Algorithm 985: Simple, efficient, and relatively accurate approximation for the evaluation of the Faddeyeva function

TL;DR

This paper introduces a new simple and efficient algorithm for computing the Faddeyeva function with high relative accuracy and faster execution time, also enabling easy calculation of its derivatives.

Contribution

The paper presents a novel algorithm that improves efficiency and accuracy in evaluating the Faddeyeva function, building on previous approximations and asymptotic expressions.

Findings

Maximum relative error less than 4.0x10^-5

Faster execution time compared to existing methods

Allows easy computation of derivatives of the function

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 Humlicek [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 4.0x10-5 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.