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