For me, working in an industrial context, even so we cared more about the practical question, the theoretical question could never be entirely ignored, because it gave us a feeling for the limits of what our competitors might come up with, if they just tried hard enough and invested sufficient resources.

The question how to work efficiently with Toeplitz matrices came up in the context of generalizations of the algorithm from Lifeng Li's paper "New formulation of the Fourier modal method for crossed surface-relief gratings" to general non-Manhattan geometries.

The issue is: "Yes, it can be done in theory, but I don't want to be the one who has to resolve the stability and robustness issues, even so I admit that they can be solved."