^{-z^2}(1 - {\rm{erf}}(-iz)) = K(x,y) + iL(x,y), \qquad z = x + iy, \]…
In order to compute Hermitian forms on representations of real reductive groups, in the unequal rank case, it is necessary to compute twisted Kazhdan-Lusztig-Vogan polynomials. These were defined by Lusztig and Vogan (Quasisplit Hecke…
Cosmological parameter inference has been dominated by the Bayesian approach for the past two decades, primarily due to its computational efficiency. However, the Bayesian approach involves integration of the posterior probability and…
With the availability of thousands of type Ia supernovae in the near future the magnitude scatter induced by lensing will become a major issue as it affects parameter estimation. Current N-body simulations are too time consuming to be…
#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of…
In this work we present a new procedure to compute optical spectra including excitonic effects and approximated quasiparticle corrections with reduced computational effort. The excitonic effects on optical spectra are included by solving…
We produce precise estimates for the Kogbetliantz kernel for the approximation of functions on the sphere. Furthermore, we propose and study a new approximation kernel, which has slightly better properties.