Pseudo-inverse (and other direct methods) do have a lot going against them, especially as problems scale. In practice, iterative methods introduce their own cha

Pseudo-inverse (and other direct methods) do have a lot going against them, especially as problems scale. In practice, iterative methods introduce their own challenges as well though. Optimal algorithm selection is highly problem dependant, and often hinges on knowing how to generate an appropriate preconditioner. GMRES is still pretty much my favorite general method for inverse problems, but it comes with plenty of nuances that you really don't see when using a direct method on a tiny problem that you can bank on being well-conditioned. It's hard to say how often those kinds of problems exist in the real world (in my case: exceedingly rare), but they are still out there.