(Journal of Mathematics Research, 2014-06) Abrarov, S. M.; Quine, B. M.
We obtain a rational approximation of the Voigt/complex error function by Fourier expansion of the exponential function ${e^{ - {{\left( {t - 2\sigma } \right)}^2}}}$ and present master-slave algorithm for its efficient computation. The error analysis shows that at $y > {10^{ - 5}}$ the computed values match with highly accurate references up to the last decimal digits. The common problem that occurs at $y \to 0$ is effectively resolved by main and supplementary approximations running computation flow in a master-slave mode. Since the proposed approximation is rational function, it can be implemented in a rapid algorithm.
In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified representation of the proposed complex error function approximation makes possible further algorithmic optimization resulting in a considerable computational acceleration without compromise on accuracy.