Temperature and energy derivatives of Doppler broadening functions by Steffensen’s inequality technique

Geetha, R.S.; Keshavamurthy, R. S.; Harish, R.

doi:10.1016/j.anucene.2010.03.003

Cited by 2 publications

(1 citation statement)

References 18 publications

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“…and τ m ≥ 12 is the margin value (Abrarov, Quine, & Jagpal, 2010a, 2010bGeetha, 2010), can be effectively applied to approximate the Voigt/complex error function. The relation (9) is limited by −τ m ≤ t ≤ τ m since its right side is periodic with period T = 2τ m .…”

Section: Rational Approximationmentioning

confidence: 99%

Master-Slave Algorithm for Highly Accurate and Rapid Computation of the Voigt/Complex Error Function

Abrarov¹,

Quine²

2014

JMR

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We obtain a rational approximation of the Voigt/complex error function by Fourier expansion of the exponential function e −(t−2σ) 2 and present master-slave algorithm for its efficient computation. The error analysis shows that at y > 10 −5 the computed values match with highly accurate references up to the last decimal digits. The common problem that occurs at y → 0 is effectively resolved by main and supplementary approximations running computation flow in a master-slave mode. Since the proposed approximation is rational function, it can be implemented in a rapid algorithm.

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Section: Rational Approximationmentioning

confidence: 99%

Master-Slave Algorithm for Highly Accurate and Rapid Computation of the Voigt/Complex Error Function

Abrarov¹,

Quine²

2014

JMR

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

Abrarov

Quine

2011

Applied Mathematics and Computation

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a b s t r a c tWe 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.

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Temperature and energy derivatives of Doppler broadening functions by Steffensen’s inequality technique

Cited by 2 publications

References 18 publications

Master-Slave Algorithm for Highly Accurate and Rapid Computation of the Voigt/Complex Error Function

Master-Slave Algorithm for Highly Accurate and Rapid Computation of the Voigt/Complex Error Function

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

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