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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2 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 languageEnglish
Article number24
JournalACM Transactions on Mathematical Software
Volume45
Issue number2
DOIs
Publication statusPublished - 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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