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Remark on “Algorithm 680: Evaluation of the Complex Error Function”: Cause and Remedy for the Loss of Accuracy Near the Real Axis

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Mofreh R. ZaghloulAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 45, Issue 2

Article No.: 24, Pages 1 - 3

https://doi.org/10.1145/3309681

Published: 26 April 2019 Publication History

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Abstract

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 the important reference routines for accuracy comparisons.

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M. Abramowitz and I. A. Stegun. 1964. Handbook of Mathematical Functions (AMS55). National Bureau of Standards, New York, NY.

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B. H. Armstrong. 1967. Spectrum line profiles: The Voigt function. Journal of Quantitative Spectroscopy and Radiative Transfer 7, 1 (1967), 61--88.

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W. J. Cody. 1993. Algorithm 715: SPECFUN—A portable Fortran package of special function routines and test drivers. ACM Transactions on Mathematical Software 19, 1 (1993), 22--32.

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W. Gautschi. 1970. Efficient computation of the complex error function. SIAM Journal on Numerical Analysis 7, 1 (1970), 187--198.

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G. P. M. Poppe and M. J. C. Wijers. 1990b. Algorithm 680: Evaluation of the complex error function. ACM Transactions on Mathematical Software 16, 1 (1990), 47.

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Z. Shippony and W. G. Read. 1993. A highly accurate Voigt function algorithm. Journal of Quantitative Spectroscopy and Radiative Transfer 50, 6 (1993), 635--646.

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M. R. Zaghloul. 2018. A Fortran package for efficient multi-accuracy computations of the Faddeyeva function and related functions of complex arguments. arXiv:1806.01656.

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M. R. Zaghloul and A. N. Ali. 2011. Algorithm 916: Computing the Faddeyeva and Voigt functions. ACM Transactions on Mathematical Software 38, 2 (2011), Article 15, 22 pages.

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Cited By

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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
Li ZLiu JLu LWang YYan XHan C(2023)Teaching reform of university botany courses based on discrete regression algorithmApplied Mathematics and Nonlinear Sciences10.2478/amns.2023.2.00270Online publication date: 30-Aug-2023
https://doi.org/10.2478/amns.2023.2.00270
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Index Terms

Remark on “Algorithm 680: Evaluation of the Complex Error Function”: Cause and Remedy for the Loss of Accuracy Near the Real Axis
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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Algorithm 916: Computing the Faddeyeva and Voigt Functions

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-...
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 715: SPECFUN–a portable FORTRAN package of special function routines and test drivers

SPECFUN is a package containing transportable FORTRAN special function programs for real arguments and accompanying test drivers. Components include Bessel functions, exponential integrals, error functions and related functions, and gamma functions and ...

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 45, Issue 2

June 2019

255 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/3326465

Editors:
Zhaojun Bai
University of California at Davis, USA
,
Wolfgang Bangerth
Colorado State University, USA

Issue’s Table of Contents

Permission to make digital or hard copies of part or all 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 third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 26 April 2019

Accepted: 01 January 2019

Revised: 01 October 2018

Received: 01 January 2018

Published in TOMS Volume 45, Issue 2

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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
Li ZLiu JLu LWang YYan XHan C(2023)Teaching reform of university botany courses based on discrete regression algorithmApplied Mathematics and Nonlinear Sciences10.2478/amns.2023.2.00270Online publication date: 30-Aug-2023
https://doi.org/10.2478/amns.2023.2.00270
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
Yang Q(2023)Translation Accuracy Correction Algorithm for English Translation SoftwareCyber Security Intelligence and Analytics10.1007/978-3-031-31860-3_37(349-357)Online publication date: 30-Apr-2023
https://doi.org/10.1007/978-3-031-31860-3_37
Hua JTao S(2022)Evaluation Algorithm of Skilled Talents’ Quality Based on Deep Belief Network ModelJournal of Interconnection Networks10.1142/S021926592143035022:Supp02Online publication date: 7-Jan-2022
https://doi.org/10.1142/S0219265921430350
Guo YChen C(2021)An Orthopedic Auxiliary Diagnosis System Based on Image Recognition TechnologyJournal of Healthcare Engineering10.1155/2021/46443922021(1-14)Online publication date: 22-Nov-2021
https://doi.org/10.1155/2021/4644392

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Algorithm 916: Computing the Faddeyeva and Voigt Functions

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

Algorithm 715: SPECFUN–a portable FORTRAN package of special function routines and test drivers

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