The Spectral Division Method is an analytic approach for sound field synthesis that determines the loudspeaker driving function in the wavenumber domain. Compact expressions for the driving function in time-frequency domain or in time domain can only be determined for a low number of special cases. Generally, the involved spatial Fourier transforms have to be evaluated numerically. We present a detailed description of the computational procedure and minimize the number of required computations by exploiting the following two aspects: 1) The interval for the spatial sampling of the virtual sound field can be selected for each time-frequency bin, whereby low time-frequency bins can be sampled more coarsely, and 2) the driving function only needs to be evaluated at the locations of the loudspeakers of a given array. The inverse spatial Fourier transform is therefore not required to be evaluated at all initial spatial sampling points but only at those locations that coincide with loudspeakers.