Algorithm 680: evaluation of the complex error function

Abstract

Given a complex number z, in the first quadrant of the complex plane, WOFZ (z) computes the value of the Faddeeva-function w(z) = exp(-z2). erfc(-iz) with an accuracy of 14 significant digits. While the body of the algorithm is the same as that of Algorithm 363 ([l, 2]), the initialization part is largely changed so as to improve both the accuracy and the speed of the algorithm. The major distinction between Algorithm 363 and Algorithm 680 lies initially in the choice of the variable QRHO and in the fact that NU isn't a constant if (QRHO.GE.l.O), but decreases with increasing ] z ]. Secondly, in the neighborhood of the origin, a different approximation for the Faddeeva function is used. A full description of the differences between this algorithm and Algorithm 363 is given in [3].

Monte-Carlo Simulation of Particle Diffusion in Various Geometries and Application to Chemistry and Biology

“…Nevertheless, it is still possible to use the Green's function given in Equation (47) by implementing the numerical evaluation of W(x,y) for complex numbers [19].…”

Exponentially correlated Gaussian functions in variational calculations. Momentum space properties of the ground state helium dimer

“…͑16͒ was converted from (͉q͉,ϱ) to ͑0,1͒ interval by a complex variable substitution. 71 The imaginary part was subsequently ruled out leading to the following integral: 73 A relative difference between pairs of these three methods never exceeded 10 Ϫ10 and, with respect to the accuracy, the methods described above can be recognized equivalent. However, evaluation times for these three methods with 1200-term wave function of He 2 were approximately like 8:2:1 for a single q, and 6:12:1 for a simultaneous evaluation of J(q) at a collection of 25 values of q.…”

A Rational Approximation for Efficient Computation of the Voigt Function in Quantitative Spectroscopy

“…(x, y) is the reference. The highly accurate reference values can be generated, for example, by using the Algorithm 680 [18,30] or recently published Algorithm 916 [31]. Figures 2a and 2b show the logarithm log 10 ∆ of the relative error of the series approximation (12) at m max = 16.…”