Algorithm 363: complex error function [S15]
Communications of the ACM
Algorithm 680: evaluation of the complex error function
ACM Transactions on Mathematical Software (TOMS)
Algorithm 916: Computing the Faddeyeva and Voigt Functions
ACM Transactions on Mathematical Software (TOMS)
| Hi-index | 0.00 |
Gautschi has developed an algorithm that calculates the value of the Faddeeva function w(z) for a given complex number z in the first quadrant, up to 10 significant digits. We show that by modifying the tuning of the algorithm and testing the relative rather than the absolute error we can improve the accuracy of this algorithm to 14 significant digits throughout almost the whole of the complex plane, as well as increase its speed significantly in most of the complex plane. The efficiency of the calculation is further enhanced by using a different approximation in the neighborhood of the origin, where the Gautschi algorithm becomes ineffective. Finally, we develop a criterion to test the reliability of the algorithm's results near the zeros of the function, which occur in the third and fourth quadrants.