research-article

Algorithm 916: Computing the Faddeyeva and Voigt Functions

Authors:

Mofreh R. Zaghloul,

Ahmed N. AliAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 38, Issue 2

Article No.: 15, Pages 1 - 22

https://doi.org/10.1145/2049673.2049679

Published: 05 January 2012 Publication History

Abstract

We present a MATLAB function for the numerical evaluation of the Faddeyeva function w(z). The function is based on a newly developed accurate algorithm. In addition to its higher accuracy, the software provides a flexible accuracy vs efficiency trade-off through a controlling parameter that may be used to reduce accuracy and computational time and vice versa. Verification of the flexibility, reliability, and superior accuracy of the algorithm is provided through comparison with standard algorithms available in other libraries and software packages.

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Software for Computing the Faddeyeva and Voigt Functions

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References

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Cited By

Pain J(2024)Extracting Physical Information from the Voigt Profile Using the Lambert W FunctionPlasma10.3390/plasma70200237:2(427-445)Online publication date: 27-May-2024
https://doi.org/10.3390/plasma7020023
Zhang CHe JZhang S(2024)Simulation Analysis and Retrieval of Venusian Lower Atmosphere Based on Microwave SoundingIEEE Transactions on Geoscience and Remote Sensing10.1109/TGRS.2024.337667462(1-14)Online publication date: 2024
https://doi.org/10.1109/TGRS.2024.3376674
Xie H(2024)Rapid computation of the plasma dispersion function: Rational and multi-pole approximation, and improved accuracyAIP Advances10.1063/5.021643314:7Online publication date: 2-Jul-2024
https://doi.org/10.1063/5.0216433
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Index Terms

Algorithm 916: Computing the Faddeyeva and Voigt Functions
1. Mathematics of computing
  1. Mathematical analysis
    1. Functional analysis
      1. Approximation
    2. Numerical analysis
  2. Mathematical software
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis

Recommendations

Remark on “Algorithm 916: Computing the Faddeyeva and Voigt Functions”: Efficiency Improvements and Fortran Translation

This remark describes efficiency improvements to Algorithm 916 [Zaghloul and Ali 2011]. It is shown that the execution time required by the algorithm, when run at its highest accuracy, may be improved by more than a factor of 2. A better accuracy vs ...
Algorithm 985: Simple, Efficient, and Relatively Accurate Approximation for the Evaluation of the Faddeyeva Function

We present a new simple algorithm for efficient, and relatively accurate computation of the Faddeyeva function w(z). The algorithm carefully exploits previous approximations by Hui et al. (1978) and Humlíček (1982) along with asymptotic expressions from ...
Remark on “Algorithm 680: Evaluation of the Complex Error Function”: Cause and Remedy for the Loss of Accuracy Near the Real Axis

In this remark, we identify the cause of the loss of accuracy in the computation of the Faddeyeva function, w(z), near the real axis when using Algorithm 680. We provide a simple correction to this problem that allows us to restore this code as one of ...

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 38, Issue 2

December 2011

136 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/2049673

Issue’s Table of Contents

Copyright © 2012 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 January 2012

Accepted: 01 May 2011

Revised: 01 July 2010

Received: 01 January 2010

Published in TOMS Volume 38, Issue 2

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Cited By

Pain J(2024)Extracting Physical Information from the Voigt Profile Using the Lambert W FunctionPlasma10.3390/plasma70200237:2(427-445)Online publication date: 27-May-2024
https://doi.org/10.3390/plasma7020023
Zhang CHe JZhang S(2024)Simulation Analysis and Retrieval of Venusian Lower Atmosphere Based on Microwave SoundingIEEE Transactions on Geoscience and Remote Sensing10.1109/TGRS.2024.337667462(1-14)Online publication date: 2024
https://doi.org/10.1109/TGRS.2024.3376674
Xie H(2024)Rapid computation of the plasma dispersion function: Rational and multi-pole approximation, and improved accuracyAIP Advances10.1063/5.021643314:7Online publication date: 2-Jul-2024
https://doi.org/10.1063/5.0216433
Rahimi MChiu AEstefania Lopez Giraldo AYoon JLee W(2024)REDEN: Interactive multi-fitting decomposition-based NMR peak picking assistantJournal of Magnetic Resonance10.1016/j.jmr.2023.107600358(107600)Online publication date: Jan-2024
https://doi.org/10.1016/j.jmr.2023.107600
Arrighi WBanks JBerger RChapman TGianesini Odu AGorman J(2024)A new approach to the evaluation and solution of the relativistic kinetic dispersion relation and verification with continuum kinetic simulationJournal of Computational Physics10.1016/j.jcp.2024.113001508(113001)Online publication date: Jul-2024
https://doi.org/10.1016/j.jcp.2024.113001
de Campos MRomero Sda Silva Lde Castro J(2024)Shape Anisotropy and Magnetic Texture Determination in Anisotropic and Isotropic Alnico MagnetsJOM10.1007/s11837-024-06586-3Online publication date: 14-May-2024
https://doi.org/10.1007/s11837-024-06586-3
Zaghloul M(2024)Efficient numerical algorithms for multi-precision and multi-accuracy calculation of the error functions and Dawson integral with complex argumentsNumerical Algorithms10.1007/s11075-023-01727-297:2(869-887)Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1007/s11075-023-01727-2
Zaghloul M(2024)Efficient multiple-precision computation of the scaled complementary error function and the Dawson integralNumerical Algorithms10.1007/s11075-023-01608-895:3(1291-1308)Online publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1007/s11075-023-01608-8
Xiong YZhang YShao S(2023)A Characteristic-Spectral-Mixed Scheme for Six-Dimensional Wigner–Coulomb DynamicsSIAM Journal on Scientific Computing10.1137/22M149429445:6(B906-B931)Online publication date: 7-Dec-2023
https://doi.org/10.1137/22M1494294
Denig AHara K(2023)Three-dimensional coupling of electron cyclotron drift instability and ion–ion two stream instabilityPhysics of Plasmas10.1063/5.012229330:3Online publication date: 21-Mar-2023
https://doi.org/10.1063/5.0122293
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