Remark on “Algorithm 680: Evaluation of the complex error function”: Cause and remedy for the loss of accuracy near the real axis

Mofreh R. Zaghloul

doi:10.1145/3309681

Remark on “Algorithm 680: Evaluation of the complex error function”: Cause and remedy for the loss of accuracy near the real axis

Mofreh R. Zaghloul

Department of Physics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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. Categories and Subject Descriptors: G.1.0 [Numerical Analysis]: General-Computer Arithmetic; Numerical Algorithms; Multiple Precision Arithmetic; G.1.2 [Numerical Analysis]: Approximation-Special Functions Approximations; G.4 [Mathematical Software]: Algorithm Design and Analysis; Efficiency.

Original language	English
Article number	24
Journal	ACM Transactions on Mathematical Software
Volume	45
Issue number	2
DOIs	https://doi.org/10.1145/3309681
Publication status	Published - Apr 2019

Keywords

Dawson function
Error function
Faddeyeva function
Fresnel integrals
Imaginary error function
Special functions evaluation

ASJC Scopus subject areas

Software
Applied Mathematics

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10.1145/3309681

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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. Categories and Subject Descriptors: G.1.0 [Numerical Analysis]: General-Computer Arithmetic; Numerical Algorithms; Multiple Precision Arithmetic; G.1.2 [Numerical Analysis]: Approximation-Special Functions Approximations; G.4 [Mathematical Software]: Algorithm Design and Analysis; Efficiency.",

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N2 - 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. Categories and Subject Descriptors: G.1.0 [Numerical Analysis]: General-Computer Arithmetic; Numerical Algorithms; Multiple Precision Arithmetic; G.1.2 [Numerical Analysis]: Approximation-Special Functions Approximations; G.4 [Mathematical Software]: Algorithm Design and Analysis; Efficiency.

AB - 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. Categories and Subject Descriptors: G.1.0 [Numerical Analysis]: General-Computer Arithmetic; Numerical Algorithms; Multiple Precision Arithmetic; G.1.2 [Numerical Analysis]: Approximation-Special Functions Approximations; G.4 [Mathematical Software]: Algorithm Design and Analysis; Efficiency.

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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

Abstract

Keywords

ASJC Scopus subject areas

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