  In this paper we investigate the computational aspects of some recently
proposed iterative methods for approximating the canonical tight and canonical
dual window of a Gabor frame (g,a,b). The iterations start with the window g
while the iteration steps comprise the window g, the k^{th} iterand \gamma_{k},
the frame operators S and S_{k} corresponding to (g,a,b) and (\gamma_{k},a,b),
respectively, and a number of scalars. The structure of the iteration step of
the method is determined by the envisaged convergence order m of the method. We
consider two strategies for scaling the terms in the iteration step: norm
scaling, where in each step the windows are normalized, and initial scaling
where we only scale in the very beginning. Norm scaling leads to fast, but
conditionally convergent methods, while initial scaling leads to
unconditionally convergent methods, but with possibly suboptimal convergence
constants. The iterations, initially formulated for time-continuous Gabor
systems, are considered and tested in a discrete setting in which one passes to
the appropriately sampled-and-periodized windows and frame operators.
Furthermore, they are compared with respect to accuracy and efficiency with
other methods to approximate canonical windows associated with Gabor frames.
