research-article

Algorithm 985: Simple, Efficient, and Relatively Accurate Approximation for the Evaluation of the Faddeyeva Function

Author:

Mofreh R. ZaghloulAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 44, Issue 2

Article No.: 22, Pages 1 - 9

https://doi.org/10.1145/3119904

Published: 29 August 2017 Publication History

Abstract

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 Laplace continued fractions. Over a wide and fine grid of the complex argument, z = x + iy, numerical results from the present approximation show a maximum relative error less than 4.0 × 10⁻⁵ for both real and imaginary parts of w while running in a relatively shorter execution time than other competitive techniques. In addition to the calculation of the Faddeyeva function, w, partial derivatives of the real and imaginary parts of the function can easily be calculated and returned as optional output.

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References

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M. R. Zaghloul. 2015. A simple reform for treating the loss of accuracy of Humlíček's w4 algorithm near the real axis. arXiv:1505.05596v1 [astro-ph.IM].

Cited By

Zhang JTennyson JYurchenko S(2024) PyExoCross : a Python program for generating spectra and cross-sections from molecular line lists RAS Techniques and Instruments10.1093/rasti/rzae0163:1(257-287)Online publication date: 24-Apr-2024
https://doi.org/10.1093/rasti/rzae016
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: 20-Feb-2024
https://doi.org/10.1007/s11075-023-01727-2
Chattopadhyay SMarante CSchneider BArgenti L(2023)Two-photon double ionization with finite pulses: Application of the virtual sequential model to heliumPhysical Review A10.1103/PhysRevA.108.013114108:1Online publication date: 20-Jul-2023
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Index Terms

Algorithm 985: Simple, Efficient, and Relatively Accurate Approximation for the Evaluation of the Faddeyeva Function
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

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

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 44, Issue 2

June 2018

242 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/3132683

Editor:
Daniel Kressner
EPF Lausanne, Switzerland

Issue’s Table of Contents

Copyright © 2017 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 the author(s) 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: 29 August 2017

Accepted: 01 June 2017

Revised: 01 May 2017

Received: 01 December 2015

Published in TOMS Volume 44, Issue 2

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Zhang JTennyson JYurchenko S(2024) PyExoCross : a Python program for generating spectra and cross-sections from molecular line lists RAS Techniques and Instruments10.1093/rasti/rzae0163:1(257-287)Online publication date: 24-Apr-2024
https://doi.org/10.1093/rasti/rzae016
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: 20-Feb-2024
https://doi.org/10.1007/s11075-023-01727-2
Chattopadhyay SMarante CSchneider BArgenti L(2023)Two-photon double ionization with finite pulses: Application of the virtual sequential model to heliumPhysical Review A10.1103/PhysRevA.108.013114108:1Online publication date: 20-Jul-2023
https://doi.org/10.1103/PhysRevA.108.013114
Yang XPeng ZDing YDu Y(2023) Spatially resolved broadband absorption spectroscopy measurements of temperature and multiple species (NH, OH, NO, and NH ) in atmospheric-pressure premixed ammonia/methane/air flames Fuel10.1016/j.fuel.2022.126073332(126073)Online publication date: Jan-2023
https://doi.org/10.1016/j.fuel.2022.126073
Zaghloul MAlrawas L(2023)Calculation of Fresnel integrals of real and complex arguments up to 28 significant digitsNumerical Algorithms10.1007/s11075-023-01654-296:2(489-506)Online publication date: 14-Sep-2023
https://doi.org/10.1007/s11075-023-01654-2
Bourgiotis SFrangos PSautbekov SPshikov M(2021)The Evaluation of an Asymptotic Solution to the Sommerfeld Radiation Problem Using an Efficient Method for the Calculation of Sommerfeld Integrals in the Spectral DomainElectronics10.3390/electronics1011133910:11(1339)Online publication date: 2-Jun-2021
https://doi.org/10.3390/electronics10111339
Ducru PAlhajri AMeyer IForget BSobes VJosey CLiang J(2021) Windowed multipole representation of -matrix cross sections Physical Review C10.1103/PhysRevC.103.064610103:6Online publication date: 14-Jun-2021
https://doi.org/10.1103/PhysRevC.103.064610
Li BZhang JZhang YYan TJiang Y(2020)Terahertz-field-induced near-cutoff even-order harmonics in a femtosecond laserPhysical Review A10.1103/PhysRevA.102.063102102:6Online publication date: 3-Dec-2020
https://doi.org/10.1103/PhysRevA.102.063102
Shajib A(2019)Unified lensing and kinematic analysis for any elliptical mass profileMonthly Notices of the Royal Astronomical Society10.1093/mnras/stz1796488:1(1387-1400)Online publication date: 1-Jul-2019
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Gimbutas ZJiang SLuo L(2019)Evaluation of Abramowitz functions in the right half of the complex planeJournal of Computational Physics10.1016/j.jcp.2019.109169(109169)Online publication date: Dec-2019
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