Sanjar M. Abrarov

Efficient algorithmic implementation of the Voigt/complex error function based on exponential series approximation

We show that a Fourier expansion of the exponential multiplier yields an exponential series that can compute high-accuracy values of the complex error function in a rapid algorithm. Numerical error analysis and computational test reveal that with essentially higher accuracy it is as fast as FFT-based Weideman’s algorithm at a regular size of the input array and considerably faster at an extended size of the input array. As this exponential series approximation is based only on elementary functions, the algorithm can be implemented utilizing freely available functions from the standard libraries of most programming languages. Due to its simplicity, rapidness, high-accuracy and coverage of the entire complex plane, the algorithm is efficient and practically convenient in numerical methods related to the spectral line broadening and other applications requiring errorfunction evaluation over extended input arrays.

A rational approximation for efficient computation of the Voigt function in quantitative spectroscopy

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 10 14 over a wide domain of practical interest 0 0 and 1 < x <1.

Sampling by incomplete cosine expansion of the sinc function

A new sampling methodology based on an 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 incomplete cosine expansion we obtain a rational approximation of the complex error function that with the same number of the summation terms provides an accuracy exceeding the Weidemans approximation accuracy by several orders of the magnitude. Application of the expansion results in an integration consisting of elementary function terms only. Consequently, this approach can be advantageous for accurate and rapid computation.

High-accuracy approximation of the complex probability function by Fourier expansion of exponential multiplier

Abstract The real K ( x , y ) and imaginary L ( x , y ) parts of the complex probability function are approximated as rapidly convergent series, based on the Fourier expansion of the exponential multiplier. This approach provides rapid and accurate calculations of the Voigt and complex error functions in the most challenging Humlicek regions 3 and 4.

Calibration and in-orbit performance of the Argus 1000 spectrometer - the Canadian pollution monitor

Argus 1000 is a new generation miniature pollution-monitoring instrument to monitor greenhouse-gas emission from the space. Argus was launched on the CanX-2 micro-satellite April 28, 2008. Operating in the near infrared and in a nadir-viewing mode, Argus provides a capability for the monitoring of Earth-based sources and sinks of anthropogenic pollution. It has 136 near infrared channels in the spectral range of 0.9-1.7 µm with an instantaneous spatial resolution of 1.25 km. With a mass of just 228 g in flight-model configuration, the instrument is a demonstrator for a future micro-satellite network that can supply near-real time monitoring of pollution events in order to facilitate the detection of the sources causing climate change. In this Letter, we describe the instrument, the analysis concept behind Argus 1000 and its in-orbit performance. Recent spectral data taken over Ontario, Canada, are presented.

A rational approximation of the Dawson’s integral for efficient computation of the complex error function

In this work we show a rational approximation of the Dawsons integral that can be implemented for high accuracy computation of the complex error function in a rapid algorithm. Specifically, this approach provides accuracy exceeding 1014 in the domain of practical importance 0y<0.1|x+iy|8. A Matlab code for computation of the complex error function with entire coverage of the complex plane is presented.

A New Application Methodology of the Fourier Transform for Rational Approximation of the Complex Error Function

This paper presents a new approach in application of the Fourier transform to the complex error function resulting in an efficient rational approximation. Specifically, the computational test shows that with only

A sampling-based approximation of the complex error function and its implementation without poles

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Rapidly convergent series for high-accuracy calculation of the Voigt function

summation terms the obtained rational approximation of the complex error function provides the average accuracy

A simple interpolating algorithm for the rapid and accurate calculation of the Voigt function

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