Remark on Algorithm 680: evaluation of the complex error function: Cause and Remedy for the Loss of Accuracy Near the Real Axis

TL;DR

This paper analyzes the accuracy issues of Algorithm 680 for computing the Faddeyeva function near the real axis and proposes a correction to improve its precision, ensuring it remains a reliable reference routine.

Contribution

It identifies the cause of accuracy loss in Algorithm 680 and offers a simple correction to enhance its computational reliability near the real axis.

Findings

Corrected Algorithm 680 restores accuracy near the real axis

The correction maintains the routine's status as a reference method

Improves the robustness of complex error function computations

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 which allows us to restore this code as one of the important reference routines for accuracy comparisons.