Master-Slave Algorithm for Highly Accurate and Rapid Computation of the Voigt/Complex Error Function

We obtain a rational approximation of the Voigt/complex error function by Fourier expansion of the exponential function $e-(t-2\sigma )2$ 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.